WO2022225559A1

WO2022225559A1 - Tapered impedance traveling wave mach-zehnder modulator

Info

Publication number: WO2022225559A1
Application number: PCT/US2021/058111
Authority: WO
Inventors: Karthikeyan Krishnamurthy; Xiao Shen; Hongbing Lei
Original assignee: FutureWei Technologies Inc
Current assignee: FutureWei Technologies Inc
Priority date: 2021-04-22
Filing date: 2021-11-04
Publication date: 2022-10-27
Anticipated expiration: 2023-10-22

Abstract

A traveling wave optical modulator includes an optical waveguide with a first arm and a second arm. A first active electrode is positioned adjacent to the first arm. The first active electrode includes a proximate end, a distal end, and a plurality of segments including a first segment and a second segment. The first segment comprises a first impedance and the second segment comprises a second impedance, the first impedance being greater than the second impedance. A first driver amplifier is electrically coupled to the proximate end of the first active electrode. A second driver amplifier is electrically coupled to the first active electrode between the first segment and the second segment. A terminal resistor is coupled to the distal end of the first active electrode.

Description

TAPERED IMPEDANCE TRAVELING WAVE MACH-ZEHNDER MODULATOR CROSS-REFERENCE TO RELATED APPLICATIONS [0001] This patent application claims the benefit of U.S. Provisional Patent Application No. 63/178,328, filed April 22, 2021 by Karthikeyan Krishnamurthy, et al., and titled “Tapered Impedance Traveling Wave Mach-Zehnder Modulator,” which is hereby incorporated by reference. TECHNICAL FIELD [0002] The present disclosure is generally related to optical network communications, and more particularly to a mechanism for reducing power consumption in a traveling wave optical modulator. BACKGROUND [0003] Optical communication is a form of communication which uses light to carry information. An optical communication system typically employs a transmitter that receives the information in the form of an electrical signal, and encodes the information into an optical signal for transmission through a channel to a destination. At the destination, an optical receiver converts the optical signal into an electrical signal. The electrical signal is further decoded to retrieve the information. In the most common form of optical communication, the channel is an optical fiber through which infrared wavelengths of light can be transmitted with low levels of attenuation and dispersion. Traditionally, optical transmitters and receivers were made using materials like lithium niobate and/or III-V compound semiconductors. A III-V compound semiconductor is a semiconductor that is an alloy including elements from groups III and V of the periodic table. Exponential increase in communication traffic has necessitated advances in silicon photonic technologies that offer the benefits of higher scale of integration, lower cost, and reduced size of optical components, with the performance approaching traditional solutions. SUMMARY [0004] In an embodiment, the disclosure includes a traveling wave optical modulator comprising: an optical waveguide having a first arm and a second arm; a first active electrode positioned adjacent to the first arm, the first active electrode including a proximate end, a distal end, a plurality of segments including a first segment and a second segment, the first segment comprising a first impedance value, the second segment comprising a second impedance value, the first impedance value being greater than the second impedance value; a plurality of driver amplifiers including a first driver amplifier electrically coupled to the proximate end of the first active electrode and a second driver amplifier electrically coupled to the first active electrode between the first segment and the second segment; and a first terminal resistor coupled to the distal end of the first active electrode.

[0005] Most traveling wave optical modulators include an optical waveguide with two arms that channel an optical carrier. The modulators also include electrodes that run parallel to the arms of the optical waveguide. An electrical signal is forwarded through the electrodes so that the signal propagates in the same direction as the carrier wave. The electrical signal is modulated onto the carrier wave. Because the electrical signal is a traveling wave, the electrical signal can also create a reflective wave that bounces back through the electrode, which causes interference with subsequent data in the traveling wave. To address this issue, a resistor is generally attached to the distal end of the electrodes (opposite the input) to absorb the traveling wave and prevent reflection. The maximum signal frequency that can be supported by a traveling wave optical modulator is a function of input power and modulator length. One approach to increasing the maximum signal frequency is to split each electrode into multiple discontinuous traveling wave segments and drive each segment separately with additional driver amplifiers. Unfortunately, this approach increases the total power usage for each additional driver amplifier added (e.g., doubles, triples, quadruples, etc.) This is partially because each segment is connected to a resistor for absorbing all unused power passing through the segment. Simply eliminating the resistors reduces overall power usage, but creates an unacceptable level of interference due to the reflected waves.

[0006] In an embodiment, certain resistors can be omitted from the traveling wave optical modulator without increasing the reflected waves. This results in reducing the power consumption of the traveling wave optical modulator while maintaining the same maximum signal frequency (or allowing for increased maximum signal frequency for the same power usage). To accomplish this, the disclosed modulator includes continuous electrodes formed from segments with varying impedance. The impedances of the segments are scaled in a tapered manner so the impedance decreases in each successive segment. Driving amplifiers are connected to the inputs of the segments. The impedances are selected to prevent/mitigate reflection between segments. This allows the signal to propagate forward between segments in a useful manner, but not reflect back. A single terminal resistor is retained to prevent reflection at the distal end of the electrode. Further, the driving amplifiers are scaled relative to the impedances to ensure the electrical signal is not altered by the impedance changes. This design supports modulators built with various numbers of electrodes and various number of segments. Hence, the disclosed design supports an increased maximum signal frequency, a decreased power consumption, or combinations thereof. As such, the disclosed designs create additional functionality, reduces resource usage, and/or solves problems that are specific to optical signal generation.

[0007] Optionally, another implementation of the aspect provides the first driver amplifier and the second driver amplifier each comprising a driving output, the driving output of the second driver amplifier being scaled relative to the driving output of the first driver amplifier based on a difference between the first impedance value and the second impedance value.

[0008] Optionally, another implementation of the aspect provides currents of the driving output of the first driver amplifier and the second driver amplifier being scaled according to:

where G_m1 is trans-conductance gain of the first driver amplifier, G_m2 is trans-conductance gain of the second driver amplifier, I₁ is output current of the first driver amplifier, I₂ is output current of the second driver amplifier, Z₁ is the first impedance value of the first segment, and Z₂ is the second impedance value of the second segment.

[0009] Optionally, another implementation of the aspect provides the first active electrode being connected to only a single resistor.

[0010] Optionally, another implementation of the aspect provides a first driving input coupled to the first driver amplifier and a second driving input coupled to the second driver amplifier, the first driving input containing a same signal as the second driving input, and comprising a delay circuit configured to time delay the signal between the first driving input and the second driving input.

[0011] Optionally, another implementation of the aspect provides the first driver amplifier applies a first radio frequency (RF) electrical signal to the first segment at the proximate end of the first active electrode for modulation onto the first arm of the optical waveguide, the second driver amplifier applies a second RF electrical signal to the second segment at a point between the first segment and the second segment for modulation onto the first arm of the optical waveguide, and the first impedance value and the second impedance value are scaled to mitigate a reverse wave in the first segment and mitigate destructive interference between the first RF electrical signal and the second RF electrical signal in the first segment. [0012] Optionally, another implementation of the aspect provides a second active electrode positioned adjacent to the second arm of the optical waveguide, the second active electrode including a proximate end, a distal end, and a plurality of segments including a third segment and a fourth segment, the third segment comprising a third impedance value, the fourth segment comprising a fourth impedance value, the third impedance value being greater than the fourth impedance value.

[0013] Optionally, another implementation of the aspect provides a reference electrode between the first arm and the second arm of the optical waveguide, the reference electrode being coupled to a reference voltage, the first driver amplifier being electrically coupled to the proximate end of the second active electrode and the second driver amplifier being electrically coupled to the second active electrode between the third segment and the fourth segment, and the first terminal resistor coupled to the distal end of the second active electrode.

[0014] Optionally, another implementation of the aspect provides a complementary electrode positioned adjacent to the second arm of the optical waveguide, the complementary electrode including a proximate end, a distal end, and a plurality of segments including a third segment and a fourth segment, the third segment comprising a third impedance value, the fourth segment comprising a fourth impedance value, the third impedance value being greater than the fourth impedance value, the complementary electrode coupled to ground; and a reference electrode positioned between the first arm and the second arm of the optical waveguide, the reference electrode being coupled to a reference voltage.

[0015] Optionally, another implementation of the aspect provides a first reference electrode positioned adjacent to the first arm of the optical waveguide, the first reference electrode being coupled to a reference voltage; a second reference electrode positioned adjacent to the second arm of the optical waveguide, the second reference electrode being coupled to a ground; and a second terminal resistor coupled to the distal end of the second active electrode, the first active electrode and the second active electrode being positioned between the first arm and the second arm of the optical waveguide, and the first driver amplifier electrically being coupled to the proximate end of the second active electrode and the second driver amplifier being electrically coupled to the second active electrode between the third segment and the fourth segment.

[0016] Optionally, another implementation of the aspect provides a first reference electrode positioned adjacent to the first arm of the optical waveguide, the first reference electrode being coupled to a reference voltage; a second reference electrode positioned adjacent to the second arm of the optical waveguide, the second reference electrode being coupled to the reference voltage; and a second terminal resistor coupled to the distal end of the second active electrode, the first active electrode and the second active electrode being positioned between the first arm and the second arm of the optical waveguide, and the first driver amplifier being electrically coupled to the proximate end of the second active electrode, and the second driver amplifier being electrically coupled to the second active electrode between the third segment and the fourth segment.

[0017] Optionally, another implementation of the aspect provides the first driver amplifier being electrically coupled to the proximate end of the second active electrode and the second driver amplifier electrically coupled to the second active electrode between the third segment and the fourth segment, and the first terminal resistor being coupled to the distal end of the second active electrode, the traveling wave optical modulator comprising: a third active electrode positioned adjacent to the second arm of the optical waveguide and positioned between the first arm and the second arm of the optical waveguide, the third active electrode including a proximate end, a distal end, and a plurality of segments including a fifth segment and a sixth segment, the fifth segment comprising a fifth impedance value, the sixth segment comprising a sixth impedance value, and the fifth impedance value being greater than the sixth impedance value; a fourth active electrode being positioned adjacent to the first arm of the optical waveguide, the fourth active electrode including a proximate end, a distal end, and a plurality of segments including a seventh segment and an eighth segment, the seventh segment comprising a seventh impedance value, the eighth segment comprising an eighth impedance value, and the seventh impedance value being greater than the eighth impedance value; and a second terminal resistor coupled to the distal end of the third active electrode and the distal end of the fourth active electrode, and the plurality of driver amplifiers further including a third driver amplifier electrically coupled to the proximate end of the third active electrode and electrically coupled to the proximate end of the fourth active electrode, and a fourth driver amplifier electrically coupled to the third active electrode between the fifth segment and the sixth segment and electrically coupled to the fourth active electrode between the seventh segment and the eighth segment. [0018] Optionally, another implementation of the aspect provides the traveling wave optical modulator is implemented as an indium phosphide (InP) modulator, a lithium niobate (LiNbO3) modulator, a silicon (Si) modulator, or any combination of the foregoing modulators.

[0019] Optionally, in any of the preceding aspects, another implementation of the aspect provides the traveling wave optical modulator is implemented as a Mach-Zehnder Modulator (MZM).

[0020] Optionally, in any of the preceding aspects, another implementation of the aspect provides the plurality of driver amplifiers being implemented in a metal oxide semiconductor field effect transistor (MOSFET), complementary metal-oxide-semiconductor (CMOS), bipolar junction transistor (BJT), heterojunction bipolar transistor (HBT), high electron mobility transistor (HEMT), or any combination of the foregoing types of transistors.

[0021] In an embodiment, the disclosure provides a traveling wave optical modulator comprising: an optical waveguide; an active electrode positioned adjacent to the optical waveguide, the active electrode including a proximate end, a distal end, and a plurality of segments including a first segment and a second segment, the first segment including a first impedance value, the second segment comprising a second impedance value, and the first impedance value being greater than the second impedance value; a plurality of electrical signal inputs including a first driving input electrically coupled to the proximate end of the active electrode and a second driving input electrically coupled to the active electrode between the first segment and the second segment; and a terminal resistor coupled to the distal end of the active electrode.

[0022] Most traveling wave optical modulators include an optical waveguide with two arms that channel an optical carrier. The modulators also include electrodes that run parallel to the arms of the optical waveguide. An electrical signal is forwarded through the electrodes so that the signal propagates in the same direction as the carrier wave. The electrical signal is modulated onto the carrier wave. Because the electrical signal is a traveling wave, the electrical signal can also create a reflective wave that bounces back through the electrode, which causes interference with subsequent data in the traveling wave. To address this issue, a resistor is generally attached to the distal end of the electrodes (opposite the input) to absorb the traveling wave and prevent reflection. The maximum signal frequency that can be supported by a traveling wave optical modulator is a function of input power and modulator length. One approach to increasing the maximum signal frequency is to split each electrode into multiple discontinuous traveling wave segments and drive each segment separately with additional driver amplifiers. Unfortunately, this approach increases the total power usage for each additional driver amplifier added (e.g., doubles, triples, quadruples, etc.) This is partially because each segment is connected to a resistor for absorbing all unused power passing through the segment. Simply eliminating the resistors reduces overall power usage, but creates an unacceptable level of interference due to the reflected waves.

[0023] In an embodiment, certain resistors can be omitted from the traveling wave optical modulator without increasing the reflected waves. This results in reducing the power consumption of the traveling wave optical modulator while maintaining the same maximum signal frequency (or allowing for increased maximum signal frequency for the same power usage). To accomplish this, the disclosed modulator includes continuous electrodes formed from segments with varying impedance. The impedances of the segments are scaled in a tapered manner so the impedance decreases in each successive segment. Driving amplifiers are connected to the inputs of the segments. The impedances are selected to prevent/mitigate reflection between segments. This allows the signal to propagate forward between segments in a useful manner, but not reflect back. A single terminal resistor is retained to prevent reflection at the distal end of the electrode. Further, the driving amplifiers are scaled relative to the impedances to ensure the electrical signal is not altered by the impedance changes. This design supports modulators built with various numbers of electrodes and various number of segments. Hence, the disclosed design supports an increased maximum signal frequency, a decreased power consumption, or combinations thereof. As such, the disclosed designs create additional functionality, reduces resource usage, and/or solves problems that are specific to optical signal generation.

[0024] Optionally, in any of the preceding aspects, another implementation of the aspect provides the active electrode is connected to only a single resistor.

[0025] Optionally, in any of the preceding aspects, another implementation of the aspect provides the first input applies a first RF electrical signal to the first segment at the proximate end of the active electrode for modulation onto the optical waveguide, the second input applies a second RF electrical signal to the second segment at a point between the first segment and the second segment for modulation onto the optical waveguide, and the first impedance value and the second impedance value are scaled to mitigate reverse wave in the first segment and mitigate destructive interference between the first RF electrical signal and the second RF electrical signal in the first segment.

[0026] Optionally, in any of the preceding aspects, another implementation of the aspect provides the traveling wave optical modulator is implemented as an InP modulator, a LiNbO3 modulator, a Si modulator, or any combination of the foregoing modulators.

[0027] Optionally, in any of the preceding aspects, another implementation of the aspect provides the traveling wave optical modulator is implemented as a MZM.

[0028] In an embodiment, the disclosure includes a method comprising: transmitting, by a first driver amplifier, a signal to a proximate end of an active electrode, the active electrode including the proximate end, a distal end, and a plurality of segments including a first segment and a second segment, the first segment comprising a first impedance value, the second segment comprising a second impedance value, the first impedance value being greater than the second impedance value; transmitting, by a second driver amplifier, the signal to the active electrode between the first segment and the second segment; modulating, by the active electrode, the signal onto an optical waveguide; and terminating, by a terminal resistor, the signal at the distal end of the active electrode.

[0029] Traveling wave optical modulators include an optical waveguide with two arms that channel an optical carrier. The modulators also include electrodes that run parallel to the arms of the optical waveguide. An electrical signal is forwarded through the electrodes so that the signal propagates in the same direction as the carrier wave. The electrical signal is modulated onto the carrier wave. Because the electrical signal is a traveling wave, the electrical signal can also create a reflective wave that bounces back through the electrode, which causes interference with subsequent data in the traveling wave. To address this issue, a resistor is generally attached to the distal end of the electrodes (opposite the input) to absorb the traveling wave and prevent reflection. The maximum signal frequency that can be supported by a traveling wave optical modulator is a function of input power and modulator length. One approach to increasing the maximum signal frequency is to split each electrode into multiple discontinuous traveling wave segments and drive each segment separately with additional driver amplifiers. Unfortunately, this approach increases the total power usage for each additional driver amplifier added (e.g., doubles, triples, quadruples, etc.) This is partially because each segment is connected to a resistor for absorbing all unused power passing through the segment. Simply eliminating the resistors reduces overall power usage, but creates an unacceptable level of interference due to the reflected waves.

[0030] The present embodiment allows certain resistors to be omitted from the traveling wave optical modulator without increasing the reflected waves. This results in reducing the power consumption of the traveling wave optical modulator while maintaining the same maximum signal frequency (or allowing for increased maximum signal frequency for the same power usage). To accomplish this, the disclosed modulator includes continuous electrodes formed from segments with varying impedance. The impedances of the segments are scaled in a tapered manner so the impedance decreases in each successive segment. Driving amplifiers are then connected to the inputs of the segments. The impedances are selected to prevent/mitigate reflection between segments. This allows the signal to propagate forward between segments in a useful manner, but not reflect back. A single terminal resistor is retained to prevent reflection at the distal end of the electrode. Further, the driving amplifiers are scaled relative to the impedances to ensure the electrical signal is not altered by the impedance changes. This design supports modulators built with various numbers of electrodes and various number of segments. Hence, the disclosed design supports an increased maximum signal frequency, a decreased power consumption, or combinations thereof. As such, the disclosed designs create additional functionality, reduces resource usage, and/or solves problems that are specific to optical signal generation.

[0031] Optionally, another implementation of the aspect provides scaling a driving output of the second driver amplifier relative to a driving output of the first driver amplifier based on a difference between the first impedance value and the second impedance value.

[0032] Optionally, another implementation of the aspect provides currents of the driving output of the first driver amplifier and the second driver amplifier are scaled according to:

[0033] Optionally, another implementation of the aspect provides time delaying the signal between a first driving input of the first driver amplifier and the second driving input of the second driver amplifier.

[0034] Optionally, another implementation of the aspect provides the signal including a first RF electrical signal transmitted by the first driver amplifier and a second RF electrical signal transmitted by the second driver amplifier, and the first impedance value and the second impedance value are scaled to mitigate a reverse wave in the first segment and mitigate destructive interference between the first RF electrical signal and the second RF electrical signal in the first segment.

[0035] For the purpose of clarity, any one of the foregoing embodiments may be combined with any one or more of the other foregoing embodiments to create a new embodiment within the scope of the present disclosure.

[0036] These and other features will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings and claims.

BRIEF DESCRIPTION OF THE DRAWINGS

[0037] For a more complete understanding of this disclosure, reference is now made to the following brief description, taken in connection with the accompanying drawings and detailed description, wherein like reference numerals represent like parts. [0038] FIG. 1 is a schematic diagram of an example driving scheme for a traveling wave optical modulator.

[0039] FIG. 2 is a schematic diagram of an example driving scheme for a segmented traveling wave optical modulator.

[0040] FIG. 3 is a schematic diagram of an example driving scheme for a traveling wave optical modulator with connected segments.

[0041] FIG. 4 is a schematic diagram of an example driving scheme for a tapered impedance traveling wave optical modulator.

[0042] FIG. 5 is a schematic diagram of an example driving scheme for a tapered impedance traveling wave optical modulator with a plurality of segments.

[0043] FIG. 6 is a schematic diagram of an example driving scheme for a single ended tapered impedance traveling wave optical modulator.

[0044] FIG. 7 is a schematic diagram of an example driving scheme for a quasi-differential tapered impedance traveling wave optical modulator.

[0045] FIG. 8 is a schematic diagram of an example driving scheme for a differential tapered impedance traveling wave optical modulator with inner active electrodes.

[0046] FIG. 9 is a schematic diagram of an example driving scheme for a dual differential tapered impedance traveling wave optical modulator.

[0047] FIG. 10 is a graph of example frequency response curves for a tapered impedance traveling wave optical modulator.

[0048] FIG. 11 is a graph of example frequency response curves for a tapered impedance traveling wave optical modulator with various peaking settings for the driver amplifiers.

[0049] FIG. 12 is a graph of example frequency response curves for a tapered impedance traveling wave optical modulator implemented by varying positive type negative type diode (PN diode) loading.

[0050] FIG. 13 is a schematic diagram of an example electro-optical device for transmitting optical data via a tapered impedance traveling wave optical modulator.

[0051] FIG. 14 is a flowchart of an example method of operating a tapered impedance traveling wave optical modulator.

DETAILED DESCRIPTION

[0052] It should be understood at the outset that although an illustrative implementation of one or more embodiments are provided below, the disclosed systems and/or methods may be implemented using any number of techniques, whether currently known or yet to be developed. The disclosure should in no way be limited to the illustrative implementations, drawings, and techniques illustrated below, including the exemplary designs and implementations illustrated and described herein, but may be modified within the scope of the appended claims along with their full scope of equivalents.

[0053] The following acronyms are used herein: Mach Zehnder Modulator (MZM), Traveling Wave (TW), Pseudo Random Bit Sequence (PRBS), Radio Frequency (RF), Continuous Wave (CW), Alternating Current (AC), Direct Current (DC), Electrical to Electrical (E-E), Electrical to Optical (E-O), Resistance Capacitance (RC), silicon (Si), silicon germanium (SiGe), gallium arsenide (GaAs), indium phosphide (InP), lithium niobate (LiNbO3), Bipolar Junction Transistor (BJT), Hetero-junction Bipolar Transistor (HBT), Metal Oxide Semiconductor Field Effect Transistor (MOSFET), High Electron Mobility Transistor (HEMT), and Silicon On Insulator (SOI).

[0054] Traveling wave optical modulators include an optical waveguide with two arms that channel an optical carrier. The modulators also include electrodes that run parallel to the arms of the optical waveguide. An electrical signal is forwarded through the electrodes so that the signal propagates in the same direction as the carrier wave. The electrical signal changes the optical characteristics of the waveguide, which has the effect of altering the amplitude and/or phase of the carrier wave. This results in modulating the electrical signal onto the optical carrier wave. The modulated carrier waves from the arms are combined to create an optical signal for transmission onto a fiber or other optical transmission medium. Because the electrical signal is a traveling wave, the electrical signal can also create a reflective wave that bounces back through the electrode, which causes interference with subsequent data in the traveling wave. To address this issue, a resistor is generally attached to the distal end of the electrodes (opposite the input) to absorb the traveling wave and prevent reflection. The maximum signal frequency that can be supported by a traveling wave optical modulator is a function of input power and modulator length. Longer modulator arms allow for longer electro-optic interaction, but the electrical signal losses in the longer electrodes especially at higher frequencies negate this benefit. One approach to increasing the maximum signal frequency is to split each electrode into multiple discontinuous traveling wave segments and drive each segment separately with additional driver amplifiers. Unfortunately, this approach increases the total power usage for each additional driver amplifier added (e.g., doubles, triples, quadruples, etc.) This is partially because each segment is connected to a resistor for absorbing all unused power passing through the segment. Simply eliminating the resistors reduces overall power usage, but creates an unacceptable level of interference due to the reflected waves. [0055] Disclosed is a mechanism to allow certain resistors to be omitted from the traveling wave optical modulator without increasing the reflected waves. This results in reducing the power consumption of the traveling wave optical modulator while maintaining the same maximum signal frequency (or allowing for increased maximum signal frequency for the same power usage). To accomplish this, the disclosed modulator includes continuous electrodes formed from segments with varying impedance. The impedances of the segments are scaled in a tapered manner so the impedance decreases in each successive segment. Driving amplifiers are then connected to the inputs of the segments. The impedances are selected to prevent/mitigate reflection between segments. This allows the signal to propagate forward between segments in a useful manner, but not reflect back. A single terminal resistor is retained to prevent reflection at the distal end of the electrode. Further, the driving amplifiers are scaled relative to the impedances to ensure the electrical signal is not altered by the impedance changes. This design supports modulators built with various numbers of electrodes and various number of segments. Hence, the disclosed design supports an increased maximum signal frequency, a decreased power consumption, or combinations thereof. As such, the disclosed designs create additional functionality, reduces resource usage, and/or solves problems that are specific to optical signal generation.

[0056] FIG. 1 is a schematic diagram of an example driving scheme for a traveling wave optical modulator 100. An optical modulator 100 is an electro-optical device configured to modulate an optical carrier 101 based on an electrical signal, also known as a radio frequency (RF) signal, to create an optical signal 103. Accordingly, the optical modulator 100 encodes the electrical signal into the optical signal 103. The optical modulator 100 may be coupled to a solid-state semiconductor laser, which produces the optical carrier 101. As such, the laser acts as a coherent source of the optical carrier 101, which may include a continuous wave of infrared light. The optical modulator 100 may then encode the information to be transmitted from the electrical signal into the optical carrier 101 by altering the fundamental characteristics of the optical carrier 101. For example, the optical modulator 100 may modulate the amplitude (intensity), phase, and/or polarization of the optical carrier 101 to create the optical signal 103. The process of varying the fundamental characteristics of the optical carrier 101 is called modulation, and any device that achieves this can be referred to as an optical modulator. Accordingly, an optical modulator 100 can be used in optical communication transmitters to encode electrical information into an optical signal 103. An optical modulator 100 can be broadly classified into intensity modulators, phase modulators, and polarization modulators based on the characteristics of the optical carrier 101 being modified. [0057] An optical modulator 100 includes an optical waveguide 110, which is a transparent medium configured to channel the optical carrier 101 for modulation. The optical modulator 100 works by varying some property of the optical waveguide 110 based on the electrical field caused by the electrical signal as the optical carrier 101 travels through the optical waveguide 110. For example, an optical modulator 100 may vary the absorption coefficient of the optical waveguide 110 (absorptive modulators) or the refractive index of the optical waveguide 110 (refractive modulators) using an electro-optic effect or a plasma dispersion effect. The change in the refractive index of the optical waveguide 110 causes a change in the phase of the optical carrier 101, causing phase modulation. This principle is used in a type of optical modulator 100 called a Mach-Zehnder modulator (MZM). In an MZM, the optical waveguide 110 is split into two arms, which creates two paths. Varying electric field(s) can then be applied to each arm of the optical waveguide 110, which results in phase modulation in each path. The light can then be recombined after modulation, which results in the optical signal 103. The combined light beam can include intensity modulation and/or phase modulation, depending on the difference in phase change between the two paths. In an MZM, the net phase change depends on the amplitude of the electrical signal and the length of the optical modulator 100. Thus, one of the design metrics for an MZM is V_πL, which is the product of voltage (V) required to obtain a phase shift of p per unit length (V_π) times the length of the phase shifter (L).

[0058] The phase shifter in optical modulator 100 includes a first active electrode 121, a second active electrode 122, a reference electrode 125, and corresponding electro-optical material that responds to electric fields created by the electrodes. The electro-optical material is positioned in the optical waveguide 110 and/or between the electrodes and the arms of the optical waveguide 110, depending on the example. The electrodes are positioned adjacent to semiconductive material to create positive type negative type (PN) diodes as shown. It should be noted that each diode is depicted in a single position for clarity, but the diode is actually distributed along the entire length of the associated electrodes. A material like indium phosphide or lithium niobate with a high electro-optic effect can be used to implement efficient phase shifters in an MZM. In Silicon photonics, Si doping is used to create the phase shifters. This allows the optical modulator 100 to be created as an integrated component on a silicon wafer. For example, a phase shifter can be implemented using carrier depletion in a reverse biased PN diode and/or using carrier accumulation in silicon-insulator-silicon capacitors. In Si implementations, the electrical voltage applied by the first active electrode 121, the second active electrode 122, and the reference electrode 125 modifies the free carrier concentration inside the optical waveguide 110, which results in a change in refractive index in the optical waveguide 110. Silicon photonic carrier depletion modulators may have lower modulation efficiency than non-Si based modulators. As such, Si photonic optical modulators 100 may require modulator lengths of several millimeters to obtain a sufficient phase shift for a high extinction ratio of the light intensity in the optical carrier 101.

[0059] The optical modulator 100 is driven by a driver amplifier 127 coupled to the first active electrode 121 and the second active electrode 122. The driver amplifier 127 includes a driving input 113 that receives the electrical signal. The driver amplifier 127 is a differential amplifier, which amplifies the difference between the two input voltages at the driving input 113 and suppresses voltage common to the input voltages. The driver amplifier 127 is configured to amplify the electrical signal for application to the first active electrode 121 as a positive voltage and the second active electrode 122 as a negative voltage. Further, the reference electrode 125 is connected to a constant DC voltage, denoted as Vdc. This creates a voltage differential between the upper arm of the waveguide 110 (positive voltage between the first active electrode 121 and the reference electrode 125) and the lower arm of the waveguide 110 (negative voltage between the reference electrode 125 and the second active electrode 122). The voltage differential is then applied to the electro-optical material and/or the waveguide 110 to modulate the optical carrier 101 to create the optical signal 103.

[0060] In general, an optical modulator can be implemented as a lumped modulator or a traveling wave modulator. A lumped modulator includes shorter electrodes, and each electrode has a single electrical connection at the center point of the electrode (between a proximate end and a distal end), which creates a capacitive effect that is applied to the electro-optical material. For a modulator to be considered lumped, the electrode length should be much smaller than the wavelength at the modulation frequency, so that the electrical signal has very little phase variation over the electrode. In contrast, optical modulator 100 is a traveling wave modulator with longer electrodes. The first active electrode 121 and the second active electrode 122 include aproximate end 121a and proximate end 122a, respectively, on the side closest to the input of the optical carrier 101 and a distal end 121b and distal end 122b, respectively, on the side closest to output of the optical signal 103. The electrical signal is connected to the proximate ends 121a and 122a. This configuration allows the electrical signal to travel along the electrodes at a similar velocity to the velocity of the optical carrier 101 passing through the adjacent waveguide 110. This increases the length of the electro-optic interaction in a traveling wave modulator (in comparison to a lumped modulator). A terminal resistor 129 is connected to the distal end 121b of the first active electrode 121 and distal end 122b of the second active electrode 122. The terminal resistor 129 may be selected to apply a load impedance to the circuit of sufficient value to absorb the electrical signal. This prevents the electrical signal from reflecting back from the distal ends 121b and 122b toward the proximate ends 121a and 121b, which creates interference. Accordingly, a lumped modulator includes a center electrical connection, shorter electrodes, and no terminal resistor, while a traveling wave modulator includes a proximate end electrode connection, longer electrodes, and a terminal resistor. The present disclosure relates to traveling wave modulators, and hence lumped modulators are not discussed in detail.

[0061] In hybrid implementations, the driver amplifier 127 and the traveling wave MZM (TW-MZM) can be manufactured in separate RF packages with long transmission line interconnects between the driver amplifier 127 and the TW-MZM. In such a case, a reverse termination resistor can be included within the driver amplifier 127 to minimize reflections related to the transmission line. However, with advanced silicon photonic packaging, the driver amplifier 127 chip and silicon photonic chip are co-packaged using two dimensional (2-D) or three dimensional (3-D) integrated flip-chip techniques. This eliminates the packaging and pc- board interconnects. This has allowed the use of high impedance open drain drivers with no reverse termination, which can save the power lost to the reverse termination resistor in the driver amplifier. A high impedance open drain driver amplifier has been assumed for all the driving architectures listed here. To the first order, the RF power for each arm of the waveguide 110 of a traveling wave MZM, denoted as P_RF,TW, in such a resistive driving case for a driving voltage for a traveling wave MZM (V_TW) and a impedance (Zo) can be calculated as

Note that compared to the capacitive drive case (lumped modulator), the resistive drive RF power is independent of bit rate to the first order. In a TW-MZM, the capacitance of the phase-shifter is distributed over the length of the inductive physical transmission line, which provides a broad- band frequency response compared to a R_LC_L limited cut-off frequency for the lumped-MZM, where R_L is the linear resistance and C_L is the capacitance per unit length. The TW-MZM offers advantages compared to the resistance and capacitance (RC) limited bandwidth of the lumped- MZM. However, the bandwidth for the TW-MZM is limited by the loaded transmission line losses.

[0062] FIG. 2 is a schematic diagram of an example driving scheme for a segmented optical modulator 200. The segmented optical modulator 200 is similar to the optical modulator 100, but segmented optical modulator 200 is split into segments. The segmented optical modulator 200 includes an optical waveguide 210 that receives an optical carrier 201 for modulation into an optical signal 203, which are substantially similar to optical waveguide 110, optical carrier 101, and optical signal 103, respectively. The optical modulator 200 includes a first segment 220 and a second segment 230. Each segment modulates part of the electrical signal onto the optical carrier 201. This results in similar functionality to the optical modulator 100, but with operations up to a higher frequency and bandwidth at the cost of increased power consumption. The first segment 220 comprises a first active electrode 221 , a second active electrode 222, a first reference electrode 225, a first terminal resistor 229, and a first driver amplifier 227, which are substantially similar to the first active electrode 121, the second active electrode 122, the reference electrode 125, the terminal resistor 129, and the driver amplifier 127, respectively. Further, the second segment 230 comprises a third active electrode 231, a fourth active electrode 232, a second reference electrode 235, a second terminal resistor 239, and a second driver amplifier 237, which are substantially similar to the first active electrode 121, the second active electrode 122, the reference electrode 125, the terminal resistor 129, and the driver amplifier 127, respectively. [0063] The segmented optical modulator 200 applies an RF electrical signal to both segments 220 and 230 at different locations along the optical waveguide 210. The RF electrical signal is therefore delayed between the first segment 220 and the second segment 230 in order to account for the delay in the optical carrier 201 through the optical waveguide 210. Accordingly, a wave of the optical carrier 201 is modulated by a corresponding portion of the RF signal at the first segment. The RF signal is delayed and the wave of the optical carrier 201 proceeds to the second segment 230. The wave of the optical carrier 201 is then further modulated by a delayed RF signal compared to what was applied at the first segment 220. Accordingly, the first driver amplifier 227 and the second driver amplifier 237 include a first driving input 213 and a second driving input 214, respectively. The first driving input 213 and the second driving input 214 are each substantially similar to the driving input 113. The driver for the segmented optical modulator 200 also comprises a delay circuit 211 connected between the first driving input 213 and the second driving input 214. The delay circuit 211 is configured to delay the electrical signal by a delay (τ) when the electrical signal passes to the second driving input 214. As such, the value of τ is selected to match the delay in the optical signal 201 as it travels from the input of the first segment 220 to the input of the second segment 230. While two segments 220 and 230 are shown, any number of segments can be added so long as suitable delay circuits 211 are positioned along the transmission lines between each segment.

[0064] Due to the high substrate losses in Silicon, silicon photonic TW-MZMs with long segments, such optical modulator 100, have high transmission line losses, which can result in insufficient bandwidth. Hence, such MZMs can cause implementation challenges for baud rates of 56 gigabaud (Gbaud) per second or higher. One approach to mitigate these issues is to employ multiple traveling wavelength segments of shorter lengths, such as segments 220 and 230, with separate driver amplifiers, such as driver amplifier 227 and 237, and separate resistive terminations, such as terminal resistor 229 and 239. In such cases the achievable bandwidth increases, but the driver power consumption scales proportionally to the number of segments and results in wasted RF signal power into multiple resistive terminations. RF power for each arm of the modulator for a n-segment case is given by where P_RF,STW is the RF

power of a segmented traveling wave MZM, n is a number of segments, V_TW is the driving voltage amplitude, and Zo is impedance for each arm. So increasing the number of segments increases bandwidth at the cost of additional power, which is caused by the increase in the number of driver amplifiers 227 and 237 to drive the circuit and the corresponding increase in the number of terminal resistors 229 and 239 to prevent signal reflection and corresponding signal noise. [0065] With the transmitter usually being the power-hungry component in an optical communication system, one of the metrics for comparing different architectures is power efficiency. The power efficiency is defined as the ratio of the DC power consumption to the bit rate and is usually expressed in pico-Joules/bit (pJ/bit). Lower power efficiency is indicative of a more efficient communication system. This metric is also a measure of benefit in advancing technologies to higher data rates. Power efficiency should decrease with every technological generation for increasing data rates. If the power efficiency remains flat with increasing data rate, the advancement for higher data rate may not offer any real benefit when compared to parallel operation of multiple lower data rate transmitters.

[0066] A simplified expression for RF power per modulator arm is presented for various MZM topologies. The DC power consumption can be calculated by dividing the RF power by the driver amplifiers DC to RF power conversion efficiency (assumed as

for lumped capacitive drivers, and

for TW resistive drivers). Thus, the power efficiency (DC power consumption / bit rate) for the various MZM architectures including lumped, TW, and segmented TW can be calculated as:

[0067] The lumped-MZM has the best power efficiency at lower data rates and can be extended to higher data rates using segmented lumped-MZM architecture. However, this does not provide any improvement in power efficiency (pJ/bit), due to the proportionally larger power consumed as the data rate increases. The TW-MZM on the other hand is very inefficient at lower data rates compared to lumped architecture due to the larger power consumed to drive a resistive termination. However, the power consumption is nearly independent of the data rate, so the power efficiency is improved with increasing data rate. The exact data rate where the TW-MZM is more beneficial is dependent on several factors including driver efficiencies and MZM parameters, but the general trend is the same. Extending the TW-MZM to higher data rates using a segmented TW-MZM architecture however consumes proportionally larger power as the number of segments increases due to the inclusion of separate drivers and resistive terminations are for each segment. Hence the segmented TW-MZM architecture has worse power-efficiency when extending the data rate.

[0068] FIG. 3 is a schematic diagram of an example driving scheme for a traveling wave optical modulator 300 with connected segments. As described above, segmented TW-MZMs increase bandwidth at the cost of increased power. As noted above, a significant portion of the input power is absorbed by terminal resistors and wasted. One approach to mitigate this issue would be to simply remove some of the terminal resistors. The optical modulator 300 is included to describe why this approach is not effective.

[0069] Optical modulator 300 is a similar to optical modulators 100 and 200. The optical modulator 300 includes an optical waveguide 310 that receives an optical carrier 301 for modulation into an optical signal 303, which are substantially similar to optical waveguide 110, optical carrier 101, and optical signal 103, respectively. The optical modulator 300 also includes a first segment 320 and a second segment 330, which are similar to the first segment 220 and the second segment 230. However, the first segment 320 is electrically connected to the second segment 330 and the terminal resistor at the distal end of the first segment 320 has been removed. Accordingly, the optical modulator 300 includes a first active electrode 321, a second active electrode 322, a reference electrode 325, and a terminal resistor 339, which are similar to the first active electrode 121, the second active electrode 122, the reference electrode 125, and the terminal resistor 129. Each active electrode is also connected for RF signal input at two points, which creates two segments for each active electrode. Accordingly, the optical modulator 300 comprises a first driver amplifier 327, a first driving input 313, a second driver amplifier 337, a second driving input 314, and a delay circuit 311, which are substantially similar to the first driver amplifier 227, the first driving input 213, the second driver amplifier 237, the second driving input 214, and the delay circuit 211, respectively. [0070] In this configuration, the first driver amplifier 327 is connected to the proximate end of the active electrodes 321 and 322. The second driver amplifier 337 is connected to the active electrodes 321 and 322 between the first segment 320 and the second segment 330. Using the principle of superposition, this configuration can be analyzed considering one driver at a time, and decoupling the other driver at the high-impedance open drain node. With the first driver 327 connected, the electrical signal includes a first RF wave 315 that is applied to the first segment 320 via the first driver amplifier 327. The first RF wave 315 propagates through the first segment 320, through the second segment 330, is modulated onto the optical carrier 301, and is absorbed by the terminal resistor 339. Accordingly, the first RF wave 315 operates correctly. Meanwhile, with the second driver 337 connected, the electrical signal includes a second RF wave 316. The second RF wave 316 passes along the transmission line via the delay circuit 311 and is applied to the active electrodes 321 and 322 via the second driver amplifier 337. The second RF wave 316 is applied to the first active electrode 321 between the first segment 320 and the second segment 330. As shown, the second RF wave 316 splits, with part of the second RF wave 316 proceeding across the second segment 330 as intended and part of the second RF wave 316 travels in the reverse direction along the first segment 320. Now, super-positioning the two cases, the portion of the second RF wave 316 that travels back across the first segment 320 interferes with the first RF wave 315 passing forward across the first segment 320. Due to the time shift caused by the delay circuit 311, the first RF wave 315 and the portion of the second RF wave 316 that proceed forward include the same signal. However, the reverse portion of the second RF wave 316 is no longer temporally aligned with the first RF wave 315 at each point along the first segment 320. Hence, the first RF wave 315 and the second RF wave 316 interact randomly in the first segment 320, resulting in noise. For example, the reflected wave may cause additive interference which increases the amplitude of the first RF wave 315 or destructive interference which decreases the amplitude of the first RF wave 315, depending on the values encoded into the waves at a corresponding instant and on the spatial location in the segment. Such noise may render the design of the optical modulator 300 unusable in most communication systems. It should be noted that the RF waves are described in terms of the positive terminals of the amplifiers and the first active electrode 321. However, an electrically equivalent effect with an opposite polarity also occurs at the negative terminals of the amplifiers and the second active electrode 322.

[0071] In summary, a segmented TW-MZM with constant impedance, such as optical modulator 200, uses multiple driver amplifiers with resistive terminations to extend the performance to higher frequencies. Doing so wastes power at both the driver amplifiers and RF power into terminal resistors. To conserve and reuse the RF power, segments 320 and 330 can be cascaded and the terminal resistors eliminated at the inner stages as shown with respect to optical modulator 300. This allows successive driver amplifiers, such as the second driver amplifier 337, to add only additional power as needed to maintain signal strength. However, this causes the second RF wave 316 from the second driver amplifier 337 to split into both a forward and a reverse direction. At each point along the MZM, the forward waves and the reverse waves add constructively or destructively based on their phases with this addition varying over frequency. This results in valleys and peaks in the frequency response, which is unacceptable for broadband applications.

[0072] FIG. 4 is a schematic diagram of an example driving scheme for a tapered impedance traveling wave optical modulator 400. The traveling wave optical modulator 400 includes a plurality of segments similar to the optical modulator 300. However, the impedances of the segments have been altered to mitigate reverse RF waves between segments. This allows for removal of terminal resistors between segments and reduction in overall power while addressing the interference problems that occur in optical modulator 300.

[0073] The optical modulator 400 comprises an optical waveguide 410 with a first arm and a second arm. The optical waveguide 410 receives an optical carrier 401 for modulation into an optical signal 403, which are substantially similar to optical waveguide 110, optical carrier 101, and optical signal 103, respectively.

[0074] The optical modulator 400 comprises electrodes that are divided into a first segment and a second segment. The optical modulator 400 includes a first active electrode 421, which is similar to the first active electrode 121. The first active electrode 421 is positioned adjacent to the first arm of the optical waveguide 410. The first active electrode 421 includes a proximate end 42 la toward the optical input receiving the optical carrier 401 and a distal end 421b toward the optical output that outputs the optical signal 403. The first active electrode 421 is split into a plurality of segments including a first segment 461 and a second segment 462. The first segment 461 comprises a first impedance and the second segment 462 comprises a second impedance. The first impedance of the first segment 461 is scaled to be greater than the second impedance of the second segment 462 to prevent reflection of the electrical signal.

[0075] The optical modulator 400 also comprises a second active electrode 422, which is similar to the second active electrode 122. The second active electrode 422 is positioned adjacent to the second arm of the optical waveguide 410. The second active electrode 422 includes a proximate end 422a toward the optical input receiving the optical carrier 401 and a distal end 422b toward the optical output that outputs the optical signal 403. The second active electrode 422 is also split into a plurality of segments including a third segment 463 and a fourth segment 464. The third segment 463 comprises a third impedance and the fourth segment 464 comprises a fourth impedance. The third impedance of the third segment 463 is scaled to be greater than the fourth impedance of the fourth segment 464. The third impedance of the third segment 463 may, but need not be, the same as the first impedance of the first segment 461. The fourth impedance of the fourth segment 464 may, but need not be, the same as the second impedance of the second segment 462.

[0076] The optical modulator 400 also comprises a terminal resistor 439, which may be similar to the terminal resistor 129. The terminal resistor 429 is coupled to the distal end 421b of the first active electrode 421 and the distal end 422b of the second active electrode 422. The optical modulator 400 also comprises a reference electrode 425, which may be similar to the reference electrode 125. The reference electrode 425 is positioned between the first arm and the second arm of the optical waveguide 410. The reference electrode 425 is also coupled to a reference voltage.

[0077] The optical modulator 400 also comprises a plurality of driver amplifiers including a first driver amplifier 427, which may be similar to the first driver amplifier 227. The first driver amplifier 427 is electrically coupled to the proximate end 421a of the first active electrode 421. The first driver amplifier 427 is also electrically coupled to the proximate end 422a of the second active electrode 422. The optical modulator 400 also comprises a second driver amplifier 437, which may be similar to the second driver amplifier 237. The second driver amplifier 437 is electrically coupled to the first active electrode 421 between the first segment 461 and the second segment 462. The second driver amplifier 437 is also electrically coupled to the second active electrode 422 between the third segment 463 and the fourth segment 464.

[0078] The first driver amplifier 427 and the second driver amplifier 437 each comprise a driving output. The driving output of the second driver amplifier 437 is scaled relative to the driving output of the first driver amplifier 427 based on a difference between the first impedance of the first segment 461 and the second impedance of the second segment 462 and/or based on a difference between the third impedance of the third segment 463 and the fourth impedance of the fourth segment 466. For example, the current of the driving output of the first driver amplifier 427 and the second driver amplifier 437 may be scaled according to:

where G_m1 is a trans-conductance gain of the first driver amplifier 427, G_m2 is a trans- conductance gain of the second driver amplifier 437, Z₁ is the first impedance of the first segment 461, and Z₂ is the second impedance of the second segment 462.

[0079] The first driver amplifier 427 comprises a first driving input 413 coupled to the first driver amplifier 427 and the second driver amplifier 437 comprises a second driving input 414 coupled to the second driver amplifier 437. The first driving input 413 is coupled to the second driving input 414 by a transmission line. The optical modulator 400 also comprises a delay circuit 411, which is substantially similar to delay circuit 211. The transmission line traverses the delay circuit 411 when passing between the first driving input 413 and the second driving input 414. Accordingly, the first driving input 413 contains the same electrical signal as the second driving input 414, but the signal is time delayed between the first driving input 413 and the second driving input 414.

[0080] It should be noted that the described configuration allows for the omission of a terminal resistor between segments. Accordingly, the first segment 461 of the first active electrode 421 is not directly connected to a resistor. Further, the third segment 463 of the second active electrode 422 is not directly connected to a resistor. For example, the impedances of successive segments can be scaled. As described in more detail below, this mitigates and/or eliminates a reverse wave reflected back through the segments, which in turn mitigates and/or eliminates the signal noise created by destructive interference between the signal and the reverse wave. This structure allows the terminal resistor between segments to be removed, which reduces power consumption of the optical modulator 400. As such, the first active electrode 421 and the second active electrode 422 are each only connected to only a single resistor.

[0081] As described with respect to optical modulator 300, the electrical signal is received as a traveling wave. A first traveling wave 415 is received at the first driving input 413 and a second traveling wave 416 is received at the second driving input 414. The first traveling wave 415 and the second traveling wave 416 are similar to the first RF wave 315 and the second RF wave 316, respectively. As such, the first traveling wave 415 and the second traveling wave 416 are the same signal, but the second traveling wave 416 is timed delayed by the delay circuit 411. The first driver amplifier 427 applies the first traveling wave 415 to the first segment 461 at the proximate end 421a of the first active electrode 421 for modulation onto the first arm of the optical waveguide 410. Further, the second driver amplifier 437 applies the second traveling wave 416 to the second segment 462 at a point between the first segment 461 and the second segment 462 for modulation onto the first arm of the optical waveguide 410. [0082] However, unlike in optical modulator 300, the first impedance of the first segment 461 and the second impedance of the second segment 462 are scaled to mitigate reflection at the junction of the two segments. Using the principle of superposition and considering one input at a time, the first traveling wave 415 enters at the proximate end 421a of the first active electrode 421 proceeds through the higher impedance first segment 461. At the junction of the two segments the first wave is partially reflected and the rest transmits into the lower impedance second segment 462 before being absorbed by the terminal resistor 439. The second traveling wave 416 enters modulator arm between the segments 461 and 462. The second traveling wave 416 is scaled to be lower power than the first traveling wave 415 due to the scaling between the first driver amplifier 427 and the second driver amplifier 437. The second traveling wave 416 splits into a forward wave in the segment 462 and reverse wave in the segment 461 in inverse proportion to their impedance ratio. The forward wave from 416 proceeds along the lower impedance second segment 462 and is absorbed by the terminal resistor 439. On superposition of the two inputs the reverse wave from 416 cancels the reflected portion of the first wave 415 in the segment 461. Thus, by proper choice of impedance tapering and amplifier gain/sizing, this configuration prevents and/or mitigates frequency/spatially dependent interference between the first traveling wave 415 and the second traveling wave 416 in the first segment 461. It should be noted that the traveling waves are described in terms of the positive terminals of the amplifiers and the first active electrode 421. However, an electrically equivalent effect with an opposite polarity also occurs at the negative terminals of the amplifiers and the second active electrode 422.

[0083] The optical modulator 400 may be implemented as an MZM as shown. However, the present principles can be applied to other optical modulator topologies. Further, the optical modulator 400 may be implemented in various material technologies as in an indium phosphide (InP) modulator, a lithium niobate (LiNbO₃) modulator, a silicon (Si) photonic modulator, or combinations thereof. In addition, the plurality of driver amplifiers, including the first driver amplifier 427 and the second driver amplifier 437, can be implemented in metal oxide semiconductor field effect transistor (MOSFET), complementary metal-oxide-semiconductor (CMOS), bipolar junction transistor (BJT), heterojunction bipolar transistor (HBT), high electron mobility transistor (HEMT), or combinations thereof.

[0084] It should be noted that the first segment 461, the second segment 462, the third segment 463, and the fourth segment 464, each form a PN diode with a corresponding section of the reference electrode 425 across the optical waveguide 410 with orientations as shown. [0085] As described above, the optical modulator 400 design allows internal resistors to be omitted from the traveling wave optical modulator 400 without increasing signal noise. This allows power output from amplifiers 427 and 437 to be reduced, which results in reducing the power consumption of the traveling wave optical modulator 400 while maintaining the same maximum signal frequency (or allowing for increased maximum signal frequency for the same power usage). To accomplish this, the optical modulator 400 includes continuous electrodes that are separated into segments with varying impedance. The impedances of the segments are scaled in a tapered manner so the impedance decreases in each successive segment (e.g., segment 461 to segment 462 or segment 463 to segment 464). Driving amplifiers 427 and 437 are connected to the inputs of the segments. The impedances are selected to prevent/mitigate reflection between segments. This allows the signal to propagate forward between segments in a useful manner, but not reflect back. A single terminal resistor 439 is retained to prevent reflection at the distal end of the electrode 421 and/or 422. Further, the driving amplifiers 427 and 437 are scaled relative to the impedances to ensure the electrical signal is not altered by the impedance changes. This design supports modulators built with various numbers of electrodes and various number of segments. Hence, the disclosed design supports an increased maximum signal frequency, a decreased power consumption, or combinations thereof. As such, the disclosed designs create additional functionality, reduces resource usage, and/or solves problems that are specific to optical signal generation.

[0086] The principles of operation of a tapered impedance TW-MZM are now discussed in more detail. The reverse portion of the electrical wave in a TW-MZM can be cancelled out by proper choice of impedance of the successive segments, which is referred to herein as impedance tapering. This results in an additive forward wave with a broadband response. In a specific example, optical modulator 400 may employ driving amplifiers with high impedance open drain output. Further, the optical modulator 400 may employ two segments, segment 461 and segment 462, with 60Ω impedance and 30Ω impedance, respectively, including the loading from the modulator positive type negative type diodes (PN diodes). The terminal resistor 439 may include 60Ω differential impedance. For simplicity, the segments can be assumed to be lossless and of equal length, which results in an electrical delay of τ for each of the segment 461 and 462. Additionally, the input to the second driving amplifier may be driven with a RF signal delayed in phase by τ relative to the first driving amplifier.

[0087] The reverse current at the interface of the first and second segments can be calculated using the principle of superposition. Current from the first driving amplifier 427 is denoted as I₁ and current from the second driving amplifier 437 is denoted as I₂. The current from the first driving amplifier 427 sees a 60Ω to 30Ω impedance transition, which results in a reflection of at that interface. Current I₂ from the second driving amplifier 437 sees two

paths with 60Ω and 30Ω impedance and splits into respectively. The output current

is the sum of As long as the two driving amplifiers are identical, the phase and

magnitude are matched between I₁ and I₂ at the interface of the first and second segment, which results in cancellation of the reverse currents and addition of the forward current to double the value. Thus, for the two-segment case, the segment impedances can be set to 2Zo and Zo for the first and second segment, respectively, with a terminal resistor 439 differential impedance of 2Zo, and the segments can be driven with identical driver amplifiers with an input delay matching the first segment delay. This configuration eliminates the reverse wave at the segment interface and allows the two segments to be cascaded while eliminating the terminal resistor at the end of the first segment. Additionally, for the same voltage swing at the MZM, each of the driver amplifiers can employ half the current capacity of the optical modulator 200, which saves fifty percent of the consumed power.

[0088] High impedance transmission line segments of more than 75Ω tend to be very lossy in silicon substrates, and hence are difficult to implement. So, the non-ideal tapering for a 2- segment case, like the optical modulator 400, is now considered where the segment impedances, denoted Z1 and Z2, respectively, are Z1 > Z2 and not necessarily in a 2:1 ratio. Further, the condition to achieve the reverse wave cancellation is derived. For example, current I₁ sees aZ1 to Z2 impedance transition between the segments causing a reflection of at the interface

of the two segments. This results in a forward current of sees two paths

with Z1 and Z2 impedances and splits into for the reverse path for the

forward path, respectively. Hence at the segment interface, the forward current is and the reverse current is For the reverse current to

cancel, For the same input voltage amplitude applied to the

two amplifiers, one way to achieve this output current ratio is to size the two driving amplifiers in the current ratio and hence their transconductance gains denoted as Gml and Gm2,

respectively, is in the ratio Thus, by proper choice of MZM section

impedances (Z1, Z2) and driver amplifier sizing (Gm1, Gm2) the reverse wave can be cancelled, allowing the two segments to be cascaded while maintaining a frequency response without resonances due to destructive interference.

[0089] This topology may be referred to as a Tapered Impedance (Tapered-Z) Traveling Wave (TW) MZM. Optical modulator 400 represents a differentially driven case with two segment tapering. For the same RF voltage swing as the optical modulator 200, the driver amplifier sizing and current drive for tapered-Z TW-MZM (driver amplifiers 427 and 437) is about half that of driver amplifiers 227 and 237 for the same far-end terminal resistor. Hence the power efficiency for the tapered-Z TW-MZM (e.g., optical modulator 400) is similar to optical modulator 100, and not a higher multiple as occurs in a segmented case such as optical modulator 200

[0090] As discussed above, a Tapered-Z TW MZM, such as optical modulator 400, includes cascaded multiple smaller driver amplifiers with smaller driving currents along the MZM length and a single resistive termination at the far end. Unlike the other segmented TW-MZMs that employ multiple larger driver amplifiers and multiple resistive terminations, the disclosed approach lowers driver power consumption, saves RF signal lost to multiple resistive termination, and enables longer MZM sizes for a higher extinction ratio / electrical to optical coupling.

[0091] The approach described for the Tapered-Z TW MZM can be extended to cases with unequal segment lengths, as shorter sections may be preferable for the higher impedance lines that tend to be more lossy. The impedances of optical modulator 400 are tapered (Z1>Z2>Z3) from segment to segment in-order to prevent the reverse wave from propagating when the segments are connected. The Tapered-Z TW MZM uses a single far-end termination. Further, the Tapered-Z TW MZM uses different amplifier driver sizing for each segment. The amplifier driver sizing is chosen in combination with tapered impedance values (Z1, Z2, etc.) to mitigate and/or minimize the reverse wave and minimize frequency response ripple. Unlike other MZMs, the use of tapered-impedance segments and proper scaling of driver size maintains a constructive addition of an electrical signal over various frequencies. Further, the DC power consumed by the Tapered-Z TW MZM is roughly the same as the single segment TW-MZM and not multiples as in traditional segmented TW-MZM.

[0092] The Tapered-Z TW-MZM is proposed for co-packaging or integrating with high impedance and/or open drain drivers. The driver amplifiers may be designed in various process technologies including Silicon, SOI, Silicon Germanium, Gallium Arsenide, Indium Phosphide, and/or Gallium Nitride based on what is suitable for the intended application. [0093] In addition, Silicon photonics MZM typically have higher V_πL, higher insertion losses, and lower bandwidths than Indium Phosphide MZMs or lithium niobate MZMs. The Tapered-Z TW-MZM is proposed to address these issues.

[0094] FIG. 5 is a schematic diagram of an example driving scheme for a tapered impedance traveling wave optical modulator 500 with a plurality of segments. The optical modulator 500 is included to show that the principles described herein can be applied to as many segments as are desired. The optical modulator 500 includes an optical waveguide 510 and a reference electrode 525, which are substantially similar to optical waveguide 410 and reference electrode 425. [0095] The optical modulator 500 also includes a first active electrode 521 and a second active electrode 522 connected by a terminal resistor 539, which are similar to the first active electrode 421, the second active electrode 422, and the terminal resistor 439, respectively. However, the first active electrode 521 includes a first segment 561, a second segment 562, and a third segment 563. The first segment 561 and second segment 562 are substantially similar to the first segment 461 and the second segment 462, respectively. The third segment 563 extends the tapered impedance. Hence, the impedance of the third segment 563 is less than the impedance of the second segment 562, which is less than the impedance of the first segment 561. Further, the second active electrode 522 includes a fourth segment 564, a fifth segment 565, and a sixth segment 566. The fourth segment 564 and fifth segment 565 are substantially similar to the third segment 463 and the fourth segment 464, respectively. The sixth segment 566 extends the tapered impedance. Hence, the impedance of the sixth segment 566 is less than the impedance of the fifth segment 565, which is less than the impedance of the fourth segment 564. This approach of adding further segments with successively lower impedances can be extended to as many segments as are desired within the physical limitations of realizing the impedances of circuitry.

[0096] The optical modulator 500 also includes a first driver amplifier 527, a second driver amplifier 537, and a third driver amplifier 547. The first driver amplifier 527 and a second driver amplifier 537 are substantially similar to the first driver amplifier 427 and the second driver amplifier 437, respectively. The third driver amplifier 547 is substantially similar to the second driver amplifier 537, applies the RF signal between the second segment 562 and the third segment 563 and between the fifth segment 565 and a sixth segment 566. The driver amplifiers 527, 537, and 547 are all scaled relative to the impedances of the relevant segments of the first active electrode 521 and the second active electrode 522 in a manner similar to the scaling of the amplifiers in optical modulator 400. This approach of adding further amplifiers between further segments and scaling such amplifiers based on segment impedance can be extended to as many segments as are desired.

[0097] The optical modulator 500 also includes a delay circuit 511, which is substantially similar to the delay circuit 411. A further delay circuit 512 is positioned along the transmission line between the second driver amplifier 537 and the third driver amplifier 547 to further match the delay in the second segment 562 for proper continuous modulation on the optical carrier by further time delaying the RF signal by an additional time value of τ. Additional delay circuits can be added between subsequent driver amplifiers as desired to support further segments. [0098] FIG. 6 is a schematic diagram of an example driving scheme for a single ended tapered impedance traveling wave optical modulator 600. The optical modulator 600 is an electrically similar alternate embodiment of optical modulator 400, but is implemented without differential amplifiers. The optical modulator 400 is shown in the context of a differentially driven electrical signal, where two complementary and opposing RF electrical signals (e.g., negative and positive) are used to drive each section of the two arms of the MZM. The topology is equally applicable to single-ended MZM where only one of the arms of the MZM is driven with an RF electrical signal.

[0099] The optical modulator 600 includes optical waveguide 610 and a reference electrode 625, which are substantially similar to the optical waveguide 410 and the reference electrode 425, respectively. The optical modulator 600 also includes a first active electrode 621 with a first segment 661 and a second segment 662, which are substantially similar to the first active electrode 421 the first segment 461 and the second segment 462, respectively. The segments of the optical modulator 600 are tapered in a similar manner to the optical modulator 400.

[00100] The optical modulator 600 also includes a first driving amplifier 627 and a second driving amplifier 637, which are similar to the first driving amplifier 427 and the second driving amplifier 437. However, the driving amplifiers 627 and 637 receive, amplify, and output a single electrical signal instead of amplifying the difference between the two input voltages. The optical modulator 600 also comprises a delay circuit 611, which is positioned on a transmission line between the input of the first driving amplifier 627 and a second driving amplifier 637. The delay circuit 611 is substantially similar to delay circuit 411.

[00101] Since the driving amplifiers 627 and 637 each have a single input, the driving amplifiers 627 and 637 are connected to the first active electrode 621, but not to the complementary electrode 622. The first driving amplifier 627 is connected to the proximate end of the first segment 661 and the second driving amplifier 637 is connected between the first segment 661 and the second segment 662. The optical modulator 600 also comprises a terminal resistor 639, which substantially similar to the terminal resistor 439. The terminal resistor 639 is connected to the distal end of the first active electrode 621 and functions in a manner similar to terminal resistor 439.

[00102] The optical modulator 600 also includes a complementary electrode 622, which is similar to the second active electrode 422. For example, the complementary electrode 622 is positioned adjacent to the second arm of the optical waveguide 610. The complementary electrode 622 includes a proximate end, a distal end, and a plurality of segments including a third segment 663 and a fourth segment 664, which are substantially similar to the third segment 463 and the fourth segment 464, respectively. The third segment 663 comprises a third impedance and the fourth segment 664 comprises a fourth impedance. The third segment 663 and fourth segment 664 can be tapered in impedance similar to 661 and 662 respectively, but this may not be necessary as the electrode is connected to ground. Further, the complementary electrode 622 is coupled to ground. The first segment 661, the second segment 662, the third segment 663, and the fourth segment 664, each form a PN diode with a corresponding section of the reference electrode 625 across the optical waveguide 610 with orientations as shown.

[00103] FIG. 7 is a schematic diagram of an example driving scheme for a quasi-differential tapered impedance traveling wave optical modulator 700. The optical modulator 700 is quasi- differential because the optical modulator 700 is driven with single ended amplifiers, but the optical modulator 700 is configured to provide a differential signal at the optical waveguide. The optical modulator 700 is similar to the optical modulator 600. Accordingly, the optical modulator 700 is an electrically similar alternate embodiment of optical modulator 400, but is implemented without differential amplifiers. In this driving scheme single-ended driver amplifiers are used to simultaneously drive two active electrodes, where one active electrode acts as a cathode to a first modulator arm and another active electrode acts as an anode to a second modulator arm. The same RF signal is applied to both the cathode and anode, but a reference voltage and a ground are applied on the complementary electrodes of the modulator to apply a DC bias to the arms resulting in a differential modulation.

[00104] The optical modulator 700 includes an optical waveguide 710, which is substantially similar to optical waveguide 410. The optical modulator 700 also includes a first active electrode 721 with a first segment 761 and a second segment 762 and a second active electrode 722 with a third segment 763 and a fourth segment 764, which are substantially similar to the first active electrode 421, the first segment 461, the second segment 462, the second active electrode 422 the third segment 463, and the fourth segment 464, respectively. The first active electrode 721 and the second active electrode 722 can be positioned inside the first arm and the second arm of the optical waveguide 710 to facilitate combined driving with the single-ended amplifiers. The optical modulator 700 also comprises a first terminal resistor 739 connected to the distal end of the first active electrode 721 and a second terminal resistor 729 coupled to the distal end of the second active electrode 722. The first terminal resistor 739 and the second terminal resistor 729 are substantially similar to terminal resistor 439 and perform a similar function.

[00105] The optical modulator 700 also comprises a first driving amplifier 727, a second driving amplifier 737, and a delay circuit 711, which are substantially similar to the first driving amplifier 627, the second driving amplifier 637, and the delay circuit 611, respectively. The first driving amplifier 727 is connected to the proximate end of the first active electrode 721 and the second active electrode 722. The second driving amplifier 737 is connected between the first segment 761 and the second segment 762 and between the third segment 763 and the fourth segment 764.

[00106] The optical modulator 700 also comprises a first reference electrode 725 adjacent to the first arm of the optical waveguide 710. The first reference electrode 725 is similar to the first reference electrode 425, but is positioned outside the arms of the optical waveguide 710. The first reference electrode 725 is coupled to a reference voltage. The optical modulator 700 also comprises a second reference electrode 735 adjacent to the second arm of the optical waveguide 710. The second reference electrode 735 is similar to the first reference electrode 725, but is positioned on the opposite side of the optical waveguide 710 and is coupled to a ground instead of a voltage. This results in the first reference electrode 725 and the second reference electrode 735 applying an opposite bias.

[00107] Accordingly, the same RF signal is applied to both the first active electrode 721 and the second active electrode 722 by the first driving amplifier 727 and the second driving amplifier 737. The reference voltage applied to the first reference electrode 725 creates a voltage bias between the first active electrode 721 and the first reference electrode 725 across the upper arm of the optical waveguide 710. Further, the ground applied to the second reference electrode 735 creates a voltage bias between the second active electrode 722 and the second reference electrode 735 across the lower arm of the optical waveguide 710. This achieves a differential between the upper arm and the lower arm. Accordingly, the first segment 761, the second segment 762, the third segment 763, and the fourth segment 764, each form a PN diode with a corresponding section of the reference electrode 725 and the reference electrode 735 across the optical waveguide 710 with orientations as shown.

[00108] FIG. 8 is a schematic diagram of an example driving scheme for a differential tapered impedance traveling wave optical modulator 800 with inner active electrodes. The optical modulator 800 is an alternate embodiment of optical modulator 400, but the active electrodes are within the arms of the waveguide with reference electrodes outside the waveguide. In this driving scheme, a differential RF electrical signal drives the inner electrodes, while a DC bias is applied to the outer electrodes. The optical modulator 800 comprises an optical waveguide 810, a first driver amplifier 827, a second driver amplifier 837, and a delay circuit 811, which are substantially similar to the optical waveguide 410, the first driver amplifier 427, the second driver amplifier 437, and the delay circuit 411, respectively.

[00109] The optical modulator 800 also comprises a first active electrode 821 with a first segment 861 and a second segment 862 and a second active electrode 822 with a third segment 863 and a fourth segment 864, which are substantially similar to the first active electrode 421, the first segment 461, the second segment 462, the second active electrode 422 the third segment 463, and the fourth segment 464, respectively. However, the first active electrode 821 and the second active electrode 822 are positioned between the first arm and the second arm of the optical waveguide 810. Further, the first driver amplifier 827 is connected to the proximate end of the first active electrode 821 and the second active electrode 822. In addition, the second driver amplifier 837 is connected to the first active electrode 821 between the first segment 861 and the second segment 862 and the second active electrode 822 between the third segment 863 and the fourth segment 864. The optical modulator 800 also comprises a first terminal resistor 839 coupled to the distal end of the first active electrode 821 and a second terminal resistor 829 coupled to the distal end of the second active electrode 822. The first terminal resistor 839 and the second terminal resistor 829 are substantially similar to terminal resistor 439 and perform a similar function.

[00110] The optical modulator 800 also comprises a first reference electrode 825 adjacent to the first arm of the optical waveguide 810 and a second reference electrode 835 adjacent to the second arm of the optical waveguide 810. The first reference electrode 825 and the second reference electrode 835 are both coupled to a reference voltage. This configuration applies the electrical signal to the first active electrode 821 and the second active electrode 822 in a manner that is substantially similar to the optical modulator 400. The first reference electrode 825 and the second active electrode 822 are each substantially similar to the reference electrode 425, but they apply a bias to the active electrodes from outside the optical waveguide 810. The first segment 861, the second segment 862, the third segment 863, and the fourth segment 864 each form a PN diode with a corresponding section of the first reference electrode 825 and the second reference electrode 835 across the optical waveguide 810 with orientations as shown. In comparison to optical modulator 400, the resulting modifications reverse the orientation of all of the PN diodes.

[00111] FIG. 9 is a schematic diagram of an example driving scheme for a dual differential tapered impedance traveling wave optical modulator 900. The optical modulator 900 is an alternate embodiment of optical modulator 400, but applies two copies of the electrical signal each in a differential format. In this driving scheme two pairs of differential drivers are used to apply the RF electrical. When one of the drivers operates from a higher voltage domain, reverse bias can be applied to the MZM through the RF inputs.

[00112] The optical modulator 900 comprises an optical waveguide 910, which is substantially similar to the optical waveguide 410. The optical modulator 900 comprises a plurality of active electrodes. The optical modulator 900 comprises a first active electrode 921 positioned inside of the arms of the optical waveguide 910 and adjacent to the first arm of the optical waveguide 910. The first active electrode 921 includes a proximate end, a distal end, and a plurality of segments including a first segment 961 and a second segment 962. The first segment 961 comprises a first impedance, the second segment 962 comprises a second impedance, and the first impedance of the first segment 961 is greater than the second impedance of the second segment 962.

[00113] Further, the optical modulator 900 comprises a second active electrode 922 positioned outside of the arms of the optical waveguide 910 and adjacent to the second arm of the optical waveguide 910. The second active electrode 922 includes a proximate end, a distal end, and a plurality of segments including a third segment 963 and a fourth segment 964. The third segment 963 comprises a third impedance, the fourth segment 964 comprises a fourth impedance, and the third impedance of the third segment 963 is greater than the fourth impedance of the fourth segment 964.

[00114] The optical modulator 900 also comprises a third active electrode 923 adjacent to the second arm of the optical waveguide 910. Also, the third active electrode 923 is positioned between the first arm and the second arm of the optical waveguide 910, and hence between the arms of the optical waveguide 910. The third active electrode 923 includes a proximate end, a distal end, and a plurality of segments including a fifth segment 965 and a sixth segment 966. The fifth segment 965 comprises a fifth impedance, the sixth segment 966 comprises a sixth impedance, and the fifth impedance of the fifth segment 965 is greater than the sixth impedance of the sixth segment 966.

[00115] The optical modulator 900 also comprises a fourth active electrode 924 positioned outside of the arms of the optical waveguide 910 and adjacent to the first arm of the optical waveguide. The fourth active electrode 924 includes a proximate end, a distal end, and a plurality of segments including a seventh segment 967 and an eighth segment 968. The seventh segment 967 comprises a seventh impedance, the eighth segment 968 comprises an eighth impedance, and the seventh impedance of the seventh segment 967 is greater than the eighth impedance of the eighth segment 968. The first active electrode 921, the second active electrode 922, the third active electrode 923, and the fourth active electrode 924 are substantially similar to the first active electrode 421 and the second active electrode 422 and include impedances that are tapered in a similar manner.

[00116] The optical modulator 900 also comprises a first terminal resistor 939 coupled to the distal end of the first active electrode 921 and the distal end of the second active electrode 922. The optical modulator 900 also comprises a second terminal resistor 929 coupled to the distal end of the third active electrode 923 and the distal end of the fourth active electrode 924. The first terminal resistor 939 and the second terminal resistor 929 are substantially similar to the terminal resistor 439 and provide a similar function.

[00117] The optical modulator 900 also comprises a plurality of driver amplifiers including a first driver amplifier 927 electrically coupled to the proximate end of the first active electrode 921 and the proximate end of the second active electrode 922. The optical modulator 900 also comprises a second driver amplifier 937 electrically coupled to the first active electrode 921 between the first segment 961 and the second segment 962 and the second active electrode 922 between the third segment 963 and the fourth segment 964. The optical modulator 900 also comprises a third driver amplifier 947 electrically coupled to the proximate end of the third active electrode 923 and electrically coupled to the proximate end of the fourth active electrode 924. The optical modulator 900 also comprises a fourth driver amplifier 957 electrically coupled to the third active electrode 923 between the fifth segment 965 and the sixth segment 966 and electrically coupled to the fourth active electrode 924 between the seventh segment 967 and the eighth segment 968. The first driver amplifier 927 and the second driver amplifier 937 are substantially similar to the first driver amplifier 427 and the second driver amplifier 437, respectively, and are scaled in a similar manner. The third driver amplifier 947 and the fourth driver amplifier 957 are also substantially similar to the first driver amplifier 427 and the second driver amplifier 437, respectively, and are scaled in a similar manner.

[00118] The first segment 961, the second segment 962, the third segment 963, the fourth segment 964, the fifth segment 965, the sixth segment 966, the seventh segment 967, the eight segment 968 each form a PN diode with a corresponding segment across the optical waveguide 910 with orientations as shown. The optical modulator 900 also comprises a delay circuit 911 and a delay circuit 912, which are both substantially similar to the delay circuit 411 and apply an electrical signal delay in a similar manner.

[00119] As shown, the first driver amplifier 927 and the second driver amplifier 937 apply a differential signal to the first active electrode 921 and the second active electrode 922. Further, the third driver amplifier 947 and the fourth driver amplifier 957 apply a differential signal to the third active electrode 923 and the fourth active electrode 924. The first active electrode 921 and the fourth active electrode 924 then modulate the electrical signal onto the upper arm of the optical waveguide 910. Further, the second active electrode 922 and the third active electrode 923 then modulate the electrical signal onto the lower arm of the optical waveguide 910.

[00120] FIG. 10 is a graph 1000 of example frequency response curves for a tapered impedance traveling wave optical modulator, such as optical modulator 400. Graph 1000 depicts electrical to electrical (E-E) responses and electrical to optical (E-O) responses of a TW-MZM, such as optical modulator 100, verses a tapered impedance (Tapered-Z) MZM, such as optical modulator 400. The graph 1000 depicts the scattering parameters (S-parameters) in decibels (dBs) versus operational frequency in gigahertz (GHz). The S-parameters indicate input to output relationships between ports, such as between an electrical input and a terminal resistor in the E- E case or between an electrical input and an optical output in the E-O case. As shown, both the E-O and E-E S-parameters of the Tapered-Z MZM are consistently higher in bandwidth than the S-parameters of the TW-MZM extending the frequency of operation, while the power efficiency is similar to the TW-MZM as described earlier.

[00121] As a proof of concept, an example Tapered-Z TW-MZM was modeled using a Verilog-A model and simulated versus an example segmented TW-MZM model. The TW- segment model may include a frequency dependent electrical model along with an optical model in Verilog-A based on the TW-segment parameters. Parameters for 44Ω, 60Ω and 80Ω differential impedance segments were used to create separate models for various impedance TW- segments with 29.6GHz, 29.1GHz and 23.6GHz 3dB E-0 bandwidth, respectively, for a 3 millimeter (mm) long segment. Using the unit length TW-segment models and Verilog-A models created for an optical splitter and combiner, a model was constructed for a 3mm 2- segment Tapered-Z TW-MZM with 80Ω and 44Ω TW-segment impedances. Note that each of the 1.5mm segments is composed of 100 unit-length TW-segment models in series to include the distributed nature of the MZM parasitics. The driver amplifier was designed in a SiGe bipolar CMOS (BiCMOS) process for a 3.5 peak to peek voltage (Vpp) swing. The output driver sizing was optimized for driving the 3mm 2-segment Tapered-Z TW-MZM. Co-simulation of the driver amplifier and tapered-Z TW-MZM was performed including bonding parasitics for a flip- chip package. The frequency response curves in graph 1000 show a 10.5% improvement in E- O 6dB bandwidth to 59GHz while maintaining similar power efficiency as the TW-MZM. [00122] FIG. 11 is a graph 1100 of example frequency response curves for a tapered impedance traveling wave optical modulator, such as optical modulator 400, with various peaking settings for the driver amplifiers. The graph 1100 shows the E-E and E-0 S-parameters in dBs for a Tapered-Z MZM with driver amplifiers set to various peaking setting versus frequency in GHz. Accordingly, the peaking of the gain-frequency response in each of the driving amplifiers can be optimized to cancel the roll-off from the transmission line losses in the two segments to minimize the ripple and maximize the bandwidth. The driver amplifier scaling for the two segments can also be used to achieve a lower ripple in the E-0 response. In an example embodiment, the E-0 response maximum ripple of less than 0.6dB may be achieved up to 45GHz as the driver gain and peaking are varied.

[00123] FIG. 12 is a graph 1200 of example frequency response curves for a tapered impedance traveling wave optical modulator, such as optical modulator 400, implemented by varying PN diode loading. For example, the impedances for the tapered-Z section can be implemented by varying physical transmission line impedances or by varying the PN diode loading on the transmission line. As an example, an 80W section was synthesized for the above case by alternating short lengths of loaded 44W sections and an unloaded transmission line. Graph 1200 shows the S-parameters in dBs for the various example embodiments versus frequency in GHz. Graph 1200 shows that there is no significant difference between either approach.

[00124] FIG. 13 is a schematic diagram of an example electro-optical device 1300 for transmitting optical data via a tapered impedance traveling wave optical modulator, such as optical modulator 400, 500, 600, 700, 800, and/or 900. For example, electro-optical device 1300 can be used to implement a method 1400 by employing an optical modulator in an optical transmitter. Hence, the electro-optical device 1300 is suitable for implementing the disclosed examples/embodiments as described herein. The electro-optical device 1300 comprises downstream ports 1320, upstream ports 1350, and/or one or more transceiver units (Tx/Rx) 1310, including transmitters and/or receivers for communicating data upstream and/or downstream over a network. The electro-optical device 1300 also includes a processor 1330 including a logic unit and/or central processing unit (CPU) to process the data and a memory 1332 for storing the data. The electro-optical device 1300 may also comprise optical-to-electrical (OE) components, electrical-to-optical (EO) components, and/or wireless communication components coupled to the upstream ports 1350 and/or downstream ports 1320 for communication of data via electrical, optical, and/or wireless communication networks.

[00125] The processor 1330 is implemented by hardware and software. The processor 1330 may be implemented as one or more CPU chips, cores (e.g., as a multi-core processor), field- programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), digital signal processors (DSPs), or any combination of the foregoing. The processor 1330 is in communication with the downstream ports 1320, Tx/Rx 1310, upstream ports 1350, and memory 1332. The Tx/Rx 1310 comprises an optical modulation module 1314. The optical modulation module 1314 implements the disclosed embodiments described herein. The optical modulation module 1314 may be employed to forward an electrical signal through scaled driver amplifiers for modulation onto an optical carrier via electrodes with tapered impedance to mitigate reflection of electric waves. Accordingly, the optical modulation module 1314 may be configured to perform mechanisms to address one or more of the problems discussed above. As such, the optical modulation module 1314 improves the functionality of the electro-optical device 1300 as well as addresses problems that are specific to the optical communication arts. Further, the optical modulation module 1314 effects a transformation of the electro-optical device 1300 to a different state. Alternatively, the various methods disclosed herein can be implemented as instructions stored in the memory 1332 and executed by the processor 1330 (e.g., as a computer program product stored on a non-transitory medium).

[00126] The memory 1332 comprises one or more memory types such as disks, tape drives, solid-state drives, read only memory (ROM), random access memory (RAM), flash memory, ternary content-addressable memory (TCAM), static random-access memory (SRAM), and other optical and/or electrical memory systems suitable for this task. The memory 1332 may be used as an over-flow data storage device, to store programs when such programs are selected for execution, and to store instructions and data that are read during program execution.

[00127] FIG. 14 is a flowchart of an example method 1400 of operating a tapered impedance traveling wave optical modulator, such as optical modulator 400, 500, 600, 700, 800, and/or 900. The method 1400 may also be implemented in the transmitter of an electro-optical device 1300. The optical modulator may receive an electrical for modulation onto an optical carrier. At step 1401, a first driver amplifier transmits an electrical signal to a proximate end of an active electrode. The active electrode includes the proximate end, a distal end, and a plurality of segments including a first segment and a second segment. The first segment comprises a first impedance. The second segment comprises a second impedance. The first impedance of the first segment is greater than the second impedance of the second segment. Accordingly, the active electrode includes a tapered impedance.

[00128] At step 1403, a second amplifier transmits the electrical signal to the active electrode between the first segment and the second segment. For example, the electrical signal includes a first traveling wave transmitted by the first driver amplifier and a second traveling wave transmitted by the second driver amplifier. The first impedance of the first segment and the second impedance of the second segment are scaled to mitigate reflection of the second traveling wave into the first segment, and hence mitigate interference between the first traveling wave and the second traveling wave in the first segment.

[00129] At step 1405, the electrical signal is time delayed between a first driving input of the first driver amplifier and the second driving input of the second driver amplifier.

[00130] At step 1407, a driving output of the second driver amplifier is scaled relative to a driving output of the first driver amplifier based on a difference between the first impedance of the first segment and the second impedance of the second segment. The driving output of the first driver amplifier and the second driver amplifier are scaled according to:

[00131]

[00132] where G_m1 is a gain of the first driver amplifier, G_m2 is a gain of the second driver amplifier, Z₁ is the first impedance of the first segment, and Z₂ is the second impedance of the second segment.

[00133] At step 1409, the active electrode modulates the electrical signal onto an optical waveguide.

[00134] At step 1411, a terminal resistor terminates the electrical signal at the distal end of the active electrode.

[00135] A first component is directly coupled to a second component when there are no intervening components, except for a line, a trace, or another medium between the first component and the second component. The first component is indirectly coupled to the second component when there are intervening components other than a line, a trace, or another medium between the first component and the second component. The term “coupled” and its variants include both directly coupled and indirectly coupled. The use of the term “about” means a range including ±10% of the subsequent number unless otherwise stated.

[00136] It should also be understood that the steps of the exemplary methods set forth herein are not necessarily required to be performed in the order described, and the order of the steps of such methods should be understood to be merely exemplary. Likewise, additional steps may be included in such methods, and certain steps may be omitted or combined, in methods consistent with various embodiments of the present disclosure.

[00137] While several embodiments have been provided in the present disclosure, it may be understood that the disclosed systems and methods might be embodied in many other specific forms without departing from the spirit or scope of the present disclosure. The present examples are to be considered as illustrative and not restrictive, and the intention is not to be limited to the details given herein. For example, the various elements or components may be combined or integrated in another system or certain features may be omitted, or not implemented.

[00138] In addition, techniques, systems, subsystems, and methods described and illustrated in the various embodiments as discrete or separate may be combined or integrated with other systems, components, techniques, or methods without departing from the scope of the present disclosure. Other examples of changes, substitutions, and alterations are ascertainable by one skilled in the art and may be made without departing from the spirit and scope disclosed herein.

Claims

CLAIMS What is claimed is:

1. A traveling wave optical modulator comprising: an optical waveguide having a first arm and a second arm; a first active electrode positioned adjacent to the first arm, the first active electrode including a proximate end, a distal end, and a plurality of segments including a first segment and a second segment, the first segment comprising a first impedance value, the second segment comprising a second impedance value, the first impedance value being greater than the second impedance value; a plurality of driver amplifiers including a first driver amplifier electrically coupled to the proximate end of the first active electrode and a second driver amplifier electrically coupled to the first active electrode between the first segment and the second segment; and a first terminal resistor coupled to the distal end of the first active electrode.

2. The traveling wave optical modulator of claim 1, the first driver amplifier and the second driver amplifier each comprising a driving output, the driving output of the second driver amplifier being scaled relative to the driving output of the first driver amplifier based on a difference between the first impedance value and the second impedance value.

3. The traveling wave optical modulator of claim 2, currents of the driving output of the first driver amplifier and the second driver amplifier being scaled according to:

4. The traveling wave optical modulator of any of claims 1-3, the first active electrode being connected to only a single resistor.

5. The traveling wave optical modulator of any of claims 1-4, comprising a first driving input coupled to the first driver amplifier and a second driving input coupled to the second driver amplifier, the first driving input containing a same signal as the second driving input, and comprising a delay circuit configured to time delay the signal between the first driving input and the second driving input.

6. The traveling wave optical modulator of any of claims 1-5, the first driver amplifier applies a first radio frequency (RF) electrical signal to the first segment at the proximate end of the first active electrode for modulation onto the first arm of the optical waveguide, the second driver amplifier applies a second RF electrical signal to the second segment at a point between the first segment and the second segment for modulation onto the first arm of the optical waveguide, and the first impedance value and the second impedance value are scaled to mitigate a reverse wave in the first segment and mitigate destructive interference between the first RF electrical signal and the second RF electrical signal in the first segment.

7. The traveling wave optical modulator of any of claims 1-6, comprising: a second active electrode positioned adjacent to the second arm of the optical waveguide, the second active electrode including a proximate end, a distal end, and a plurality of segments including a third segment and a fourth segment, the third segment comprising a third impedance value, the fourth segment comprising a fourth impedance value, the third impedance value being greater than the fourth impedance value.

8. The traveling wave optical modulator of claim 7, comprising: a reference electrode between the first arm and the second arm of the optical waveguide, the reference electrode being coupled to a reference voltage, the first driver amplifier being electrically coupled to the proximate end of the second active electrode and the second driver amplifier electrically coupled to the second active electrode between the third segment and the fourth segment, and the first terminal resistor being coupled to the distal end of the second active electrode.

9. The traveling wave optical modulator of any of claims 1-6, comprising a complementary electrode positioned adjacent to the second arm of the optical waveguide, the complementary electrode including a proximate end, a distal end, and a plurality of segments including a third segment and a fourth segment, the third segment comprising a third impedance value, the fourth segment comprising a fourth impedance value, the third impedance value being greater than the fourth impedance value, the complementary electrode coupled to ground; and a reference electrode positioned between the first arm and the second arm of the optical waveguide, the reference electrode being coupled to a reference voltage.

10. The traveling wave optical modulator of claim 7, comprising: a first reference electrode positioned adjacent to the first arm of the optical waveguide, the first reference electrode being coupled to a reference voltage; a second reference electrode positioned adjacent to the second arm of the optical waveguide, the second reference electrode being coupled to a ground; and a second terminal resistor coupled to the distal end of the second active electrode, the first active electrode and the second active electrode being positioned between the first arm and the second arm of the optical waveguide, and the first driver amplifier being electrically coupled to the proximate end of the second active electrode and the second driver amplifier being electrically coupled to the second active electrode between the third segment and the fourth segment.

11. The traveling wave optical modulator of claim 7, comprising: a first reference electrode positioned adjacent to the first arm of the optical waveguide, the first reference electrode being coupled to a reference voltage; a second reference electrode positioned adjacent to the second arm of the optical waveguide, the second reference electrode being coupled to the reference voltage; and a second terminal resistor coupled to the distal end of the second active electrode, the first active electrode and the second active electrode being positioned between the first arm and the second arm of the optical waveguide, and the first driver amplifier being electrically coupled to the proximate end of the second active electrode, and the second driver amplifier being electrically coupled to the second active electrode between the third segment and the fourth segment.

12. The traveling wave optical modulator of claim 7, the first driver amplifier being electrically coupled to the proximate end of the second active electrode and the second driver amplifier electrically coupled to the second active electrode between the third segment and the fourth segment, and the first terminal resistor being coupled to the distal end of the second active electrode, the traveling wave optical modulator comprising: a third active electrode positioned adjacent to the second arm of the optical waveguide and positioned between the first arm and the second arm of the optical waveguide, the third active electrode including a proximate end, a distal end, and a plurality of segments including a fifth segment and a sixth segment, the fifth segment comprising a fifth impedance value, the sixth segment comprising a sixth impedance value, the fifth impedance value being greater than the sixth impedance value; a fourth active electrode being positioned adjacent to the first arm of the optical waveguide, the fourth active electrode including a proximate end, a distal end, and a plurality of segments including a seventh segment and an eighth segment, the seventh segment comprising a seventh impedance value, the eighth segment comprising an eighth impedance value, and the seventh impedance value being greater than the eighth impedance value; and a second terminal resistor coupled to the distal end of the third active electrode and the distal end of the fourth active electrode, and the plurality of driver amplifiers further including a third driver amplifier electrically coupled to the proximate end of the third active electrode and electrically coupled to the proximate end of the fourth active electrode, and a fourth driver amplifier electrically coupled to the third active electrode between the fifth segment and the sixth segment and electrically coupled to the fourth active electrode between the seventh segment and the eighth segment.

13. The traveling wave optical modulator of any of claims 1-12, implemented as an indium phosphide (InP) modulator, a lithium niobate (LiNbO3) modulator, a silicon (Si) modulator, or any combination of the foregoing modulators.

14. The traveling wave optical modulator of any of claims 1-13, implemented as a Mach- Zehnder Modulator (MZM).

15. The traveling wave optical modulator of any of claims 1-14, the plurality of driver amplifiers being implemented in metal oxide semiconductor field effect transistor (MOSFET), complementary metal-oxide-semiconductor (CMOS), bipolar junction transistor (BJT), heterojunction bipolar transistor (HBT), high electron mobility transistor (HEMT), or any combination of the foregoing transistors.

16. A traveling wave optical modulator comprising: an optical waveguide; an active electrode positioned adjacent to the optical waveguide, the active electrode including a proximate end, a distal end, and a plurality of segments including a first segment and a second segment, the first segment comprising a first impedance value, the second segment comprising a second impedance value, and the first impedance value being greater than the second impedance value; a plurality of electrical signal inputs including a first driving input electrically coupled to the proximate end of the active electrode and a second driving input electrically coupled to the active electrode between the first segment and the second segment; and a terminal resistor coupled to the distal end of the active electrode.

17. The traveling wave optical modulator of claim 16, the active electrode being connected to only a single resistor.

18. The traveling wave optical modulator of any of claims 16-17, the first input applies a first radio frequency (RF) electrical signal to the first segment at the proximate end of the active electrode for modulation onto the optical waveguide, the second input applies a second RF electrical signal to the second segment at a point between the first segment and the second segment for modulation onto the optical waveguide, and the first impedance value and the second impedance value are scaled to mitigate reverse wave in the first segment and mitigate destructive interference between the first RF electrical signal and the second RF electrical signal in the first segment.

19. The traveling wave optical modulator of any of claims 16-18, implemented as an indium phosphide (InP) modulator, a lithium niobate (LiNbO3) modulator, a silicon (Si) modulator, or any combination of the foregoing modulators.

20. The traveling wave optical modulator of any of claims 16-19, implemented as a Mach- Zehnder Modulator (MZM).

21. A metho d comp rising : transmitting, by a first driver amplifier, a signal to a proximate end of an active electrode, the active electrode including the proximate end, a distal end, and a plurality of segments including a first segment and a second segment, the first segment comprising a first impedance value, the second segment comprising a second impedance value, and the first impedance value being greater than the second impedance value; transmitting, by a second driver amplifier, the signal to the active electrode between the first segment and the second segment; modulating, by the active electrode, the signal onto an optical waveguide; and terminating, by a terminal resistor, the signal at the distal end of the active electrode.

22. The method of claim 21, comprising scaling a driving output of the second driver amplifier relative to a driving output of the first driver amplifier based on a difference between the first impedance value and the second impedance value.

23. The method of any of claims 21-22, currents of the driving output of the first driver amplifier and the second driver amplifier are scaled according to:

24. The method of any of claims 21 -23, comprising time delaying the signal between a first driving input of the first driver amplifier and the second driving input of the second driver amplifier.

25. The method of any of claims 21-24 the signal including a first radio frequency (RF) electrical signal transmitted by the first driver amplifier and a second RF electrical signal transmitted by the second driver amplifier, and the first impedance value and the second impedance value are scaled to mitigate reverse wave in the first segment and mitigate destructive interference between the first RF electrical signal and the second RF electrical signal in the first segment.