WO2025165990A1

WO2025165990A1 - Periodically poled waveguides and methods of making and use thereof

Info

Publication number: WO2025165990A1
Application number: PCT/US2025/013775
Authority: WO
Inventors: Daniel Gauthier
Original assignee: Ohio State Innovation Foundation
Current assignee: Ohio State Innovation Foundation
Priority date: 2024-02-01
Filing date: 2025-01-30
Publication date: 2025-08-07
Anticipated expiration: 2026-08-01

Abstract

Disclosed herein are periodically poled waveguides and methods of making and use thereof. In some examples, the disclosed subject matter relates to devices and methods for reducing the temperature sensitivity of spontaneous parametric down conversion. For example, disclosed herein are periodically poled waveguides comprising two or more poling regions, each having a different poling period that is phase matched at a different temperature.

Description

PERIODICALLY POLED WAVEGUIDES

AND METHODS OF MAKING AND USE THEREOF

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority to U.S. Provisional Application No. 63/627,918 filed February 1, 2024, which is hereby incorporated herein by reference in its entirety.

STATEMENT OF GOVERNMENT SUPPORT

This invention was made with government support under contract No. 80NSSC22PB197 awarded by The National Aeronautics and Space Administration to SRICO, Inc., and under contract No. 22053OSUD awarded by SRICO, Inc.. The government has certain rights in the invention.

BACKGROUND

Spontaneous parametric down conversion is a process for generating entangled photon pairs. This is a key technology for the rapidly expanding field of quantum information science. In current approaches, the temperature of the device has to be controlled to well below 1 degree centigrade, increasing the cost and complexity of the device. There will likely be a world-wide effort in developing long-distance quantum communication networks using these sources and so there is a great desire to develop a source that can operate over a wide temperature range in the field without the complexity and cost of using a large size, weight, and power temperature controller. The devices and methods discussed herein address these and other needs.

SUMMARY

In accordance with the purposes of the disclosed devices and methods as embodied and broadly described herein, the disclosed subject matter relates to periodically poled waveguides and methods of making and use thereof. In some examples, the disclosed subject matter relates to devices and methods for reducing the temperature sensitivity of spontaneous parametric down conversion.

For example, disclosed herein are periodically poled waveguides comprising: a first poling region having a first poling period; and a second poling region having a second poling period; wherein the first poling period is phase matched at a first temperature and the second poling period is phase matched at a second temperature, the first poling period being different than the second poling period such that the first temperature is different than the second temperature.

In some examples, the periodically poled waveguide comprises barium borate, barium titanate, bismuth germanate, cadmium zinc telluride, cesium lithium borate, gallium(II) selenide, lithium iodate, lithium niobate (LiNbCh), lithium tantalate, lithium triborate, Nd:YCOB (Nd- doped YCOB, Nd:YCa4O(BO3)3), potassium aluminum borate, potassium dideuterium phosphate, potassium niobate, potassium titanyl phosphate, tellurium dioxide, terbium gallium garnet, yttrium iron garnet, or a combination thereof.

In some examples, the periodically poled waveguide comprises LiNbCh. In some examples, the periodically poled waveguide comprises LiNbCh doped with a dopant.

In some examples, the periodically poled waveguide consists essentially of LiNbCh. In some examples, the periodically poled waveguide consists of LiNbCh.

In some examples, the periodically poled waveguide consists essentially of the first poling region and the second poling region.

In some examples, the periodically poled waveguide consists of the first poling region and the second poling region. In some examples, the periodically poled waveguide has a total length, the first poling region has a first length, and the second poling region has a second length, the first length and the second length combining to provide the total length. In some examples, the first length and the second length are the same. In some examples, the temperature bandwidth of the device is increased to 17°C relative to a temperature bandwidth of 5°C for similar device consisting of a single poling region.

In some examples, the periodically poled waveguide further comprises a third poling region having a third poling period, the third poling period being phase matched at a third temperature, the third poling period being different than both the first poling period and the second poling period, such that the third temperature is different than both the first temperature and the second temperature. In some examples, the periodically poled waveguide comprises one or more additional poling regions, each of the one or more additional poling regions having a poling period that is phase matched a temperature, wherein each of the poling periods is different than each other such that each phase matched temperature is different than each other. In some examples, the total number of poling regions in the periodically poled waveguide is 3 or more, 4 or more, 5 or more, 10 or more, 25 or more, 50 or more, or 100 or more.

In some examples, the periodically poled waveguide is monolithic.

In some examples, the periodically poled waveguide is not monolithic. In some examples, each of the poling regions comprises a separate crystal, each of the crystals being separated from a neighboring crystal by a gap, which together form the periodically poled waveguide.

In some examples, the periodically poled waveguide is less temperature sensitive relative to a waveguide consisting of a single poling region.

In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is increased relative to the temperature bandwidth of a waveguide consisting of a single poling region.

In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is increased by a factor of two or more (e.g., three or more) relative to the temperature bandwidth of a waveguide consisting of a single poling region.

In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is 5°C or more, 10°C or more, 15°C or more, 35°C or more, 40°C or more, 50°C or more, 75°C or more, 100°C or more, 150°C or more, or 180°C or more.

In some examples, the periodically poled waveguide has a temperature bandwidth; during use, the periodically poled waveguide is operated at an operation temperature; and the periodically poled waveguide is configured such that the operation temperature is within the temperature bandwidth of the periodically poled waveguide.

Also disclosed herein are devices comprising any of the periodically poled waveguides described herein. In some examples, the device further comprises a temperature controller. In some examples, the temperature controller is configured to stabilize the temperature differential between the first and second poling regions. In some examples, the first poling region is a high- temperature region and the second poling region is a low-temperature region, and wherein the temperature controller is configured to stabilize the temperature of the high-temperature region relative to the low-temperature region.

In some examples, the device generates photon pairs via spontaneous parametric down conversion. In some examples, the photon pairs are entangled.

In some examples, the device generates entangled photon pairs via spontaneous parametric down conversion.

In some examples, the device generates a plurality of photons (e.g., two or more, three or more, or four or more) via spontaneous parametric down conversion

In some examples, the device is a quantum information device.

In some examples, the device comprises a drone, a satellite, or a combination thereof.

In some examples, the device is configured for a terrestrial application.

In some examples, the device is configured for an extra-terrestrial application.

Also disclosed herein are methods of use of any of the periodically poled waveguides described herein. In some examples, the method comprises using the periodically poled waveguide in any of the devices disclosed herein.

Also disclosed herein are methods of use of any of the devices disclosed herein.

In some examples, the method comprises using the periodically poled waveguide or device to generate photon pairs via spontaneous parametric down conversion. In some examples, the photon pairs are entangled.

In some examples, the method comprises using the periodically poled waveguide or device to generate entangled photon pairs via spontaneous parametric down conversion.

In some examples, the method comprises using the periodically poled waveguide or device to generate a plurality of photons (e.g., two or more, three or more, or four or more) via spontaneous parametric down conversion.

In some examples, the method comprises using the periodically poled waveguide or device in a quantum information application.

In some examples, the method comprises using the periodically poled waveguide or device in a drone, a satellite, or a combination thereof.

In some examples, the method comprises using the periodically poled waveguide or device in a terrestrial application.

In some examples, the method comprises using the periodically poled waveguide or device in an extra-terrestrial application.

Also disclosed herein are methods of making any of the periodically poled waveguides disclosed herein.

Also disclosed herein are periodically-poled LiNbCh waveguides comprising: a first poling region; and a second poling region, wherein a poling period of the first poling region or the second poling region is phase matched at two different temperatures. In some examples, a respective poling period of each of the first poling region and the second poling region is phase matched at two different temperatures. In some examples, a temperature bandwidth is increased from about 5 °C to about 17 °C. In some examples, the first poling region is a high-temperature region and the second poling region is a low-temperature region. In some examples, only the first poling region is stabilized. In some examples, a differential heating method is used for the waveguide.

Also disclosed herein are waveguides and methods as described herein.

Additional advantages of the disclosed devices and methods will be set forth in part in the description which follows, and in part will be obvious from the description. The advantages of the disclosed devices and methods will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosed systems and methods, as claimed.

The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying figures, which are incorporated in and constitute a part of this specification, illustrate several aspects of the disclosure, and together with the description, serve to explain the principles of the disclosure.

Figure 1 shows the phase-matching curve for the two cases using 7 = 20.0°C (poling period of 18.990 pm when the temperature is 20.0°C) and Z2 = 30.8°C (poling period of 18.956 pm when the temperature is 30.8°C) according to an implementation described herein.

Figure 2A shows the efficiency curve for the two-region case when the poling period in the second region is 18.950 pm when the temperature is 30.8°C according to an implementation described herein.

Figure 2B shows the efficiency curve when AZ= 1.9°C, showing that the ideal efficiency curve is restored according to an implementation described herein.

Figure 3. Temperature bandwidths for Type-0 SPDC in 2 cm periodically-poled lithium niobate (PPLN) waveguides using uniform poling phase-matched to 20°C (orange curve) and two cascaded regions of different poling periods phase-matched to T1 = 20°C and T2 = 30.8°C (blue curve, oscillating around the horizontal black line at 1/4). Detuning the second region’s nominally 18.956 pm poling period by 6.3 nm (dashed red curve). The dashed red curve returns to the shape of the blue curve with a corrective temperature difference between the two regions of 1.9°C.

Figure 4A-Figure 4B. Figure 4A) The deviation of each index of refraction for LiNbCh from its value at an ambient temperature of 20°C. The extraordinary index of refraction is more sensitive to changes in temperature. Figure 4B) The change in region thickness compared to its phase-matched value at 20 °C (18.990 pm). The plots are generated using the Sellmeier equation with coefficients given in Bartnick et al., Phys. Rev. Appl. 2021, 15, 024028 and the thermal expansion perpendicular to the crystal axis from https://www.bostonpiezooptics.com/lithium- niobate.

Figure 5A-Figure 5B. Figure 5A) The typical design of periodically-poled waveguides, with one poling period, and Figure 5B) the waveguide described herein, where a second region is introduced with a different poling period. The regions are not to scale, the large difference in poling period is for illustrative purposes.

Figure 6. Temperature bandwidth for one and two regions of different poling period in periodically-poled lithium niobate.

Figure 7A-Figure 7B. Compensating a manufacturing error using a differential temperature adjustment.

Figure 8A-Figure 8B. The effect of pump wavelength detuning on the shape of the relative efficiency curve over the crystal’s temperature for both the Figure 8 A) one-region and Figure 8B) two-region waveguide. Three cases of pump wavelength detuning are shown for each.

Figure 9. Sensitivity of the one-region (blue curve) and two-region (yellow curve) to detuning of the pump wavelength.

Figure 10. Changing the poling period’s phase matching temperature according to a positively sloped linear (blue), tangent (yellow), and Gaussian (purple) functions, with ten regions of different poling period along the length of the waveguide. These are the most coherent choices. The red line is the minimum expected efficiency of ten regions given no coherent addition of efficiencies.

Figure 11. The diminishing returns in 2 (blue), 10 (red), and 100 (orange) linearly increasing phase-matched temperature regions.

Figure 12. The temperature dependent relative efficiency for 3 (purple), 10 (blue), 50 (yellow), and 100 (red) regions of poling periods with linearly increasing phase-matching temperature.

Figure 13A-Figure 13B. The relative efficiency of down conversion for Figure 13A) one- region and a Figure 13B) two-region waveguide. The curves represent different phase-matching configurations: Type 0 eee (blue), Type 0 ooo (red), and Type II oeo (yellow).

Figure 14. Energy and momentum conservation in spontaneous parametric down conversion.

Figure 15. SPDC efficiency for a 2-cm-long crystal.

Figure 16. An example waveguide described herein, having a first region with a first poling period and a second region is with a different poling period, where the first poling region and the second poling region are different crystals separated by a gap. The regions and the gap are not to scale, the large difference in poling period is for illustrative purposes.

DETAILED DESCRIPTION

The devices and methods described herein may be understood more readily by reference to the following detailed description of specific aspects of the disclosed subject matter and the Examples included therein.

Before the present devices and methods are disclosed and described, it is to be understood that the aspects described below are not limited to specific synthetic methods or specific reagents or specific materials, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting.

Also, throughout this specification, various publications are referenced. The disclosures of these publications in their entireties are hereby incorporated by reference into this application in order to more fully describe the state of the art to which the disclosed matter pertains. The references disclosed are also individually and specifically incorporated by reference herein for the material contained in them that is discussed in the sentence in which the reference is relied upon.

General Definitions

In this specification and in the claims that follow, reference will be made to a number of terms, which shall be defined to have the following meanings.

Throughout the description and claims of this specification, the word “comprise” and other forms of the word, such as “comprising” and “comprises,” means including but not limited to, and is not intended to exclude, for example, other additives, components, integers, or steps.

As used in the description and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a composition” includes mixtures of two or more such compositions, reference to “an agent” includes mixtures of two or more such agents, reference to “the component” includes mixtures of two or more such components, and the like.

“Optional” or “optionally” means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where the event or circumstance occurs and instances where it does not.

Ranges can be expressed herein as from “about” one particular value, and/or to “about” another particular value. By “about” is meant within 5% of the value, e.g., within 4, 3, 2, or 1% of the value. When such a range is expressed, another aspect includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another aspect. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. Values can be expressed herein as an “average” value. “Average” generally refers to the statistical mean value.

By “substantially” is meant within 5%, e.g., within 4%, 3%, 2%, or 1%.

“Exemplary” means “an example of’ and is not intended to convey an indication of a preferred or ideal embodiment. “Such as” is not used in a restrictive sense, but for explanatory purposes.

It is understood that throughout this specification the identifiers “first” and “second” are used solely to aid in distinguishing the various components and steps of the disclosed subject matter. The identifiers “first” and “second” are not intended to imply any particular order, amount, preference, or importance to the components or steps modified by these terms.

References in the specification and concluding claims to parts by weight of a particular element or component in a composition denotes the weight relationship between the element or component and any other elements or components in the composition or article for which a part by weight is expressed. Thus, in a compound containing 2 parts by weight of component X and 5 parts by weight component Y, X and Y are present at a weight ratio of 2:5, and are present in such ratio regardless of whether additional components are contained in the compound.

A weight percent (wt. %) of a component, unless specifically stated to the contrary, is based on the total weight of the formulation or composition in which the component is included.

The term “or combinations thereof’ as used herein refers to all permutations and combinations of the listed items preceding the term. For example, “A, B, C, or combinations thereof’ is intended to include at least one of: A, B, C, AB, AC, BC, or ABC, and if order is important in a particular context, also BA, CA, CB, CBA, BCA, ACB, BAC, or CAB. Continuing with this example, expressly included are combinations that contain repeats of one or more item or term, such as BB, AAA, AB, BBC, AAABCCCC, CBBAAA, CAB ABB, and so forth. The skilled artisan will understand that typically there is no limit on the number of items or terms in any combination, unless otherwise apparent from the context.

Periodically poled waveguides

Described herein are periodically poled waveguides and methods of making and use thereof. In some examples, the disclosed subject matter relates to devices and methods for reducing the temperature sensitivity of spontaneous parametric down conversion.

For example, disclosed herein are periodically poled waveguides comprising at least two poling regions, where in each poling region is phase matched at a different temperature. For example, disclosed herein are periodically poled waveguides comprising: a first poling region having a first poling period; and a second poling region having a second poling period; wherein the first poling period is phase matched at a first temperature and the second poling period is phase matched at a second temperature, the first poling period being different than the second poling period such that the first temperature is different than the second temperature.

The periodically poled waveguide can comprise a suitable material, such as a crystal. Examples of periodically poled waveguide materials include, but are not limited to, barium borate, barium titanate, bismuth germanate, cadmium zinc telluride, cesium lithium borate, gallium(II) selenide, lithium iodate, lithium niobate (LiNbCh), lithium tantalate, lithium triborate, Nd:YCOB (Nd-doped YCOB, Nd:YCa4O(BO3)3), potassium aluminum borate, potassium dideuterium phosphate, potassium niobate, potassium titanyl phosphate, tellurium dioxide, terbium gallium garnet, yttrium iron garnet, or a combination thereof.

In some examples, the periodically poled waveguide consists essentially of the first poling region and the second poling region. In some examples, the periodically poled waveguide consists of the first poling region and the second poling region.

In some examples, the periodically poled waveguide consists essentially of LiNbCh and the periodically poled waveguide consists essentially of the first poling region and the second poling region.

In some examples, the periodically poled waveguide consists of LiNbCh and the periodically poled waveguide consists of the first poling region and the second poling region.

In some examples, the periodically poled waveguide has a total length, the first poling region has a first length, and the second poling region has a second length, the first length and the second length combining to provide the total length. In some examples, the first length and the second length are the same.

In some examples, the periodically poled waveguide consists of the first poling region and the second poling region, the periodically poled waveguide has a total length, the first poling region has a first length, and the second poling region has a second length, the first length and the second length combining to provide the total length, wherein the first length and the second length are the same, wherein the periodically poled waveguide consists of LiNbCh, and the temperature bandwidth of the periodically poled waveguide is increased to 17°C relative to a temperature bandwidth of 5°C for a waveguide consisting of a single poling region.

In some examples, the periodically poled waveguide further comprises a third poling region having a third poling period, the third poling period being phase matched at a third temperature, the third poling period being different than both the first poling period and the second poling period, such that the third temperature is different than both the first temperature and the second temperature. In some examples, the periodically poled waveguide comprises one or more additional poling regions, each of the one or more additional poling regions having a poling period that is phase matched a temperature, wherein each of the poling periods is different than each other such that each phase matched temperature is different than each other. In some examples, the total number of poling regions in the periodically poled waveguide is 3 or more (e.g., 4 or more, 5 or more, 10 or more, 15 or more, 20 or more, 25 or more, 30 or more, 35 or more, 40 or more, 45 or more, 50 or more, 55 or more, 60 or more, 65 or more, 70 or more, 75 or more, 80 or more, 85 or more, 90 or more, 95 or more, or 100 or more). In some examples, the total number of poling regions in the periodically poled waveguide is 4 or more. In some examples, the total number of poling regions in the periodically poled waveguide is 5 or more. In some examples, the total number of poling regions in the periodically poled waveguide is 10 or more. In some examples, the total number of poling regions in the periodically poled waveguide is 25 or more. In some examples, the total number of poling regions in the periodically poled waveguide is 50 or more. In some examples, the total number of poling regions in the periodically poled waveguide is 100 or more.

In some examples, the periodically poled waveguide is monolithic.

In some examples, the periodically poled waveguide is not monolithic. For example, each of the poling regions can comprise a separate crystal, each of the crystals being separated from the neighboring crystal by a gap, that together form the periodically poled waveguide, for example as shown in Figure 16. For example, the periodically poled waveguide can comprise a first poling region and a second poling region, the first poling region comprising a first crystal having a first length, the second poling region comprising a second crystal having a second length, the first crystal being separated from the second crystal by a gap. In some examples, the first length and the second length are the same.

In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is increased by a factor of two or more (e.g., three or more) relative to the temperature bandwidth of a waveguide consisting of a single poling region. In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is increased by a factor of three or more relative to the temperature bandwidth of a waveguide consisting of a single poling region. In some examples, the temperature bandwidth of the periodically poled waveguide is increased to 17°C relative to a temperature bandwidth of 5°C for a waveguide consisting of a single poling region.

In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is 5°C or more (e.g., 10°C or more, 15°C or more, 20°C or more, 25°C or more, 30°C or more, 35°C or more, 40°C or more, 45°C or more, 50°C or more, 60°C or more, 70°C or more, 80°C or more, 90°C or more, 100°C or more, 110°C or more, 120°C or more, 130°C or more, 140°C or more, 150°C or more, 160°C or more, 170°C or more, or 180°C or more). In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is 10°C or more. In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is 15°C or more. In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is 35°C or more. In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is 40°C or more. In some examples, the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is 50°C or more.

In some examples, the periodically poled waveguide has a temperature bandwidth, and, during use, the periodically poled waveguide is operated at an operation temperature, and the periodically poled waveguide is configured such that the operation temperature is within the temperature bandwidth of the periodically poled waveguide.

Disclosed herein are periodically-poled LiNbCh waveguides comprising: a first poling region; and a second poling region, wherein a poling period of the first poling region or the second poling region is phase matched at two different temperatures. In some examples, a respective poling period of each of the first poling region and the second poling region is phase matched at two different temperatures. In some examples, a temperature bandwidth is increased from about 5 °C to about 17 °C.

In some examples, the first poling region is a high-temperature region and the second poling region is a low-temperature region. In some examples, only the first poling region is stabilized. In some examples, a differential heating method is used for the waveguide.

Also disclosed herein are waveguides and methods as described herein.

Devices

Also disclosed herein are devices comprising any of the periodically poled waveguides described herein.

In some examples, the device further comprises a temperature controller. In some examples, the temperature controller is configured to stabilize the temperature differential between the first and second poling regions. In some examples, the first poling region is a high- temperature region and the second poling region is a low-temperature region, and wherein the temperature controller is configured to stabilize the temperature of the high-temperature region relative to the low-temperature region.

In some examples, the device generates a plurality of photons (e.g., two or more, three or more, or four or more) via spontaneous parametric down conversion.

In some examples, the device is less temperature sensitive relative to a device comprising a waveguide consisting of a single poling region.

In some examples, the device is a quantum information device.

In some examples, the device is configured for a terrestrial application.

Methods

Also disclosed herein are methods of making any of periodically poled waveguides described herein.

Also disclosed herein are methods of use of any of the periodically poled waveguides described herein. In some examples, the method comprises using the periodically poled waveguide in any of the devices described herein. Also described herein are methods of use of any of the devices described herein.

In some examples, wherein the method comprises using the periodically poled waveguide or device in an extra-terrestrial application.

A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims.

The examples below are intended to further illustrate certain aspects of the systems and methods described herein and are not intended to limit the scope of the claims.

EXAMPLES

The following examples are set forth below to illustrate the methods and results according to the disclosed subject matter. These examples are not intended to be inclusive of all aspects of the subject matter disclosed herein, but rather to illustrate representative methods and results. These examples are not intended to exclude equivalents and variations of the present invention, which are apparent to one skilled in the art.

Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.) but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in °C or is at ambient temperature, and pressure is at or near atmospheric. There are numerous variations and combinations of measurement conditions, e.g., component concentrations, temperatures, pressures and other measurement ranges and conditions that can be used to optimize the described process.

Example 1

Spontaneous parametric down conversion is a process for generating entangled photon pairs. This is a key technology for the rapidly expanding field of quantum information science. In current approaches, the temperature of the device has to be controlled to well below 1 degree centigrade, increasing the cost and complexity of the device. There will likely be a world-wide effort in developing long-distance quantum communication networks using these sources and so there is a great desire to develop a source that can operate over a wide temperature range in the field without the complexity and cost of using a large size, weight, and power temperature controller.

One key resource for quantum communication technologies is a source of entangled photon pairs. Here, a birefringent and nonlinear crystal is pumped by a laser beam at a wavelength of A,_Pum_P and a pair of photons are generated at the signal Aignai and kidier wavelengths. Energy must be conserved in the interaction, thus requiring that l/A,_Pum_P = 1/ Aignai + 1/ kidier.

For efficient generation, the interaction must also conserve momentum of the photons. This is known as phase-matching. Phase-matching can be achieved by adjusting the direction of propagation of the pump, signal, and idler waves with respect to the crystalline axes (so-called angle tuning). Another approach is to take advantage of the dependence of the index of refraction of the material with respect to temperature (temperature tuning). Depending on the wavelengths of the pump, signal, and idler waves, it is not always possible to achieve phase matching. In some of these cases, it is possible to periodically invert the direction of the crystal axis to achieve what is known as phase-matching by periodic poling (MM Fejer et al. IEEE J. Quantum Electron. 1992, 28, 2631).

For essentially all approaches to phase-matching, the temperature must be tightly controlled to maintain perfect phase-matching. The typical temperature stabilization method is to place the nonlinear crystal in a large oven that creates a uniform and controlled temperature over the entire crystal length. More compact designs are possible by directly depositing heating elements on one side of the crystal (G Chen et al. IEEE Photonics J. 2021, 13, 6600409), although the range in achievable temperatures may be limited in this method because large thermal gradients will crack the crystal.

Described herein are devices and methods for realizing a temperature insensitive design. For example, a design for reducing the temperature sensitivity for spontaneous parametric down conversion (SPDC) with a specific design presented for periodically-poled LiNbCh waveguides is provided. The design uses two distinct poling regions, each with a poling period selected for phase matching at two different temperatures. The temperature bandwidth is increased from ~5°C to ~17°C using this approach, while only reducing the overall efficiency of the process by a factor of 4. The bandwidth is large enough so that controlling the overall temperature of the nonlinear crystal is likely not needed in a laboratory environment or can be achieved using a low size, weight, and power temperature controller design for field-deployed sources. To improve the stability of the design, a differential heating method is used where only the temperature of the high-temperature region is stabilized relative to the low-temperature region. The differential temperature stabilization method requires a smaller, lighter weight heater and lower power than other approaches, thus greatly simplifying the overall design.

Consider the case for SPDC pumped at X_Pum_P = 775 nm and producing degenerate pairs at 1550 nm in a lithium niobate waveguide. If these wavelengths are held as fixed, the temperature is adjusted, and the normalized efficiency given by sinc²(A&Z) is calculated, where k = 27t[(w_Pump - («signai -Hidier)/2)/ pump-l//wA], L is the crystal length assumed to be 2 cm for the simulations below, /?_Pum_P, ^signal, and //idler are the index of refraction at the pump, signal, and idler wavelengths, respectively, m is the order of the interaction, and A is the poling period. The temperature-dependent refractive index (Bartnick et al., Phys. Rev. Appl. 2021, 15, 024028) and the thermal expansion of the grating is considered using a thermal expansion coefficient of 7.5* 10'⁶ along a direction perpendicular to the crystalline “c” axis (https://www.bostonpiezooptics.com/lithium-niobate), that is, along the direction of propagation of the light in the waveguide. The highest efficiency for SPDC occurs when k = 0, known as the condition for perfect phase-matching.

One aspect of the design is to adjust the poling period along the length of the crystal so that different regions are phase-matched at different temperatures. Thus, there is always one region that will contribute to the SPDC process at some temperature. The downside of this approach is that the effective length of the interaction region is less than the crystal length, thereby reducing the efficiency . For future reference, the efficiency scales as L² for an ideal SPDC interaction.

The idea of adjusting the poling period is known in the literature for increasing the spectral bandwidth of the SPDC interaction (see X Wu et al. Opt. Lett. 2022, 47, 1574 for a recent example). Methods include using discrete steps in the poling period along the crystal or a continuous linearly increasing variation (chirp) in the poling period, apodization to reduce ripples in the spectral curve, etc.

Conventional approaches have not considered these methods for improving the temperature bandwidth of the SPDC process. Any of these methods described above for increasing the spectral bandwidth can be adapted to increasing the temperature bandwidth. Here, the case of using only two regions with distinct poling periods (step change) is considered.

The phase-mismatch is predicted as a function of temperature for the Type 0 phasematching configuration (pumping with an e-wave, generating two e-waves), which has the highest nonlinearity and hence the highest SPDC efficiency for a given pump power. Two cases: 1) the entire crystal length has a single poling period that phase-matches the interaction at temperature Zi; and 2) the first half of the crystal has the same poling period as the first case and the second half has a poling period that phase-matches the interaction at temperature Ti> T\, have been considered. The value of Ti is optimized by re-running the simulation for different values of Ti and selecting the one that has the most uniform response over the temperature range. Other variations are possible, such as having the first region at a different temperature or having the second region cooler than the first region.

Figure 1 shows temperature bandwidth for different SPDC polarization configurations in periodically-poled lithium niobate. Figure 1 shows the phase-matching curve for the two cases using Zi = 20.0°C (poling period of 18.990 pm when the temperature is 20.0°C) and Ti = 30.8°C (poling period of 18.956 pm when the temperature is 30.8°C). The first case using a single poling period (blue line) has its efficiency peaked at 20.0°C as expected and a temperature bandwidth (full width at half maximum of the efficiency curve) of ~5°C.

For the case of two regions (orange line), there are substantial interactions between the efficiency curves for each region, somewhat “pulling” their peak efficiency away from the phase-matching temperature in each region and creating a peak in efficiency about halfway between the two regions. Given that each region is half the crystal length, it is suspected that that the efficiency should be 1/4 of the efficiency of a single region that spans the full crystal length (horizontal red line). It is seen that the efficiency goes somewhat above and below this line. Importantly, the temperature bandwidth has expanded to ~17°C, which over three times the nominal bandwidth of a single region.

The ripples in the efficiency curve can be reduced by using more step regions, using a continuous linear chirp in the poling period, apodizing the grating, etc. However, these approaches come at an increased manufacturing cost but may be worthwhile in some designs where a flat efficiency curve is an important metric. Another approach is to adjust the pump laser power as the temperature changes, thus reducing the variation in efficiency of the overall system.

The shape of the efficiency curve is sensitive to small errors in the relative poling period between the two regions because there is interference from the generated SPDC fields in the two regions. Described herein is a technique to compensate from such errors by making a small adjustment to the temperate AZ to the second region relative to the first; that is, by making a differential change in the temperature along the crystal.

Figure 2A-Figure 2B shows compensating a manufacturing error using a differential temperature adjustment. Figure 2A shows the efficiency curve for the two-region case when the poling period in the second region is 18.950 pm when the temperature is 30.8°C. This is a 6.3 nm error in the poling period. The efficiency curve is clearly distorted in comparison to the ideal case shown in Figure 1 when the temperature is uniform along the crystal. Figure 2B shows the efficiency curve when AZ= 1.9°C, showing that the ideal efficiency curve is restored.

This result is important from a practical perspective. The overall temperature of the crystal does not need to be controlled, but only the temperature difference of the two regions. Furthermore, AZis small, which will only require a small, lightweight and low power temperature controller to maintain a relatively flat efficiency curve over a wide overall temperature range.

It should be understood that the various techniques described herein may be implemented in connection with hardware components or software components or, where appropriate, with a combination of both. Illustrative types of hardware components that can be used include Field- programmable Gate Arrays (FPGAs), Application-specific Integrated Circuits (ASICs), Application-specific Standard Products (ASSPs), System-on-a-chip systems (SOCs), Complex Programmable Logic Devices (CPLDs), etc. The methods and apparatus of the presently disclosed subject matter, or certain aspects or portions thereof, may take the form of program code (i.e., instructions) embodied in tangible media, such as floppy diskettes, CD-ROMs, hard drives, or any other machine-readable storage medium where, when the program code is loaded into and executed by a machine, such as a computer, the machine becomes an apparatus for practicing the presently disclosed subject matter.

Although exemplary implementations may refer to utilizing aspects of the presently disclosed subject matter in the context of one or more stand-alone computer systems, the subject matter is not so limited, but rather may be implemented in connection with any computing environment, such as a network or distributed computing environment. Still further, aspects of the presently disclosed subject matter may be implemented in or across a plurality of processing chips or devices, and storage may similarly be effected across a plurality of devices. Such devices might include personal computers, network servers, and handheld devices, for example.

Although the subject matter has been described in language specific to structural features and/or methodological acts, it is to be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example forms of implementing the claims.

Example 2

A design for reducing the temperature sensitivity for spontaneous parametric down conversion (SPDC) with a specific design presented for periodically-poled LiNbCh waveguides is provided. The design uses two distinct poling regions, each with a poling period selected for phase matching at two different temperatures. The temperature bandwidth is increased from ~5°C to ~17°C using this approach, while only reducing the overall efficiency of the process by a factor of 4. The bandwidth is large enough so that controlling the overall temperature of the nonlinear crystal is likely not needed in a laboratory environment or can be achieved using a low size, weight, and power temperature controller design for field-deployed sources. To improve the stability of the design, a differential heating method is used where only the temperature of the high-temperature region is stabilized relative to the low-temperature region. The differential temperature stabilization method requires a smaller, lighter weight heater and lower power than other approaches, thus greatly simplifying the overall design.

Described herein is a periodically-poled LiNbCh waveguide comprising: a first poling region; and a second poling region, wherein a poling period of the first poling region or the second poling region is phase matched at two different temperatures.

In some examples, a respective poling period of each of the first poling region and the second poling region is phase matched at two different temperatures.

In some examples, a temperature bandwidth is increased from about 5°C to about 17°C. In some examples, the first poling region is a high-temperature region and the second poling region is a low-temperature region. In some examples, only the first poling region is stabilized. In some examples, a differential heating method is used for the waveguide.

Also disclosed herein is a waveguide and method as described herein.

Example 3 - Temperature Tolerant Quantum Entangled Light Source

Abstract: Spontaneous parametric down-conversion sources are typically highly temperature sensitive. Periodically poled waveguides with two cascading regions that are phase- matched to different temperatures can potentially more than double the operating temperature bandwidth.

Introduction. Entangled photon sources based on spontaneous parametric downconversion (SPDC) are foundational in many quantum communication/information-based technologies. SPDC is the process whereby a nonlinear crystal spontaneously converts pump light of frequency co_P to down-converted, correlated pairs of photons named the signal (co_s) and idler (coi). Energy must be conserved in this process, requiring co_P = cos+coi. The efficiency of this process is significantly increased by phase-matching (conservation of momentum). In cases where phase-matching is not possible, quasi -phase-matching (QPM) is realized through periodic poling (flipping the crystal axis orientation by 180° every characteristic length), which introduces an additional momentum component (wavenumber kqpM) to the phase-matching condition. The phase mismatch — the magnitude of momentum conservation violation in bulk crystal (Ak = k_P -ks -ki -kqpM where kj is the j field wavenumber in the crystal) — allows the characteristic length (length of each section) to be calculated (MM Fejer et al. IEEE J. Quantum Electron. 1992, 28, 2631).

The indices of refraction of nonlinear optical materials (given in terms of Sellmeier equations) are temperature-dependent. Additionally, the characteristic length (and therefore the phase-matching) of periodic poling changes due to the thermal expansion of the waveguide. Entanglement sources in practical implementations typically need fine control about an often quite high temperature, e.g. 100 °C, which requires bulky, high-power temperature controllers. Some environments, such as aboard drones or satellites, require strict limitations on size, weight, and power (SWaP). It is therefore prudent to design a compact down-conversion device capable of operating at a broader range of temperatures while maintaining the highest possible efficiencies. This eliminates the need for powerful temperature controllers and dramatically reduces the SWaP. No purposeful design of a periodically poled waveguide for broad temperature range down-conversion exists.

Methods

Multi-region technique. Periodically poled lithium niobate (PPLN) performs well as a high pair production rate down-conversion source for type-0 phase-matching (Z Zhang et al. npj Quantum Inf. 2021, 7, 123). To increase the operational temperature range, a two-region approach is used herein; half the PPLN waveguide is phase-matched to a higher temperature (T2), and the other half to a lower temperature (Tl). The combination of temperatures is chosen by choosing Tl, and iteratively scanning over many values for T2, choosing the best-shaped temperature tuning curve. The simulated results of relative down-conversion intensity are visualized in Figure 3 for a 2 cm waveguide phase-matched for Type-0 SPDC, where the horizontal line indicates 1/4 the optimal efficiency of a singular phase-matched poling period. The two-region waveguide’s temperature bandwidth is more than twice that of the one-region waveguide — the FWHM increases from ~ 5°C to ~ 17°C.

The method of using multiple regions with different poling periods sandwiched together has been used in previous works to increase the spectral bandwidth of down-converted photons (A Tehranchi et al. Opt. Express 2008, 16, 18970; N Balaji et al. J. Lightwave Tech. 2019, 37, 845; X Wu et al. Opt. Lett. 2022, 47, 1574). The application of this technique specifically for temperature bandwidth broadening is new and previously unstudied. The model herein of the crystal’s relative intensity as a function of temperature enables the design of multi-region crystals with wide temperature bandwidths centered around the expected mean ambient temperature in the environment they will be used.

Temperature differential to correct manufacturing errors. Controlling the temperature differential between the two PPLN regions can help stabilize the temperature-dependent intensity response of the waveguide. In Figure 3, a 6.3 nm error in the second region (T2 = 30.8°C phase-matched, nominal poling period of 18.956 pm) of the two-region PPLN waveguide is shown. The thermal response curve is corrected with a constant temperature differential of 1.9°C between the two regions. This technique does not involve controlling the temperature of the entire waveguide, but rather just the difference in temperature between the two regions. The corrective temperature differential is small, and therefore only requires small, lightweight, and low-power solutions (putting us on a path toward realizing a low-SWaP SPDC source).

Results. Type-0 (extraordinarily polarized pump, signal, and idler, to access the strong nonlinearity in PPLN) collinear SPDC is used herein to demonstrate how the ambient temperature bandwidth of SPDC can be increased. Figure 3 shows the results from two different waveguides, one that has one poling period phase-matched to an ambient temperature of 20°C, and one that has two poling periods phase-matched to 20°C in one half of the waveguide and to 30.8°C in the other half. Although the normalized relative intensity of the two-region waveguide is reduced by a factor of 4, the temperature bandwidth is increased from an FWHM of 5°C to 17°C. The efficiency scales as the square of the length of the crystal (L²) and effectively two crystals of length L/2 are being used, which causes the factor of 4 loss in efficiency of the two- region waveguide. It is possible to further increase temperature bandwidth by using additional regions. However, the bandwidth increases become smaller, and the efficiency scaling continues as 1/n² where n is the number of regions. Any inaccuracies in the poling periods in three-region waveguides become harder to correct with temperature differences, furthering the idea that having more than two regions is an impractical design. The dramatic increase predicted in the two-region waveguide’s operating temperature bandwidth has space-based and terrestrial real- world applications.

Example 4 - Temperature-insensitive source for entangled time-frequency quantum photonic states

Abstract. Described herein is a method for reducing the temperature sensitivity for spontaneous parametric down conversion (SPDC) suitable for generating entangled timefrequency quantum photonic states in the telecommunication band at a wavelength of 1550 nm. Specific design examples are presented using periodically-poled LiNbCh waveguides, which are commercially available and have a high second-order nonlinear coefficient that improves the overall device efficiency. One method uses two distinct poling regions, each with a poling period selected for phase-matching at different temperatures. The temperature bandwidth is increased from ~5°C to ~17°C using this approach, while only reducing the overall efficiency of the process by a factor of 4. The bandwidth is large enough so that controlling the overall temperature of the nonlinear crystal is likely not needed in a laboratory environment or can be achieved using a low size, weight, and power temperature controller design for field-deployed sources. To improve the stability of the design, it is proposed to use a differential heating method where only the difference in the temperature is stabilized. The differential temperature stabilization method requires a smaller, lighter weight heater and lower power than other approaches, thus greatly simplifying the overall design. Additionally, it is shown that the system is less sensitive to fluctuations in the pump laser’s wavelength for the two-region approach. Finally, the design is generalized to multiple poling regions.

Introduction. A key resource for quantum communication technologies is a source of entangled photon pairs. One of the most widely used means of generating entangled photons is through the process of spontaneous parametric down conversion (SPDC), whereby a birefringent nonlinear crystal is pumped by a laser beam at a wavelength of _Pum_P and a pair of photons are generated at the signal ( signai) and idler (Aidier) wavelengths. Energy must be conserved in the interaction, thus requiring that l/ _Pum_P = 1/ signai + 1/ idier.

Waveguide SPDC sources are of great current interest because they confine both the pump and generated pairs, thereby greatly increasing the overall device efficiency and lowering the required pump power. Designing the waveguide is substantially simplified if all waves have the same state of polarization. This polarization configuration lends itself to time-frequency entangled states (N Gisin et al. Nature Photon. 2007, 1, 165), where the conjugate variables are the time-of-arrival and frequency (energy) of the photons. Here, a focus is on methods for generating these states that are more robust to changes in the device temperature.

For efficient SPDC generation, the interaction must also conserve momentum of the photons. This is known as phase-matching. Phase-matching can be achieved by adjusting the direction of propagation of the pump, signal, and idler waves with respect to the crystalline axes (so-called angle tuning). Another approach is to take advantage of the temperature dependence of the index of refraction of the material (temperature tuning). Depending on the wavelengths of the pump, signal, and idler waves, it is not always possible to achieve phase-matching. In some of these cases, it is possible to periodically invert the direction of the crystal axis to achieve what is known as phase-matching by periodic poling (MM Fejer et al. IEEE J. Quantum Electron. 1992, 28, 2631). This technique allows access to high nonlinearity in some materials (such as lithium niobate) that would otherwise be unattainable. For essentially all approaches to phase-matching, the temperature must be tightly controlled to maintain phase-matching. This is due to both changes in poling period (thermal expansion/contraction) as well as changes in the indices of refraction, both shown in Figure 4A- Figure 4B for LiNbCh and degenerate SPDC producing pairs at 1550 nm. The typical temperature stabilization method is to place the nonlinear crystal in a large oven that creates a uniform and controlled temperature over the entire crystal length. Compact designs are possible by directly depositing heating elements on one side of the crystal (MM Fejer et al. IEEE J. Quantum Electron. 1992, 28, 2631), although the range in achievable temperatures may be limited in this method because large thermal gradients will crack the crystal. These methods both increase the size, weight, and power (SWaP) of the overall photonic entanglement source. This is problematic for applications involving drones, satellites, and any other SWaP-sensitive environment. In environments typical of these applications (space, varying altitudes, etc.), temperatures fluctuate greatly, making temperature insensitivity even more important.

A design for improving the temperature bandwidth (reducing the temperature sensitivity) of SPDC has not been presented in the literature, although it is known that different polarization configurations of the waves have different temperature bandwidths (G Chen et al. IEEE Photonics J. 2021, 13, 6600409) and that methods for increasing the spectral bandwidth of the device improves the temperature bandwidth (A Tehranchi et al. Opt. Express 2008, 16, 18970; N Balaji et al. J. Lightwave Tech. 2019, 37, 845). The authors are not aware of a purposeful design to increase the temperature bandwidth, which is presented here.

The devices and methods described herein is to alter a traditional periodically-poled waveguide to instead include two or more regions of different poling periods (/I) chosen for achieving phase-matching at different temperatures, which broadens the temperature bandwidth. The usual one-region design is illustrated in Figure 5A and a two-region design is shown in Figure 5B. The underlying principle of the design herein relies on a trade-off between phase matching at more temperatures, shortening the interaction length where a certain wavelength is down-converted most efficiently, and making combinations of the spectra from each different poling region coherent. This is discussed further in below, where incoherences due to manufacturing errors is discussed.

In the Methods section, the groundwork of the simulations is laid out and similar work that has been done using a variation of poling period across a waveguide is discussed. The Results section illustrates the efficiency advantage that two-region waveguides have over a range of ambient temperatures. The correction of manufacturing error using a differential heating design is discussed below. Further, how the relative efficiency vs. ambient temperature curve changes for pump wavelength detuning, and its implications for the additional efficacy of the two-region waveguide approach for full system temperature insensitivity is discussed below. Also, the extension of this technique to additional poling periods with a few different techniques for altering them across the waveguide is examined. Lastly, the trade-off between the magnitude of nonlinearity and temperature bandwidth for different phase-matching configurations, specifically for LiNbCh, is discussed.

Methods. The case for SPDC pumped at _Pum_P = 775 nm and producing degenerate pairs at 1550 nm in a lithium niobate waveguide is considered. These wavelengths are held fixed, the temperature is adjusted, and the normalized efficiency given by sinc²( k L) is calculated, where the phase mismatch is k = 27r[(n_Pump - (n_signai-nidier)/2)/A_Pump-l/(mL)], L is the crystal length assumed to be 2 cm for the simulations below, n_Pum_P, nsignai, and maier are the indices of refraction at the pump, signal, and idler wavelengths, respectively, m is the order of the interaction, and A is the poling period. The temperature-dependent refractive index (Bartnick et al. Phys. Rev. Appl. 2021, 15, 024028) and the thermal expansion of the grating using a thermal expansion coefficient of 7.5 x 10'⁶ along a direction perpendicular to the crystalline “c” axis (https://www.bostonpiezooptics.com/lithium-niobate), that is, along the direction of propagation of the light in the waveguide, are considered. The highest efficiency for SPDC occurs when k = 0, known as the condition for perfect phase-matching.

One key concept of the design herein is to adjust the poling period along the length of the crystal so that different regions are phase-matched at different temperatures. Thus, there is always one region that will contribute to the SPDC process at some temperature. A downside of this approach is that the effective length of the interaction region is less than the L, thereby reducing the efficiency. For future reference, the efficiency scales as L² for an ideal SPDC interaction. Furthermore, the SPDC fields must add constructively between the two regions, requiring precise control over the relative poling periods between the regions.

The idea of adjusting the poling period is known in the literature for increasing the spectral bandwidth of the SPDC interaction (see X Wu et al. Opt. Lett. 2022, 47, 1574 for a recent example). Methods for increasing the spectral bandwidth include using discrete steps in the poling period along the crystal or a continuous linearly increasing variation (chirp) in the poling period, apodization to reduce ripples in the spectral curve, etc.

The authors are not aware of anyone that has considered these methods for improving the temperature bandwidth of the SPDC process. Any of these methods described above for increasing the spectral bandwidth can be adapted to increasing the temperature bandwidth. Initially, a focus herein is on the case of using only two regions with distinct poling periods (step change) and later it is generalized to more complicated configurations.

Results. It is predicted that the phase-mismatch as a function of temperature for the Type 0 eee phase-matching configuration (pumping with an extraordinary polarized wave or e-wave, generating two e-waves), which has the highest nonlinearity and hence the highest SPDC efficiency for a given pump power. Two cases are considered: 1) the entire crystal length has a single poling period that phase-matches the interaction at temperature Ti; and 2) the first half of the crystal has the same poling period as the first case and the second half has a poling period that phase-matches the interaction at temperature T2 > Ti. The value of T2 was optimized by rerunning the simulation for different values of T2 and selecting the one that has the most uniform response over the temperature range. Other variations are possible, such as having the first region at a different temperature or having the second region cooler than the first region.

Figure 6 shows the phase-matching curve for the two cases using Ti = 20.0°C (poling period of 18.990 pm when the temperature is 20.0 °C) and T2 = 30.8°C (poling period of 18.956 pm when the temperature is 30.8°C). The first case using a single poling period (blue line) has its efficiency peaked at 20.0°C as expected and a temperature bandwidth (full width at half maximum of the efficiency curve) of ~5°C.

For the case of two regions (orange line), there are substantial interactions between the efficiency curves for each region, somewhat “pulling” their peak efficiency away from the phase-matching temperature in each region and creating a peak in efficiency about halfway between the two regions that arises from constructive interference between the generated fields in each region. Given that each region is half the crystal length, it is expected that the efficiency should be 1/4 of the efficiency of a single region that spans the full crystal length (horizontal red line) if the phase-matching peaks are well separated so there is no interaction of the field generated in the first and second regions. It is seen that the efficiency goes somewhat above and below this line. Importantly, the temperature bandwidth has expanded to ~17°C, which over three times the nominal bandwidth of a single region.

The ripples in the efficiency curve can be reduced by using more step regions, using a continuous linear chirp in the poling period, apodizing the grating, etc. However, these approaches come at an increased manufacturing cost but may be worthwhile in some designs where a flat efficiency curve is an important metric. These points are discussed more below. Another approach is to adjust the pump laser power as the temperature changes, thus reducing the variation in down-converted photon pair production of the overall system.

Compensating a manufacturing error using a differential temperature. The shape of the efficiency curve is sensitive to small errors in the relative poling period between the two regions because there is interference from the generated SPDC fields in the two regions. Here, a second innovation is described to compensate for such errors by making a small adjustment to the temperature difference T between the regions. This technique exploits a combination of the thermal expansion of the crystal along the direction the light propagates alongside the temperature dependence of the refractive indices.

Figure 7A shows the efficiency curve for the two-region case when the poling period in the second region is 18.950 mm when the temperature is 30.8°C. This is a 6.3 nm error in the poling period. The efficiency curve is clearly distorted in comparison to the ideal case shown in Figure 5A-Figure 5B when the temperature is uniform along the crystal. This is a case of incoherent addition of the efficiency curves for the two regions and is an important example of the sensitivity of their interaction with one another. Figure 7B shows the efficiency curve when T = 1.9°C, showing that the ideal efficiency curve is restored.

This result is important from a practical perspective. The overall temperature of the crystal does not need to be controlled, but only the temperature difference of the two regions. Furthermore, T is small, which will only require a small, lightweight, and low power temperature controller to maintain a relatively flat efficiency curve over a wide overall temperature range.

Sensitivity to pump wavelength detuning. Lasers typically have a finite spectral width and a change in wavelength with temperature due to temperature dependent changes in the lasing medium, thermal expansion/contraction of the resonator cavity, or both. Therefore, reducing the periodically-poled waveguide efficiency’s sensitivity to changes in the pump laser’s wavelength and reducing the temperature sensitivity of the crystal for efficient SPDC are of similar interest. The former is focused on here.

As a result of the pump wavelength changing, the degenerate pairs produced will change wavelength as well to maintain signai = idier = 2 _Pum_P in accordance with energy conservation. The effects of changing the pump laser’s wavelength on the shape of the relative efficiency curve over ambient temperature were simulated. The results are shown in Figure 8A-Figure 8B and Figure 9, where the pump wavelength detuning is _P = _Pum_P - 775 nm. It is evident that the two-region approach is less sensitive to changes in pump wavelength compared to the one-region design because the efficiency curve is broader for the two-region design.

It should be noted that a higher temperature will result in the laser producing a longer wavelength, so the shifts in the efficiency curves in Figure 8A-Figure 8B may be less detrimental than they currently appear. To achieve an SPDC system with a one-region waveguide that has the full 5°C temperature bandwidth (in the one-region case) or more, the system would have to be designed such that the laser spectrum and the waveguide’s efficiency have compatible temperature responses. The efficiency curve in Figure 8B shows that the two- region case can benefit similarly from considering how the crystal’s efficiency and the laser spectrum both shift with ambient temperature. Importantly, the efficiency curve is hardly deformed with changes in pump wavelength, resulting in a much greater overlap in the efficiency curves over temperature for detuned pump wavelengths.

This result shows that the two-region approach is doubly robust to temperature fluctuations - not only is the relative efficiency of SPDC in the crystal less temperature sensitive, but also the temperature-dependent effects from the pump laser are mitigated. Figure 9 illustrates this same idea over a range of pump wavelength detunings, again keeping the down- converted photons degenerate ( signai = idier = 2 _Pum_P). Unsurprisingly, the efficiency curves over pump wavelength detuning resemble those over ambient temperature. Crystal temperature and pump wavelength both determine how well the waveguide phase-matches degenerate SPDC interactions, and therefore they have a similar impact on SPDC efficiency.

A typical spectral tuning rate over temperature for semiconductor lasers in the visible wavelength range is about 0.2-0.3 nm/°C. In Figure 9, this corresponds to a full width at half maximum pump wavelength detuning bandwidth of approximately 1-2 °C and about 3-5 °C for one- and two-region waveguides, respectively. There are designs that mitigate this temperature sensitivity at the source, such as incorporating a Bragg grating, as is done in a distributed- feedback (DFB) laser. These methods can lower temperature tuning coefficient of the laser by about an order-of-magnitude, which makes the pump laser’s temperature bandwidth wider than that of the crystal’s efficiency curve for both the one- and two-region waveguides.

In addition to the two-region waveguide approach, several other approaches to varying the poling periods across the waveguide were tried. These additional attempts involve choosing some functional form for the phase-matching temperature of different regions along length of the waveguide. For example, the authors looked at altering the phase-matching temperature of each region according to a Gaussian function, such that the first and last regions are phase matched to the lowest temperatures and the middle regions to the highest temperatures. The authors also looked at linearly increasing the phase-matching temperature, as well as altering it according to a tangent curve.

Linearly increasing the phase-matching temperature. Figure 10 shows the relative efficiency of a ten-region waveguide with phase-matching temperatures that vary linearly, as a tangent and Gaussian functions. By first choosing the total number of regions, then iteratively altering the shape of the functional form the phase-matching temperatures followed (lowest and highest phase-matching temperature, width of Gaussian, range of tangent, etc.), the authors were able to find the smoothest and highest relative efficiency over a range of ambient temperatures. The best method for increasing the temperature bandwidth was, as is shown in Figure 10, linearly increasing the phase-matching temperature from 8°C and 34.5°C over the length of the waveguide.

The relative efficiency of each curve far outperforms the factor of 1/(10²) = 0.01 (red line) that modulates the sum of the different efficiency curves. This is due to the coherent addition of many overlapping regions - the 1/N² scaling would only be expected strictly for the case where there the efficiency curves are separated so far that they do not overlap. It is by careful choice, through optimization, that the result of so many overlapping efficiency curves adds more coherently than incoherently. The regions’ efficiency curves add more coherently over the different regions for the case of linearly increasing phase-matching temperature, so it has the broadest temperature bandwidth. For this method, the full width at half maximum temperature bandwidth is about 40 °C, which is over a two-fold improvement over the findings for an optimal two-region waveguide and approximately an eightfold improvement over a traditional uniformly poled waveguide.

Problems with using more than two regions. The difficulty with realizing the ten-region waveguide is in its fabrication. Ten steps between phase-matching temperatures of 8°C and 34.5°C corresponds to changes in poling period on the order of nanometers per region, challenging the precision of current fabrication techniques. Therefore, it is more practical to try replicating these results experimentally for a waveguide with few regions that have larger poling period differences between them. However, as is shown in Figure 10, there are diminishing returns on each additional region, with an increase in fabrication difficulties.

Even in the simpler case of fewer regions in a waveguide, it is likely that the efficiency vs. temperature curve will still be plagued by interference caused by inconsistencies in the fabrication process. The introduction of differential heating, as discussed above, can help correct these inconsistencies, but correcting multiple regions with different temperatures is almost certainly an unreasonable goal. Therefore, although theoretically the waveguide’s operating temperature bandwidth could be made much wider, the two-region waveguide with corrective differential heating approach may be the best overall solution.

Diminishing returns. The most dramatic improvement in the temperature bandwidth comes from the addition of a second region of a different poling period. Figure 11 shows the relative efficiency curves for 2, 10, and 100 regions of linearly increasing phase-matching temperature. This further reinforces the claim that the most practical solution is to use the two- region waveguide approach, alongside the fabrication difficulties.

Extension to a longer crystal. For some systems, it may be more desirable to have a flatter response to changes in temperature, such that the SPDC efficiency is approximately constant throughout the temperatures considered. For this technique, this is simply not possible - the three-peak efficiency curve from the two-region waveguide is as flat a response can be achieved given the two interacting efficiency curves from the two regions.

A longer waveguide sharpens the efficiency peaks over temperature and lowers maximum efficiencies due to more destructive interference over the longer interaction length L. However, the additional length can compensate for lower efficiencies caused by greater separation between the efficiency curves for different poling periods. As a reminder, the intensity of photon pairs generated scales as L². Therefore, if a flat efficiency response to changes in temperature is required for a given application, the use of a longer waveguide is recommended.

Figure 12 shows the relative efficiency curves of waveguides with 3, 10, 50, and 100 regions. Each has a linearly increasing phase-matching temperature from 15 to 35 °C. These results clearly illustrate how the region-to-region interactions contribute to the overall efficiency curve of the waveguide. The response of the three-region waveguide is clearly three separate efficiency curves, only interacting on the far fringes. The response of the one-hundred-region waveguide is much flatter, with a very broad (almost 50 °C) temperature bandwidth. The difficulties listed in above will still plague this waveguide though, so unless there is a great deal of progress in fabrication techniques, this method is generally inadvisable.

Temperature Gradient. Another option available to more reliably alter the poling period across the length of the waveguide would be to introduce a temperature gradient to a uniformly poled waveguide. This method would be similar to a constant linear chirp, with the addition of changes due to the temperature-sensitive refractive indices. Simulations of this setup are difficult - there is finite temperature diffusion across the waveguide. Therefore, to see how the waveguide behaves under a temperature gradient, one would have to solve the heat diffusion equation in the volume of the crystal for a given heater setup. The results would then be used alongside the thermal expansion/contraction, as well as the refractive indices’ temperaturedependent response to get an accurate picture of the efficiency curve over ambient temperature range. This is recommended as a possible solution to producing a flatter efficiency response while avoiding engineering difficulties discussed above.

Other phase matching configurations. The phase-matching configuration used in the simulations herein was the Type 0 eee (extraordinarily polarized pump, signal, and idler photons, respectively). This choice is both practical and customary - the eee interaction in lithium niobate has a particularly large effective second-order nonlinear susceptibility d_eff, which is equal to half the sum of nonzero elements of the second-order nonlinear susceptibility %⁽²⁾ after projecting the three interacting photons onto their corresponding polarization state. Specifically, deir for the eee interaction in lithium niobate is about a factor of ten greater than that of the Type 0 ooo interaction, and about a factor of five greater than that of the Type II oeo interaction. The down- converted photon pair production rate scales as den², so the Type 0 eee produces 100 times more photon pairs than Type 0 ooo for a given pump power. The relative efficiency curves over temperature for these three phase-matching configurations are shown in Figure 13A-Figure 13B.

It is clear from the efficiency curves in Figure 13A-Figure 13B that the ooo interaction has nearly twice the temperature bandwidth of the eee interaction (and oeo is narrower) for both the one- and two-region waveguide. This result is due to the ordinary refractive index having a smaller temperature sensitivity, as seen in Figure 4A-Figure 4B. Therefore, if using 100 times the pump laser power for the same number of down converted photons is not an issue, the ooo interaction is something that should be considered for its greatly reduced temperature sensitivity.

Conclusions. Periodically-poled SPDC sources are naturally suited for producing timefrequency entangled photonic states, but traditional one-region waveguides are typically quite sensitive to temperature fluctuations in their environment often requiring precise temperature control. Additionally, setups that rely on degenerate photon pairs without strict down-converted photon wavelength requirements need to also have careful control over laser temperature because the pump wavelength’s changes with temperature may push the efficient operating temperature range out of reach for current ambient conditions. Both of these difficulties are eased herein by shifting from a one-region to a two-region design of periodically-poled waveguides, minimizing the amount of thermal control needed for efficient down conversion.

Furthermore, it is shown that manufacturing error in the poling periods can be remediated by differential heating of the two regions, which is less costly in terms of SWaP than heating the entire crystal. The technique is extended to more poling periods and it is shown that this approach has diminishing returns due to increased fabrication difficulties. It is also shown that different phase-matching configurations have varying temperature bandwidth, and it was explained that any benefit from choosing Type 0 ooo over Type 0 eee must be weighed against a smaller magnitude of effective nonlinear susceptibility.

Example 5 - Temperature-insensitive source for entangled time-frequency quantum photonic states

Time-Frequency entangled states. Quantum photonic entangled states are a resource for quantum information science, including communication and sensing applications; timefrequency states are insensitive to polarization disturbances, can access a high-dimensional Hilbert space (N Gisin et al. Nature Photon. 2007, 1, 165).

Spontaneous parametric down conversion. Nonlinear optical interaction destroys one pump photon and creates signal and idler photons (Figure 14). Usually, refractive indices are adjusted by orienting the crystal or using temperature.

Periodic poling to achieve phase matching. Periodic poling to achieve phase matching is shown in Figure 5 A. Further, lk = 27t[(w_Pump - («signai -Hidier)/2)/Xpump-l//wA], L is the crystal length, //puiTip, ^signal, and //idler are the index of refraction at the pump, signal, and idler wavelengths, respectively, m is the order of the interaction, and A is the poling period.

Phase matching temperature sensitivity. An example for lithium niobate is shown in Figure 4A-Figure 4B.

Temperature sensitivity of the down conversion efficiency. SPDC efficiency for a 2- cm-long crystal is shown in Figure 15.

Temperature must be stabilized. Typical means for stabilizing the temperature include, but are not limited to, crystal clips, PPLN ovens, and temperature controllers, however the system typically consumes a power of many Watts.

New approach: Use two poling regions. A new approach using two poling regions is described herein, for example as shown in Figure 5B, where Ai is chosen to phase match at temperature T and A2 is shown to phase match at temperature T’. There have been previous studies on improving the spectral bandwidth of SPDC using multiple regions, but the authors are not aware of any attempt to improve temperature bandwidth.

Temperature tolerance using two poling regions. The temperature tolerance using two poling regions is shown in Figure 6 (poling periods were 18.990 pm and 8.956 pm, a 34 nm difference). Each region has half the length, and conversion efficiency scales at (length)².

Address manufacturing error using a temperature difference. Manufacturing error can be addressed using a temperature difference, as shown in Figure 7A-Figure 7B, where a 6.3 nm poling error in one region was compensated by a 1.9 °C temperature difference. These results indicate that it is not the absolute temperature that needs to be controlled, only the relative temperature of the two regions.

Sensitivity to change in pump wavelength and bandwidth. Figure 9 illustrates the sensitivity to change in pump wavelength and bandwidth. The single region system is very a narrow band, such that the laser needs to be stabilized to ~0.1 nm. Volume holographic grating stabilization can be used. Figure 9 also shows that using two poling regions helps with the pump bandwidth.

Many regions. The concept was expanded to many poling regions, with results shown in Figure 11. The results indicate coherent interference between regions can improve efficiency. However, devices with many regions can be challenging to manufacture. A linear chirp in poling period can also work.

Conclusions. Spontaneous parametric down conversion generates time-frequency entangled states, a key resource for high-dimensional information encoding in quantum communication systems. Nonlinear crystals used for down conversion are temperature sensitive. Typical approach is a bulky and power-hungry heater. A temperature-insensitive device was realized using two or more poling regions. The most temperature sensitive device might be the laser (if pumping with a diode laser).

EXEMPLARY ASPECTS

In view of the described compositions and methods, herein below are described certain more particularly described aspects of the inventions. The particularly recited aspects should not, however, be interpreted to have any limiting effect on any different claims containing different or more general teaching described herein or that the “particular” aspects are somehow limited in some way other than the inherent meanings of the language and formulas literally used therein.

Example 1 : A periodically poled waveguide comprising: a first poling region having a first poling period; and a second poling region having a second poling period; wherein the first poling period is phase matched at a first temperature and the second poling period is phase matched at a second temperature, the first poling period being different than the second poling period such that the first temperature is different than the second temperature.

Example 2: The periodically poled waveguide of any examples herein, particularly example 1, wherein the periodically poled waveguide comprises barium borate, barium titanate, bismuth germanate, cadmium zinc telluride, cesium lithium borate, gallium(II) selenide, lithium iodate, lithium niobate (LiNbCh), lithium tantalate, lithium triborate, Nd:YCOB (Nd-doped YCOB, Nd:YCa4O(BO3)3), potassium aluminum borate, potassium dideuterium phosphate, potassium niobate, potassium titanyl phosphate, tellurium dioxide, terbium gallium garnet, yttrium iron garnet, or a combination thereof.

Example 3 : The periodically poled waveguide of any examples herein, particularly example 1 or example 2, wherein the periodically poled waveguide comprises LiNbCh. Example 4: The periodically poled waveguide of any examples herein, particularly examples 1-3, wherein the periodically poled waveguide comprises LiNbCh doped with a dopant.

Example 5: The periodically poled waveguide of any examples herein, particularly examples 1-4, wherein the periodically poled waveguide consists essentially of LiNbCh.

Example 6: The periodically poled waveguide of any examples herein, particularly examples 1-5, wherein the periodically poled waveguide consists of LiNbCh.

Example 7: The periodically poled waveguide of any examples herein, particularly examples 1-6, wherein the periodically poled waveguide consists essentially of the first poling region and the second poling region.

Example 8: The periodically poled waveguide of any examples herein, particularly examples 1-7, wherein the periodically poled waveguide consists of the first poling region and the second poling region.

Example 9: The periodically poled waveguide of any examples herein, particularly example 8, wherein the periodically poled waveguide has a total length, the first poling region has a first length, and the second poling region has a second length, the first length and the second length combining to provide the total length.

Example 10: The periodically poled waveguide of any examples herein, particularly example 9, wherein the first length and the second length are the same.

Example 11 : The periodically poled waveguide of any examples herein, particularly example 9 or example 10, wherein the temperature bandwidth of the device is increased to 17°C relative to a temperature bandwidth of 5°C for similar device consisting of a single poling region.

Example 12: The periodically poled waveguide of any examples herein, particularly examples 1-6, wherein the periodically poled waveguide further comprises a third poling region having a third poling period, the third poling period being phase matched at a third temperature, the third poling period being different than both the first poling period and the second poling period, such that the third temperature is different than both the first temperature and the second temperature.

Example 13: The periodically poled waveguide of any examples herein, particularly example 12, wherein the periodically poled waveguide comprises one or more additional poling regions, each of the one or more additional poling regions having a poling period that is phase matched a temperature, wherein each of the poling periods is different than each other such that each phase matched temperature is different than each other. Example 14: The periodically poled waveguide of any examples herein, particularly example 12 or example 13, wherein the total number of poling regions in the periodically poled waveguide is 3 or more, 4 or more, 5 or more, 10 or more, 25 or more, 50 or more, or 100 or more.

Example 15: The periodically poled waveguide of any examples herein, particularly examples 1-14, wherein the periodically poled waveguide is monolithic.

Example 16: The periodically poled waveguide of any examples herein, particularly examples 1-14, wherein the periodically poled waveguide is not monolithic.

Example 17: The periodically poled waveguide of any examples herein, particularly example 16, wherein each of the poling regions comprises a separate crystal, each of the crystals being separated from a neighboring crystal by a gap, which together form the periodically poled waveguide.

Example 18: The periodically poled waveguide of any examples herein, particularly examples 1-17, the periodically poled waveguide is less temperature sensitive relative to a waveguide consisting of a single poling region.

Example 19: The periodically poled waveguide of any examples herein, particularly examples 1-18, wherein the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is increased relative to the temperature bandwidth of a waveguide consisting of a single poling region.

Example 20: The periodically poled waveguide of any examples herein, particularly examples 1-19, wherein the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is increased by a factor of two or more (e.g., three or more) relative to the temperature bandwidth of a waveguide consisting of a single poling region.

Example 21 : The periodically poled waveguide of any examples herein, particularly examples 1-20, wherein the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is 5°C or more, 10°C or more, 15°C or more, 35°C or more, 40°C or more, 50°C or more, 75°C or more, 100°C or more, 150°C or more, or 180°C or more.

Example 22: The periodically poled waveguide of any examples herein, particularly examples 1-21, wherein: the periodically poled waveguide has a temperature bandwidth; during use, the periodically poled waveguide is operated at an operation temperature; and the periodically poled waveguide is configured such that the operation temperature is within the temperature bandwidth of the periodically poled waveguide. Example 23: A device comprising the periodically poled waveguide of any examples herein, particularly examples 1-22.

Example 24: The device of any examples herein, particularly example 23, wherein the device further comprises a temperature controller.

Example 25: The device of any examples herein, particularly example 24, wherein the temperature controller is configured to stabilize the temperature differential between the first and second poling regions.

Example 26: The device of any examples herein, particularly example 24 or example 25, wherein the first poling region is a high-temperature region and the second poling region is a low-temperature region, and wherein the temperature controller is configured to stabilize the temperature of the high-temperature region relative to the low-temperature region.

Example 27: The device of any examples herein, particularly examples 23-26, wherein the device generates photon pairs via spontaneous parametric down conversion.

Example 28: The device of any examples herein, particularly example 27, wherein the photon pairs are entangled.

Example 29: The device of any examples herein, particularly examples 23-28, wherein the device generates entangled photon pairs via spontaneous parametric down conversion.

Example 30: The device of any examples herein, particularly examples 23-29, wherein the device generates a plurality of photons (e.g., two or more, three or more, or four or more) via spontaneous parametric down conversion.

Example 31 : The device of any examples herein, particularly examples 23-30, wherein the device is a quantum information device.

Example 32: The device of any examples herein, particularly examples 23-31, wherein the device comprises a drone, a satellite, or a combination thereof.

Example 33: The device of any examples herein, particularly examples 23-32, wherein the device is configured for a terrestrial application.

Example 34: The device of any examples herein, particularly examples 23-33, wherein the device is configured for an extra-terrestrial application.

Example 35: A method of use of the periodically poled waveguide of any examples herein, particularly examples 1-22.

Example 36: The method of any examples herein, particularly example 35, wherein the method comprises using the periodically poled waveguide in the device of any examples herein, particularly examples 23-34. Example 37: A method of use of the device of any examples herein, particularly examples 23-34.

Example 38: The method of any examples herein, particularly examples 35-37, wherein the method comprises using the periodically poled waveguide or device to generate photon pairs via spontaneous parametric down conversion.

Example 39: The method of any examples herein, particularly example 38, wherein the photon pairs are entangled.

Example 40: The method of any examples herein, particularly examples 35-39, wherein the method comprises using the periodically poled waveguide or device to generate entangled photon pairs via spontaneous parametric down conversion.

Example 41 : The method of any examples herein, particularly examples 35-40, wherein the method comprises using the periodically poled waveguide or device to generate a plurality of photons (e.g., two or more, three or more, or four or more) via spontaneous parametric down conversion.

Example 42: The method of any examples herein, particularly examples 35-41, wherein the method comprises using the periodically poled waveguide or device in a quantum information application.

Example 43: The method of any examples herein, particularly examples 35-42, wherein the method comprises using the periodically poled waveguide or device in a drone, a satellite, or a combination thereof.

Example 44: The method of any examples herein, particularly examples 35-43, wherein the method comprises using the periodically poled waveguide or device in a terrestrial application.

Example 45: The method of any examples herein, particularly examples 35-44, wherein the method comprises using the periodically poled waveguide or device in an extra-terrestrial application.

Example 46: A method of making the periodically poled waveguide of any examples herein, particularly examples 1-22.

Example 47: A periodically-poled LiNbCh waveguide comprising: a first poling region; and a second poling region, wherein a poling period of the first poling region or the second poling region is phase matched at two different temperatures.

Example 48: The waveguide of any examples herein, particularly example 47, wherein a respective poling period of each of the first poling region and the second poling region is phase matched at two different temperatures. Example 49: The waveguide of any examples herein, particularly example 47, wherein a temperature bandwidth is increased from about 5 °C to about 17 °C.

Example 50: The waveguide of any examples herein, particularly example 47, wherein the first poling region is a high-temperature region and the second poling region is a low- temperature region.

Example 51 : The waveguide of any examples herein, particularly example 50, wherein only the first poling region is stabilized.

Example 52: The waveguide of any examples herein, particularly example 50, wherein a differential heating method is used for the waveguide.

Example 53: A waveguide and method as described herein.

Other advantages which are obvious and which are inherent to the invention will be evident to one skilled in the art. It will be understood that certain features and sub-combinations are of utility and may be employed without reference to other features and sub-combinations. This is contemplated by and is within the scope of the claims. Since many possible embodiments may be made of the invention without departing from the scope thereof, it is to be understood that all matter herein set forth or shown in the accompanying drawings is to be interpreted as illustrative and not in a limiting sense.

The methods of the appended claims are not limited in scope by the specific methods described herein, which are intended as illustrations of a few aspects of the claims and any methods that are functionally equivalent are intended to fall within the scope of the claims. Various modifications of the methods in addition to those shown and described herein are intended to fall within the scope of the appended claims. Further, while only certain representative method steps disclosed herein are specifically described, other combinations of the method steps also are intended to fall within the scope of the appended claims, even if not specifically recited. Thus, a combination of steps, elements, components, or constituents may be explicitly mentioned herein or less, however, other combinations of steps, elements, components, and constituents are included, even though not explicitly stated.

Claims

CLAIMS What is claimed is:

1. A periodically poled waveguide comprising: a first poling region having a first poling period; and a second poling region having a second poling period; wherein the first poling period is phase matched at a first temperature and the second poling period is phase matched at a second temperature, the first poling period being different than the second poling period such that the first temperature is different than the second temperature.

2. The periodically poled waveguide of claim 1, wherein the periodically poled waveguide comprises barium borate, barium titanate, bismuth germanate, cadmium zinc telluride, cesium lithium borate, gallium(II) selenide, lithium iodate, lithium niobate (LiNbCh), lithium tantalate, lithium triborate, Nd:YCOB (Nd-doped YCOB, Nd:YCa4O(BO3)3), potassium aluminum borate, potassium dideuterium phosphate, potassium niobate, potassium titanyl phosphate, tellurium dioxide, terbium gallium garnet, yttrium iron garnet, or a combination thereof.

3. The periodically poled waveguide of claim 1 or claim 2, wherein the periodically poled waveguide comprises LiNbCh.

4. The periodically poled waveguide of any one of claims 1-3, wherein the periodically poled waveguide comprises LiNbCh doped with a dopant.

5. The periodically poled waveguide of any one of claims 1-4, wherein the periodically poled waveguide consists essentially of LiNbCb.

6. The periodically poled waveguide of any one of claims 1-5, wherein the periodically poled waveguide consists of LiNbCb.

7. The periodically poled waveguide of any one of claims 1-6, wherein the periodically poled waveguide consists essentially of the first poling region and the second poling region.

8. The periodically poled waveguide of any one of claims 1-7, wherein the periodically poled waveguide consists of the first poling region and the second poling region.

9. The periodically poled waveguide of claim 8, wherein the periodically poled waveguide has a total length, the first poling region has a first length, and the second poling region has a second length, the first length and the second length combining to provide the total length.

10. The periodically poled waveguide of claim 9, wherein the first length and the second length are the same.

11. The periodically poled waveguide of claim 9 or claim 10, wherein the temperature bandwidth of the device is increased to 17°C relative to a temperature bandwidth of 5°C for similar device consisting of a single poling region.

12. The periodically poled waveguide of any one of claims 1-6, wherein the periodically poled waveguide further comprises a third poling region having a third poling period, the third poling period being phase matched at a third temperature, the third poling period being different than both the first poling period and the second poling period, such that the third temperature is different than both the first temperature and the second temperature.

13. The periodically poled waveguide of claim 12, wherein the periodically poled waveguide comprises one or more additional poling regions, each of the one or more additional poling regions having a poling period that is phase matched a temperature, wherein each of the poling periods is different than each other such that each phase matched temperature is different than each other.

14. The periodically poled waveguide of claim 12 or claim 13, wherein the total number of poling regions in the periodically poled waveguide is 3 or more, 4 or more, 5 or more, 10 or more, 25 or more, 50 or more, or 100 or more.

15. The periodically poled waveguide of any one of claims 1-14, wherein the periodically poled waveguide is monolithic.

16. The periodically poled waveguide of any one of claims 1-14, wherein the periodically poled waveguide is not monolithic.

17. The periodically poled waveguide of claim 16, wherein each of the poling regions comprises a separate crystal, each of the crystals being separated from a neighboring crystal by a gap, which together form the periodically poled waveguide.

18. The periodically poled waveguide of any one of claims 1-17, the periodically poled waveguide is less temperature sensitive relative to a waveguide consisting of a single poling region.

19. The periodically poled waveguide of any one of claims 1-18, wherein the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is increased relative to the temperature bandwidth of a waveguide consisting of a single poling region.

20. The periodically poled waveguide of any one of claims 1-19, wherein the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is increased by a factor of two or more (e.g., three or more) relative to the temperature bandwidth of a waveguide consisting of a single poling region.

21. The periodically poled waveguide of any one of claims 1-20, wherein the periodically poled waveguide has a temperature bandwidth, and the temperature bandwidth of the periodically poled waveguide is 5°C or more, 10°C or more, 15°C or more, 35°C or more, 40°C or more, 50°C or more, 75°C or more, 100°C or more, 150°C or more, or 180°C or more.

22. The periodically poled waveguide of any one of claims 1-21, wherein: the periodically poled waveguide has a temperature bandwidth, during use, the periodically poled waveguide is operated at an operation temperature, and the periodically poled waveguide is configured such that the operation temperature is within the temperature bandwidth of the periodically poled waveguide.

23. A device comprising the periodically poled waveguide of any one of claims 1-22.

24. The device of claim 23, wherein the device further comprises a temperature controller.

25. The device of claim 24, wherein the temperature controller is configured to stabilize the temperature differential between the first and second poling regions.

26. The device of claim 24 or claim 25, wherein the first poling region is a high-temperature region and the second poling region is a low-temperature region, and wherein the temperature controller is configured to stabilize the temperature of the high-temperature region relative to the low-temperature region.

27. The device of any one of claims 23-26, wherein the device generates photon pairs via spontaneous parametric down conversion.

28. The device of claim 27, wherein the photon pairs are entangled.

29. The device of any one of claims 23-28, wherein the device generates entangled photon pairs via spontaneous parametric down conversion.

30. The device of any one of claims 23-29, wherein the device generates a plurality of photons (e.g., two or more, three or more, or four or more) via spontaneous parametric down conversion.

31. The device of any one of claims 23-30, wherein the device is a quantum information device.

32. The device of any one of claims 23-31, wherein the device comprises a drone, a satellite, or a combination thereof.

33. The device of any one of claims 23-32, wherein the device is configured for a terrestrial application.

34. The device of any one of claims 23-33, wherein the device is configured for an extraterrestrial application.

35. A method of use of the periodically poled waveguide of any one of claims 1-22.

36. The method of claim 35, wherein the method comprises using the periodically poled waveguide in the device of any one of claims 23-34.

37. A method of use of the device of any one of claims 23-34.

38. The method of any one of claims 35-37, wherein the method comprises using the periodically poled waveguide or device to generate photon pairs via spontaneous parametric down conversion.

39. The method of claim 38, wherein the photon pairs are entangled.

40. The method of any one of claims 35-39, wherein the method comprises using the periodically poled waveguide or device to generate entangled photon pairs via spontaneous parametric down conversion.

41. The method of any one of claims 35-40, wherein the method comprises using the periodically poled waveguide or device to generate a plurality of photons (e.g., two or more, three or more, or four or more) via spontaneous parametric down conversion.

42. The method of any one of claims 35-41, wherein the method comprises using the periodically poled waveguide or device in a quantum information application.

43. The method of any one of claims 35-42, wherein the method comprises using the periodically poled waveguide or device in a drone, a satellite, or a combination thereof.

44. The method of any one of claims 35-43, wherein the method comprises using the periodically poled waveguide or device in a terrestrial application.

45. The method of any one of claims 35-44, wherein the method comprises using the periodically poled waveguide or device in an extra-terrestrial application.

46. A method of making the periodically poled waveguide of any one of claims 1-22.

47. A periodically-poled LiNbCh waveguide comprising: a first poling region; and a second poling region, wherein a poling period of the first poling region or the second poling region is phase matched at two different temperatures.

48. The waveguide of claim 47, wherein a respective poling period of each of the first poling region and the second poling region is phase matched at two different temperatures.

49. The waveguide of claim 47, wherein a temperature bandwidth is increased from about 5 °C to about 17 °C.

50. The waveguide of claim 47, wherein the first poling region is a high-temperature region and the second poling region is a low-temperature region.

51. The waveguide of claim 50, wherein only the first poling region is stabilized.

52. The waveguide of claim 50, wherein a differential heating method is used for the waveguide.

53. A waveguide and method as described herein.