WO2025064088A2 - Regenerative amplifier with optical fiber - Google Patents

Abstract

A regenerative amplifier includes a plurality of reflective elements, a doped optical fiber, and an optical switch. The plurality of reflective elements form an optical cavity having a plurality of optical-cavity modes. The doped optical fiber is located within the optical cavity and has a plurality of waveguide modes. The optical switch is located within the optical cavity and is controllable between first and second states. In the first state, the optical switch transmits light exiting the doped optical fiber such that the light resonates within the optical cavity. In the second state, the optical switch one or both of (i) couples a seed pulse into the optical cavity and (ii) couples an amplified pulse out of the optical cavity An optical-cavity mode, of the plurality of optical-cavity modes, having the lowest loss and highest gain includes a mode of the plurality of waveguide modes.

Description

REGENERATIVE AMPLIFIER WITH OPTICAL FIBER

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63/532,536, filed on 14 August 2023, the disclosure of which is incorporated herein by reference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under grant number ECCS-1912742 awarded by the National Science Foundation, grant number N00014-20- 1-2789 awarded by the Office of Naval Research, and grant numbers R01EB033179 and U01NS128660 awarded by the National Institutes of Health. The government has certain rights in the invention.

BACKGROUND

[0003] Ultrafast lasers are increasingly in-demand for applications across industry, science, and healthcare. The number of relevant applications, use-cases, and the ultimate impact of an ultrafast laser technology scales directly with the performance (high pulse energy, short duration) and practicality (cost, size) of the laser. Fiber lasers are well-known to have practical advantages over the traditional solid-state laser architecture, but it remains difficult to design ultrafast fiber lasers that reach the performance of solid-state lasers. This is due to the large optical nonlinear effects that occur in fibers, owing to small transverse mode areas and long propagation lengths. Fundamentally, improving fiber laser performance requires either using fibers with larger and larger modes and/or designing pulse evolutions that are resilient to nonlinear effects.

SUMMARY OF THE EMBODIMENTS

[0004] In a first aspect, a regenerative amplifier is disclosed. The regenerative amplifier includes a plurality of reflective elements, a doped optical fiber, and an optical switch. The plurality of reflective elements form an optical cavity having a plurality of optical-cavity modes. The doped optical fiber is located within the optical cavity and has a plurality of waveguide modes. The optical switch is located within the optical cavity and is controllable between first and second states. In the first state, the optical switch transmits light exiting the doped optical fiber such that the light resonates within the optical cavity. In the second state, the optical switch one or both of (i) couples a seed pulse into the optical cavity and (ii) couples an amplified pulse out of the optical cavity. An optical-cavity mode, of the plurality of optical-cavity modes, having the lowest loss and highest gain includes a mode of the plurality of waveguide modes.

[0005] In a second aspect, a method for regenerative amplification is disclosed. The method includes controlling an optical switch to couple a seed pulse into an optical cavity that includes a doped optical fiber. The method also includes pumping the doped optical fiber with pump light such that the seed pulse is amplified into an amplified pulse within the fundamental mode of a plurality of waveguide modes of the doped optical fiber. The method also includes controlling the optical switch to couple the amplified pulse out of the optical cavity.

BRIEF DESCRIPTION OF THE FIGURES

[0006] FIG. 1 is a functional block diagram of a regenerative amplifier, in an embodiment.

[0007] FIG. 2 is a flowchart illustrating an embodiment of a regenerative amplification method.

[0008] FIG. 3 depicts spectra resulting from double-pass amplification generated by an embodiment of the regenerative amplifier of FIG. 1.

[0009] FIG. 4 shows an amplified pulse spectrum from the embodiment of the regenerative amplifier of FIG. 3.

[0010] FIG. 5 shows schematics demonstrating the capability of embodiments of the regenerative fiber amplifier of FIG. 1 to realize pulse evolutions that are not available in typical amplifiers or oscillators.

[0011] FIG. 6 illustrates dissipative solitons from an embodiment of the regenerative amplifiers of FIG. 1.

[0012] FIG. 7 demonstrates the action of an embodiment of the regenerative amplifier of FIG. 1 that includes an intracavity dispersive pulse stretcher.

[0013] FIG. 8. shows a spectrum and pulse produced by self-similar regenerative amplification, extended by inclusion of added dispersion. [0014] FIG. 9 illustrates runaway nonlinear evolution in a simulation of an embodiment of the amplifier FIG. 1 with no added dispersion.

[0015] FIG. 10 shows simulation results of a stable, high-energy (> 10 pj) selfsimilar pulse evolution in an embodiment of the amplifier of FIG. 1.

[0016] FIG. 11 is a schematic of an embodiment of the amplifier of FIG. 1 designed to operate multimode fiber in the fundamental fiber mode.

[0017] FIG. 12 illustrates mode profiles of output beams from embodiments of the amplifier of FIG 1. Different panels show results for different numbers of round trips.

[0018] FIG. 13. shows fundamental mode content as a function of round trips in an optical cavity of an embodiment of the amplifier of FIG. 1.

[0019] FIG. 14 shows measurement of beam quality factor of a single-mode beam generated by embodiment of the amplifier of FIG. 1 where the doped optical fiber is a multimode fiber.

[0020] FIG. 15 includes a plots of a simulated optical fiber mode and an experimentally-measured beam profile from an embodiment of the regenerative amplifier of FIG. 1.

[0021] FIG. 16 is a schematic of a regenerative amplifier, which is an example of the regenerative amplifier of FIG. 1.

[0022] FIG. 17 includes a spectrum, a mode plot, and a temporal profile of an amplified pulse output by an embodiment of the regenerative amplifier of FIG. 1.

[0023] FIG. 18 is functional block diagram of a regenerative amplifier, which an example of the regenerative amplifier of FIG. 1.

[0024] FIG. 19 is a functional block diagrams of optical cavities, which are examples of the optical cavity of the regenerative amplifier of FIG. 18.

[0025] FIG. 20 is a plot illustrating pulse buildup within an embodiment of the regenerative amplifier of FIG. 1.

[0026] FIG. 21 includes schematics of regenerative amplifiers, each of which is an example of regenerative amplifier of FIG 1.

DETAILED DESCRIPTION OF THE EMBODIMENTS

[0027] Embodiments described herein- regenerative amplification in fiber (Tiber regens’) - enables scaling the performance of ultrafast fiber amplifier systems by orders of magnitude. Fiber regens enable both larger mode areas and resilient nonlinear evolutions. This will ultimately allow for fiber laser systems that compete with the performance of solid-state systems. The potential advantages of a fiber regen over a solid-state system are many: they will be easier and cheaper to construct and operate, be significantly more compact and reliable in operation, in addition to enabling new levels of performance. This technology can therefore have significant impact in realizing low-cost, reliable, high-performance ultrafast lasers for a wide variety of applications where solid-state systems are too bulky, unreliable, and costly.

[0028] A regen is a laser amplifier that includes a cavity, a gain medium, and some form of optical switch. This configuration allows a pulse to be input and output from the cavity, and the pulse can make many round trips through the gain medium in order to experience high levels of gain before being switched out of the cavity. In embodiments, the regenerative configuration is necessary to achieve large gain (above 30 dB) in solid- state gain media, since the single-pass gain of typical solid-state media is small (less than 1 dB). Regenerative amplification underlies the majority of the commercial, high- performance solid-state amplifier systems that occupy a major portion of the ultrafast laser market today.

[0029] One advantage of fiber over solid-state laser media is that the interaction length in fiber is long (meter-scale), so the single-pass gain of a fiber amplifier is comparatively quite high (20 dB). Additionally, the primary factor that limits fiber amplifier performance is the onset of nonlinear optical effects due to the tight confinement of the light in fiber over these long distances. Regenerative amplification enables much larger gain (much more than 30 dB), but with these gain levels a pulse in fiber typically becomes severely or catastrophically distorted and unusable. As a result, regenerative amplification in fiber has hardly been explored — it isn’t necessary or feasible.

[0030] High performance ultrafast pulses are useful for a wide range of applications, including but not limited to spectroscopy, microscopy, nonlinear microscopy, machining and material processing, surgery, high-field physics, materials research, and medicine. Embodiments of regenerative amplifiers disclosed herein potentially have significant impact in these areas, and enable applications where previous femtosecond sources are currently too costly and impractical. 1.1. Fiber chirped-pulse amplification

[0031] The highest-energy ultrafast fiber amplifier systems rely on chirped-pulse amplification (CPA). The idea of CPA is to stretch pulses to durations for which nonlinear phase accumulation in the amplifier is negligible - the system is linear. These systems typically rely on cascaded amplifiers with increasing mode areas in order to reach large pulse energies. Typically, a total gain around 60 dB is desired. Cascaded amplifiers are necessary to achieve large net gain (with 20 dB gain-per-stage), and the mode area (fiber core diameter) of each stage must be increased in order to limit nonlinear effects as the pulse energy increases in each stage. The highest-performance systems typically culminate in the largest quasi-fiber amplifiers available- ‘rod-type’ photonic crystal fibers — which are expensive, non-flexible waveguide amplifiers with large dimensions (meter scale). Notably, these rod-type fiber amplifiers cannot be integrated with fiberized components, such as fiber combiners for pumping. Thus, the use of a rod sacrifices some of the practical advantages of fiber.

[0032] The limitations of this technique are well-defined. Increasing the pulse energy without sacrificing pulse quality requires increasing the pulse stretching, increasing the mode areas, and typically accommodating additional amplification stages. Pulse stretching beyond several nanoseconds becomes impractical due to large footprints of dispersive components. Mode diameter scaling is limited by multimode content (even in photonic-crystal type fibers) to 50-75 pm. While microjoule-scale fiber CPA systems can be quite compact and suitable for common applications, the cost and complexity of higher-performance fiber CPA systems quickly becomes prohibitive. A high-performance (10s of pj) fiber CPA might have 2-5 pre-amplifier stages before such a rod-type final stage. Gain narrowing presents an additional complication. To generate pulses with durations below 400 fs, methods like spectral filtering are employed between each stage to flatten the gain’s spectral profile and avoid gain narrowing.

[0033] Millijoule pulse energies and gigawatt peak power can be achieved with fiber CPA systems that work at the limits of pulse stretching and mode area, and to go beyond that, coherent combination of multiple amplifiers is used. This technique requires very sophisticated laser design, and these systems are much larger, more complex, costly, and sensitive than typical fiber amplifiers. In many cases sophisticated stabilization electronics are necessary. This technique has resulted in the highest- performance fiber amplifier systems, but is not suitable for practical applications. 1.2. Nonlinear Fiber Amplifiers

[0034] Another category of high-performance ultrafast fiber amplifier accommodates highly nonlinear pulse evolutions. Such amplifiers generally have much lower energy than CPA systems, but can have considerable practical and performance advantages. These systems are more difficult to design than fiber CPA systems, but they are typically much simpler to construct. Nonlinear fiber amplifiers typically do not require extensive dispersion compensation, saving costand complexity. Additionally, nonlinear fiber amplifiers usually generate pulses with shorter durations than those from fiber CPA systems owing to nonlinear spectral broadening effects. Examples include self-similar amplifiers, and the best-in-class gain-managed evolution.

[0035] Scaling the performance of nonlinear fiber amplifiers is more complex than scaling CPA performance. While nonlinear amplifiers also see performance improvements with larger mode areas, the limits of a nonlinear amplifiers are generally not well-established. These limits can depend on the particular pulse evolution being employed, and are generally more tightly linked to the parameters of the fiber itself and the seed pulse undergoing amplification, compared to CPA. This can make energy scaling (by means other than increasing mode area) quite difficult.

[0036] For example, it is known that the dispersion parameter of a fiber determines the pulse energy of the self-similar evolution. However, this parameter is a fixed value for common fiber. Increasing the dispersion would require either highly- specialized fiber design or a chain of many fiber amplifiers separated by dispersive elements, which is impractical. As another example, it is known that repeated spectral- filtering of a nonlinearly-evolving pulse can result in stable, high-quality pulses known as dissipative solitons. This nonlinear evolution underlies many mode-locked fiber oscillators, and is in principle scalable to very high energies under amplification. However, this evolution has not been realized in an amplifier, since it too would require either a continuous piece of highly-specialized fiber (with built-in spectral filtering), or a chain of many fiber amplifiers separated by spectral filters. Scaling nonlinear amplification in fiber could in principle enable low-cost sources with excellent performance, but the existing platforms and fibers are prohibitive to this end. 1.3. Multimode Fiber Amplifiers

[0037] Fiber amplifier performance scales with mode area, but as the transverse dimensions of a fiber are increased, the fiber begins to accommodate multiple transverse modes. The use of highly-multimode fibers with very large mode areas is an active field of research. Although multimode fiber in principle enables much higher energy than single mode fiber, no performance improvements have been demonstrated using multimode fiber in amplifiers so far. This is due to several difficult problems facing their use:

[0038] Multimode propagation distorts the temporal and spatial profiles of an ultrafast pulse, leading to low-quality pulses and beams. Efforts have been made to control this propagation using either nonlinear effects or adaptive optics and wavefront shaping. However, these techniques have not resulted in performance improvements: multimode fiber amplifiers are still not capable of generating beams/pulses that are near-diffraction-limited (high spatial quality) and near-transform-limited (high temporal quality).

[0039] The laser physics of multimode fiber is more complex than that of singlemode fiber. The gain of any fiber amplifier is limited by spontaneous emission, which becomes trapped in the fiber waveguide and decreases the population inversion available for the signal (signal gain) and the output signal-noise contrast. In multimode fibers, this amplified spontaneous emission (ASE) problem becomes acute owing to the multiple guided modes, which trap spontaneous emission more effectively than singlemode fibers. Overcoming the ASE problem typically requires increasing the average power of operation, in many cases to the 100-1000 W regime. While high-average- power operation is a key benefit of fiber amplifiers, this parameter regime is highly restrictive and can be difficult to reach with ultrafast lasers. Even if the aforementioned multimode propagation problem were solved, operating multimode fiber amplifiers with femtosecond pulses with reasonable (1-10 W) average powers would become difficult due to the ASE problem.

[0040] Due to these issues, multimode fiber is generally restricted to amplification of high-average power, nanosecond-scale sources with very highly multimode (low- quality) output beams. Using multimode fiber to amplify ultrafast pulses with high- quality beams will require new techniques that address not only the multimode propagation problem (pulse distortion), but also the ASE and gain problem. 2. Distinctive Features of the Embodiments

[0041] Regenerative amplification in fiber addresses many of the issues discussed in section 1. These features include higher gain, scaling of amplifier evolutions, and single mode operation of multimode optical fiber, as discussed in sections 2.1, 2.2, and 2.3, respectively.

[0042] A regenerative amplifier, or “regen,” is a laser amplifier that has a cavity, a gain medium inside the cavity, and some form of optical switch. This configuration allows a pulse to be coupled into and out of the cavity. Within the cavity, the pulse makes many round trips through the gain medium to experience high levels of gain before being switched out of the cavity. The regenerative configuration is used to achieve large gain (e.g., typically above 30 dB) in solid-state gain media since the singlepass gain of a typical mm-scale solid-state media is small (e.g., less than 1 dB).

[0043] FIG. 1 is a functional block diagram of a regenerative fiber amplifier 100, in accordance with the present embodiments. Regenerative fiber amplifier 100 includes a plurality of reflective elements 102 forming an optical cavity 140 having a cavity axis 142 that defines a longitudinal direction.

[0044] Examples of a reflective element 102 include a planar mirror, a curved mirror, and a fiber Bragg grating. In embodiments, one of reflective elements 102 is a fiber Bragg grating that has a first grating facet directly affixed to a facet 134 of doped optical fiber 144. Regenerative fiber amplifier 100 may include a passive optical fiber that couples pump light 121 into the fiber Bragg grating, e.g., at a second grating facet opposite the first grating facet. The fiber Bragg grating transmits pump light 121 into doped optical fiber 144.

[0045] In FIG. 1, this longitudinal direction is taken to be parallel to the z axis of a right-handed coordinate system 198, thereby establishing the x and y axes as the two transverse directions. Regenerative fiber amplifier 100 also includes a doped optical fiber 144 and an optical switch 110, both of which are located inside optical cavity 140. In embodiments, doped optical fiber 144 supports a plurality of waveguide modes, including a mode 144M denoted in FIG. 1. Mode 144M may be the fundamental mode of doped optical fiber 144. Regenerative fiber amplifier 100 may further include, within optical cavity 140, at least one of a spectrally-selective optical element, a temporally- dispersive optical element, and a saturable absorber. [0046] Regenerative fiber amplifier 100 receives a seed pulse 122 that is coupled into optical cavity 140 via optical switch 110. Inside optical cavity 140, seed pulse 122 is amplified into an intracavity pulse 124 as it propagates back-and-forth through doped optical fiber 144. After several passes, intracavity pulse 124 is coupled out of the cavity, via optical switch 110, as an amplified pulse 126. Seed pulse 122 may be a femtosecond pulse, e.g., a pulse with a duration between 1 fs and 1,000 fs including any value therewithin or any subranges therebetween. Pulse 122 may have a duration that does not exceed one or more of 500 fs, 400 fs, 300 fs, or 200 fs. In other embodiments, seed pulse 122 may have a longer duration, e.g. 1 ps to 1,000 ps.

[0047] Doped optical fiber 144 may be a single-mode optical fiber or a multimode fiber, and may be a photonic crystal optical fiber or a micro-structured fiber, or a combination thereof. Doped optical fiber 144 may be rare-earth-doped fiber, where the dopant may include one or more of ytterbium, erbium, neodymium, praseodymium, thulium, and holmium. Doped optical fiber 144 may be double-clad or triple-clad, and may be large-mode-area optical fiber, an extra-large-mode-area optical fiber, or a combination thereof. The core diameter of doped optical fiber 144 may be greater than or equal to 25 micrometers.

[0048] When doped optical fiber 144 is a multimode optical fiber, it has a core diameter large enough to support a plurality of transverse waveguide modes. Each transverse mode defines an intensity pattern in the two transverse directions. One of these transverse waveguide modes is a fundamental waveguide mode, whose intensity pattern is given by a two-dimensional Gaussian profile. Optical cavity 140 supports a plurality of cavity modes, each of which has a transverse component and a longitudinal component. Each cavity mode resonates within optical cavity 140. The longitudinal component creates a standing wave within optical cavity 140. For clarity, FIG. 1 shows one cavity mode 128 as a transverse intensity envelope. In embodiments, the optical- cavity mode, of the plurality of optical-cavity modes of optical cavity 140, that has the lowest loss and highest gain, is or includes the fundamental mode of the plurality of waveguide modes of doped optical fiber 144.

[0049] One aspect of the present embodiments is the realization that one of the cavity modes has both the highest gain and the lowest loss among all of the cavity modes. This “optimal” cavity mode has a transverse component that equals the fundamental waveguide mode. Specifically, all cavity modes whose transverse component is a higher-order waveguide mode will have lower gain and/or higher loss than the optimal cavity mode. As result, amplification of seed pulse 122 preferentially occurs in the fundamental waveguide mode, even when seed pulse 122 has higher- order transverse modes excited. As intracavity pulse 124 passes through doped optical fiber 144, the transverse mode gets amplified while higher-order transverse modes become relatively attenuated. The result is that amplified pulse 126 has a transverse profile that may be substantially more Gaussian, or “cleaner,” than that of seed pulse 122. This ability to clean the transverse mode of intracavity pulse 124 as it is regeneratively amplified is referred to herein as “mode-cleaning regenerative amplification.”

[0050] Doped optical fiber 144 provides gain when it is pumped with pump light 121. Regenerative fiber amplifier 100 may include pump laser 105 that emits pump light 121. As shown in FIG. 1, pump light 121 may be coupled into optical cavity 140 via transmission through one of reflective elements 102. Similarly, residual pump light 129 that is unabsorbed by doped optical fiber 144 may be coupled out of optical cavity 140 via transmission another one of reflective elements 102. Thus, it should be understood that while optical cavity 140 forms cavity modes for wavelengths that lie within the bandwidth of seed pulse 122, optical cavity 140 need not form a cavity at the wavelength of the residual pump light 129.

[0051] As an alternative to coupling pump light 121 and residual pump light 129 through reflective elements 102, intracavity dichroic mirrors may be used to couple pump light 121 into optical cavity 140 and couple the residual pump light 129 out of the optical cavity (e.g., see dichroic mirrors 1142 and 1182 of amplifier 1100, FIG. 11).

[0052] Optical switch 110 is shown in FIG. 1 four ports labeled A, B, C, and D. Ports A and C couple into to optical cavity 140 while ports B and D couple out of optical cavity 140. Optical switch 110 may be controlled (e.g., via an electrical signal) to switch between a transmissive state and a reflective state. In the transmissive state, optical switch 110 transmits light coupled into all of the four ports, i.e., light entering port C may be transmitted to port A (and vice versa) and light entering port B may be transmitted to port D (and vice versa). In the reflective state, optical switch 110 reflects light coupled into all four of the ports, i.e., light entering port B may be reflected to port C (and vice versa) and light entering port A may be reflected to port D (and vice versa). [0053] Optical switch 110 may be controlled to be in the reflective state as seed pulse 122 approaches optical switch 110. After optical switch 110 has fully reflected seed pulse 122, and therefore seed pulse 122 has fully exited port C, the optical switch 110 is controlled to transition into the transmissive state before the seed pulse reflects off of reflective element 102(1) and reaches port C. Optical switch 110 may be held in the transmissive state for a fixed number of round-trip passes through optical cavity 140 (e.g., 4, 10, 30, 300, etc.). After the fixed number of round-trip passes, optical switch 110 may be controlled again to transition back into the reflective state. Optical switch 110 is then held in the reflective state until optical switch 110 has fully reflected intracavity pulse 124 and intracavity pulse 124 has fully exited port D as amplified pulse 126. At this point, the process may be started again to amplify a new seed pulse 122.

[0054] For this optical switching to work without clipping seed pulse 122, the distance 112 between port C and reflective element 102(1) may be large enough that the propagation time T of seed pulse 122 from port C to reflective element 102(1) and back to port C is greater than the temporal duration, or width, of the seed pulse 122. In embodiments, optical cavity 140 has a length such that a temporal duration of seed pulse 122 is less than one-half of a round-trip propagation time of seed pulse 122 through optical cavity 140 .

[0055] Optical switch 110 may include an acousto-optic or electro-optic modulator (or both), along with accompanying optics (e.g., polarization rotators, wave plates, polarizers, etc.) which perform the function of allowing an optical pulse to enter the cavity, keeping the cavity closed, or allowing an optical pulse to leave the cavity.

[0056] While FIG. 1 shows optical switch 110 being used for both coupling seed pulse 122 into optical cavity 140 and coupling amplified pulse 126 out of the optical cavity 140, two different optical switches 110 may be used for in-coupling and out- coupling.

[0057] FIG. 1 shows optical cavity 140 as a Fabry-Perot cavity formed from two reflective elements 102(1) and 102(2). In some of these embodiments, regenerative fiber amplifier 100 includes a first lens system 106 that images a facet 132 of the doped optical fiber 144 onto reflective element 102(1). Regenerative fiber amplifier 100 may further include a second lens system 108 that images facet 134 of the doped optical fiber 144 onto reflective element 102(2). In FIG. 1, each of the first lens system 106 and second lens system 108 is shown as a 4f lens system. However, one or both of the first lens system 106 and second lens system 108 may be configured differently without departing from the scope hereof. In other embodiments, optical cavity 140 is alternatively a ring cavity formed from three or more reflective elements 102.

[0058] Section 2.2 describes additional embodiments that are based on the idea that an optical fiber with specified properties may not be commercially available, yet may be implemented using “standard” commercially available optical fiber combined with one or more free-space or fiber-optic components. The standard optical fiber may be single-mode or multi-mode. Accordingly, some of the present embodiments are regenerative amplifiers that use single-mode optical fibers instead of multi-mode optical fibers. The standard optical fiber may also be a “passive” optical fiber (i.e., undoped). Accordingly, some of the present embodiments include a combination of one or more doped optical fibers and one or more passive optical fibers.

[0059] In some aspects, the present embodiments (including regenerative fiber amplifier 100 of FIG. 1) and disclosed concepts may be implemented in various systems, digital electronic circuitry, or in computer software, firmware, or hardware, including the structures disclosed in this specification and their structural equivalents, or in combinations of one or more of them. Such digital circuitry and/or computer software /hard ware may be used to control regenerative fiber amplifier 100. For example, an analog driver (e.g., a high-voltage amplifier) may be used to control optical switch 110 for in-coupling and out-coupling. In other example, the digital circuitry and computer software /hardware is used to control the intensity of pump light 121.

[0060] The digital circuitry and/or computer software /hard ware may additionally or alternatively be used to measure or monitor operation of regenerative fiber amplifier 100. For example, a parasitic reflection may be recorded with a photodiode to monitor the power build-up of intracavity pulse 124 within optical cavity 140 (see section (c) of FIG. 11). Other parasitic reflections may be similarly recorded and used for monitoring regenerative fiber amplifier 100 and/or controlling regenerative fiber amplifier 100.

2.1. Higher Gain

[0061] Regenerative amplification in fiber enables higher gain than available in single or double-pass fiber amplifiers (typically ~ 20-30 dB). This is demonstrated explicitly in experiment, with supporting data shown in FIGs. 2 and 3. Regenerative amplification and regenerative feedback in fiber amplifiers enables higher gain than available in single- or double-pass fiber amplifiers in single- or multi-mode fiber. This higher gain may include, or by achieved by one or more of the following: a reduction in the ASE content of an amplified pulse for a given amount of gain in fiber, compared to single-pass amplification; amplification of low-average-power pulses in highly- multimode fiber, despite ASE trapping; and higher absolute gain (> 40 dB) than available in single- or double-pass fiber amplifiers (< 40 dB, typically ~ 20 dB).

[0062] FIG. 2 is a flowchart illustrating an embodiment of a regenerative amplification method 200. In embodiments, method 200 is implemented within one or more aspects of regenerative fiber amplifier 100. Method 200 includes at least one of steps 210, 220, and 230.

[0063] The following description of method 200 includes parenthetical numbers following terms used in a method step. The parenthetical number indicates that the element associated with the number in parenthesis is an example of the term. For example, the description of step 210 below recites “controlling the optical switch (110),” which means that optical switch 110 of FIG. 1 is an example of the optical switch introduced in step 210.

[0064] Step 210 includes controlling an optical switch (110) to couple a seed pulse (122) into the optical cavity (140) the includes a doped optical fiber (144). Step 220 includes pumping the doped optical fiber (144) with pump light (121) such that the seed pulse is amplified into an amplified pulse (126) within a mode (144M) of a plurality of waveguide modes of the doped optical fiber. The mode may be the fundamental mode of the doped optical fiber. Step 230 includes controlling the optical switch (110) to couple the amplified pulse (126) out of the optical cavity (140).

[0065] FIG. 3 depicts spectra resulting from double-pass amplification in highly multimode fiber at various repetition rates. Without regenerative amplification, signal- to-noise contrast of the amplified pulse degrades dramatically as the repetition rate (seed average power) is reduced from 50 MHz (5 mW) to 10 kHz (1 pW). In this experiment, the gain available for the highest repetition rate seed (50 MHz) is under 10 dB (for up to 50 W pump power), and the gain available for the lowest repetition rate seed is negligible.

[0066] For a single- or double-pass amplifier, the signal-noise contrast and amplification efficiency suffer as the seed average power is reduced. FIG. 3 shows this explicitly, where the signal-background contrast degrades as the repetition rate and average power of the seed pulse are reduced. This lack of gain is a consequence of ASE trapping in the fiber, which is especially problematic for highly-multimode fibers since the ASE trapping scales as the number of modes guided by the fiber.

[0067] This lack of available gain for low-average power sources can be solved by regenerative feedback. FIG. 4 shows an amplified pulse spectrum from the same amplifier used to generate the data in FIG. 3, but configured to support regenerative amplification with 12 total passes through the fiber (six round trips in this case). The spectrum of FIG. 4 results from high-gain (> 55 dB) amplification of a low repetitionrate (10 kHz), low-average-power (1 pW) seed pulse in highly-multimode fiber. Accounting for the loss in the input and output coupling, the actual gain is closer to 60 dB. The enormous gain shown here is enabled by regenerative feedback, in contrast to the negligible gain shown from the same seed pulse in double-pass configuration shown in FIG. 3. The signal-noise contrast is over 30 dB, compared to negligible gain in doublepass (FIG. 3.).

[0068] This demonstration shows explicitly that the regenerative configuration can enable efficient amplification of low average-power seed sources in very large-core multimode fiber, which is typically only used to amplify 10-100W scale seed pulses. The gain advantages of the regenerative configuration do not only benefit multimode fiber amplifiers, but can extract larger gain than single- or double-pass configuration for single-mode fibers as well.

2.2. Scaling of Amplifier Evolutions

[0069] The regenerative fiber amplifier is a platform with which to realize high- performance amplifier pulse evolutions. The regenerative fiber amplifier can realize pulse evolutions that are impossible to host in either single/double pass amplifiers, or in mode-locked oscillators.. Such evolutions include scaling of nonlinear and linear pulse evolutions via control over the pulse evolutions using intracavity optical elements. Examples include, but are not limited to scaling of dissipative-soliton-like pulse shaping, scaling of self-similar amplification, and implementing measures to counteract gainnarrowing

[0070] The ability to include optical elements within a regenerative amplifier cavity can allow control over a pulse evolution to an extent that is impossible in single- or double-pass amplifiers. This can be understood from several perspectives. A basic illustration of this concept is shown in FIG. 5.

[0071] FIG. 5 is shows schematics demonstrating the capability of regenerative fiber amplifier 100 to realize pulse evolutions that are not available in typical amplifiers or oscillators. Top row compares a hypothetical fiber with properties that may be desirable to host an advantageous nonlinear evolution (e.g., dissipative soliton or selfsimilar evolution). Such a fiber would enable excellent performance of a nonlinear pulse evolution, but is difficult or impossible to obtain in practice. The fiber may be approximated by using discretized elements within a regenerative amplifier cavity, by using a regular gain fiber, a dispersive element, and a spectral filter. The bottom row illustrates a similar principle from the perspective of a mode-locked oscillator platform. While mode-locked oscillators can in theory host pulse evolutions with excellent performance, in practice they are severely restricted. This is because at high energy levels, pulses within oscillators become unstable. This is not a problem with a regenerative amplifier, since the pulse may be removed from the cavity once it becomes unstable, and a new, low-energy pulse takes its place. The result is a high-performance laser that accesses regimes of operation that are not accessible to a mode-locked oscillator.

[0072] From one perspective, the components within the regenerative amplifier cavity may be designed to behave together like fibers that have custom optical properties. Such fibers are not commercially available, or are difficult or impossible to manufacture.

[0073] For example a fiber with large dispersion may be approximated by a standard fiber with the addition of a stretching element (or dispersive delay line) in a regenerative amplifier. This particular configuration extends the limits of the self similar evolution. FIG. 7 demonstrates the action of a regenerative amplifier cavity with an intracavity dispersive pulse stretcher. Despite the short length of fiber, the pulse duration increases by several picoseconds after each round trip, due to the increased stretching from the intracavity stretcher. In this way, the regenerative configuration allows the standard fiber to behave like fiber with arbitrarily large dispersion.

[0074] By including a stretcher within optical cavity 140, the effective fiber dispersion may be greatly increased. Measurements show temporal broadening with increasing number of round trips through the amplifier. The broadening is consistent with a fiber having a dispersion (1 ps²) that is 50-times that of typical fiber (0.02 ps²).

[0075] The output pulse from a similar dispersion-enhanced fiber regen cavity is shown in FIG. 8. In embodiments, optical cavity 140 has a small amount of intracavity dispersion as a result of including using pieces of high-density glass in order to extend the self-similar evolution to the pj regime, which is impossible with standard fiber in a single-pass configuration. FIG. 8 includes plots 810 and 820, which show results of spectrum and pulse measurements, respectively, of a self-similar regenerative amplifier which contains small dense-flint glass rods that increase the dispersion of optical cavity 140. The stable pulse energy (1,000 nJ) is therefore four times higher than single-pass self-similar amplifiers, which have fixed dispersion.

[0076] This scaling technique is also demonstrated by the numerical simulations shown in FIGs. 9 and 10. In FIG. 9, the output pulse (chirped, compressed, transformlimited, and spectrum) is of low quality resulting from runaway nonlinear effects, which greatly broaden the spectrum and distort its phase. Without added dispersion (compared to FIG. 10) the pulse is completely deteriorated and useless due to runaway spectral broadening and nonlinear effects.

[0077] In FIG. 10, we use the same amplifier but include a small SF11 (dense-flint) glass rod within cavity 140, which marginally increases the overall dispersion. The result is evolution within the self-similar (parabolic) regime, which results in highly- compressible pulses despite large nonlinear phase accumulation. FIG. 10 includes plots 1010, 1020, and 1030. Plot 1010 includes a chirped parabolic pulse 1011, which acquires nonlinear phase that does not distort or degrade the quality of the compressed pulse. The resulting compressed pulses are very close to transform-limited in duration. Plot 1020 depicts a compressed output pulse 1021 and transform limited pulse 1022. Plot 1030 shows an output pulse spectrum 1031 and a transform-limited spectrum 1032. Plots 1040, 1050, and 1060 show temporal, spectral, and energy evolution, respectively, with each round trip through the regenerative fiber amplifier (ten round trips through a ten-cm fiber).

[0078] The same technique can in principle scale the performance of a gainmanaged evolution in embodiments of amplifier 100. This evolution is closely linked to the self-similar pulse evolution, but is capable of generating pulses with durations below the small-signal gain bandwidth of ytterbium and other fiber gain media. [0079] From another viewpoint, the regenerative amplifier will enable energy scaling of pulse evolutions that are frequently used in mode-locked fiber oscillators. For example, it is known that the dissipative soliton evolution can theoretically obtain much higher energies (tens to hundreds of nJ) than what is typically available from such oscillators (~ 1-5 nJ). At high energies, the evolution becomes unstable, both due to the limits of typically-used saturable absorbers and because the pulse evolution can no longer become periodic. In a regenerative amplifier, these high-performance pulses may be obtained, and the entire pulse may be removed from the cavity before the instability destroys the pulse. The pulse is replaced with a new, low-energy seed pulse to re-start the evolution.

[0080] This is shown by example in FIG. 6, which shows that dissipative solitons from regenerative amplifiers achieve higher energies than those from mode-locked oscillators. FIG. 6 includes plots 610, 620, and 630. Plots 610 and 620 shows temporal and spectral pulse measurements, respectively, from a dissipative soliton generated with a regenerative fiber amplifier. Compared to plot 630, a spectrum of a dissipative soliton generated within a mode-locked laser cavity [6], the energy is nearly 10 times higher.

[0081] In plots 610 and 620, a 26 nJ, 90 fs dissipative soliton is generated experimentally using fiber with a 6-|im core diameter. Such fiber typically supports ~1- 5 nJ pulses in a mode-locked oscillator (shown in plot 630), but the regenerative amplifier permits scaling of this evolution because it is not subject to the periodic boundary conditions of mode-locking. Intracavity elements that are not typically implemented in oscillators also enable scaling of such evolutions, as previously discussed.

[0082] The previous examples (FIGs. 6, 7, and 8) show extension of the self-similar amplifier and dissipative soliton oscillator by use of dispersive and dissipative intracavity elements. Any number of dissipative, dispersive, and diffractive elements may be used in order to tailor and extend a particular pulse evolution beyond what is possible in single- or double-pass amplifiers. This capability is generally not available in solid-state regenerative amplifiers, since the single-pass gain in such amplifiers is too small (~1 dB) to tolerate intracavity components with significant amounts of loss. In a fiber regen, the gain-per-pass may be quite large (several dB or more), so tolerating losses from intracavity components is not difficult. Another method for scaling the

Y1 performance of a nonlinear regenerative amplifier is to include elements within the cavity with effective nonlinearities that cancel those acting within the fiber. This technique has been demonstrated in a solid-state regenerative amplifier, but the higher gain-per-pass would make this technique more feasible in a fiber regenerative amplifier.

[0083] Amplifier schemes without strong nonlinear optical effects can also benefit from the regenerative fiber amplifier platform together with intracavity components. For high-gain chirped-pulse-amplifier systems, gain narrowing limits the minimum amplified pulse duration. This may be effectively counteracted in a regenerative amplifier by including a dissipative element (spectral filter) that effectively flattens the gain profile, resulting in pulses that achieve durations near the transform-limit of the small-signal gain bandwidth. This technique has been demonstrated in solid-state regenerative amplifiers. In single-pass fiber amplifier chains, this technique is usually implemented by inclusion of one or several such gain-flattening filters in between amplifier stages. This has limited effectiveness, since the gain-per-stage is large and the strong filtering necessary greatly reduces the overall efficiency. In a regenerative fiber amplifier, this technique may be implemented more efficiently because the gain filtering can occur within each round trip, each of which has smaller gain.

2.3. Single mode operation of highly-multimode optical fiber

[0084] The regenerative amplifier platform enables single-mode operation of even highly-multimode optical fiber. When a multimode waveguide (like an optical fiber) is within an optical cavity- or when the waveguide forms an optical cavity- the modes of the optical cavity are linked to the modes of the waveguide. The interaction of the cavity optics with the waveguide modes present a meaningful degree of control with which to influence the spatial profile of the cavity output. This can enable single-mode operation of even a highly-multimode waveguide, and can enable other levels of control over the spatial profile (excited modes) of a multimode waveguide.

[0085] First, we demonstrate that for an optical cavity (regenerative amplifier) designed such that the cavity modes are identical to those of the intracavity waveguide, the lowest-loss and highest-gain cavity mode is identical to the fundamental waveguide mode. For this discussion we refer to the schematic shown in FIG. 11, section (a)), which shows a regenerative fiber amplifier made with large-core (100 pm) fiber that accommodates about 250 transverse modes in each polarization. The cavity is designed to image the fiber endfaces to the cavity end mirrors, and vice versa. As a result, the modes of the fiber are the same as the modes of the cavity.

[0086] The fundamental mode of the fiber is the lowest-loss and highest-gain cavity mode. This enables fundamental mode operation of the highly-multimode fiber, even when higher-order modes are excited by the input seed. The beam profiles in FIG. 12 demonstrate this behavior.

[0087] FIG. 11 is a schematic of a regenerative fiber amplifier 1100 designed to operate multimode fiber in the fundamental fiber mode. Amplifier 1100 is an example amplifier 100, and includes a switch-reflector unit 1180. Switch-reflector unit 1180 includes reflective elements 102, two polarizing beam splitters (PBS), a half-wave plate (HWP), a Faraday rotator (FR), a Pockels cell (PC), a quarter-wave plate (QWP), a dichroic mirror 1182, and doped optical fiber 1144. An incoming pulse train 1122 enters the cavity through an isolator comprised of the two polarizing beam splitters (PBS), the half-wave plate (HWP), and the Faraday rotator (FR). Input and output switching through the intracavity PBS is accomplished with the Pockels cell (PC) and the quarter-wave plate (QWP). Each pulse of pulse train 1122 is an example of seed pulse 122.

[0088] Optical fiber 1144 may be a Yb-doped multimode fiber. In a use scenario, optical fiber 1144 is pumped with pump light 1121 that is free-space-coupled into fiber 1144 via dichroic mirror 1182. Pump light 1121 is an example of pump light 121. The wavelength of pump light 1121 may be 976 nm. Amplifier 1100 may also include a dichroic mirror 1142. Dichroic mirrors 1142 and 1182 reflect amplified pulse 126 and transmit pump light 1121.

[0089] Two lenses on each side of the fiber form 4-f telescopes to image the fiber facets to the cavity mirrors, which image the fiber facets back to themselves. Lenses are omitted from the schematic for visual clarity. A spectral filter (SF) on one side of the amplifier prevents CW-lasing at long-wavelengths (A = 1055 nm) but does not filter the signal. This is necessary due to the limited bandwidth of the PBS used here, but should not be necessary for PBS with wider bandwidth.

[0090] FIG. 11 also includes plots 1120 and 1130. Plot 1120 includes a photodiode trace 1122 of the output pulse of amplifier 1100. An inset 1124 shows the same for a wider time window. Plot 1130 has a photodiode trace 1132 showing the pulse buildup, obtained from a parasitic reflection off the intracavity PBS. [0091] The discussions in section 2.2 shows how particular amplification schemes (dissipative soliton, self-similar, chirped pulse amplification) can benefit from dissipative (stretcher, either Offner-type, Martinez-type, or bulk material) and diffractive (spectral filter) control elements. For the highest-performance fiber regenerative amplifiers, large multimode fibers may be used, operated in the fundamental mode as demonstrated in section 2.3.

[0092] FIG. 12 shows mode profiles 1201, 1206, and 1215 of output beams from an embodiments of amplifier 100 where doped optical fiber is a multimode fiber. These mode profiles illustrate mode-cleaning regenerative amplification. Mode profiles 1201, 1206, and 1215 show the output profile of an embodiment of amplifier 100 after one, six, and fifteen round trips, respectively. For this experiment, the seed pulse is deliberately misaligned from the fundamental mode in order to excite higher-order modes. As demonstrated in FIG. 12, embodiments of regenerative fiber amplifier 100 enable fundamental-mode operation of even highly-multimode fiber.

[0093] The seed pulse is deliberately aligned off-axis to excite a few higher-order modes, generating the structured beam shown in mode profile 1201. After six round trips through the cavity the output beam profile is noticeably cleaner, and includes one main lobe off-center from the fiber core, shown in mode profile 1206. After fifteen round trips, the beam appears to be nearly pure fundamental mode, as shown in mode profile 1215. FIG. 12 shows one initial condition (or equivalently, one seed alignment), but similar behavior occurs for other initial conditions.

[0094] A simple simulation of this cavity corroborates this behavior, as shown in FIG. 13. FIG. 13 shows fundamental mode content as a function of round trips for a simulated cavity with the same initial conditions (equal excitation of the first ten transverse modes) and various types of cavity aberrations. FIG. 13 includes data curves 1300, 1305, 1315, and 1320, which corresponds to, respectively, a cavity with: no aberrations, 5 pm gaussian convolution blur, small defocusing (15 pm) of the fiber tip from the focal plane under the Fresnel approximation, and both defocusing and blur.

[0095] FIG. 13 shows that small unavoidable perturbations to a perfect imaging system tend to generate loss in higher-order modes and couple energy from higher- order modes into the fundamental mode. This results in fundamental mode operation of the regenerative amplifier, despite the multimode fiber accommodating many modes. [0096] The losses and couplings resulting from regenerative feedback are a consequence of small, unavoidable aberrations in the intracavity beam. While they are small in magnitude, they compound over many round trips and are sufficient to yield nearly 100% fundamental mode content. This is achieved without any explicit spatial filtering in the cavity. Simulations also indicate that the aberrations necessary to achieve this condition are not stringent, as similar behavior occurs for a wide variety of small, common aberrations acting alone or together.

[0097] Evidence of near-100% fundamental mode operation is shown in FIGs. 14 and 15. FIG. 14 shows measurements of beam qualify factor M² for the single-mode beam generated by a multimode fiber regenerative amplifier indicates excellent quality (M² * 1.4). Curves for M² = 1 and M² = 2 are shown for comparison.

[0098] The beam quality factor M² < 1.3, as shown in FIG. 14. An analysis by Yoda et. al. (/. Lightwave Technol. 24, 1350 (2006)) includes semi-analytic expressions for the beam quality of superpositions of modes from multimode step index fiber. This work shows that superpositions of the fundamental mode and other modes rapidly degrades the M² of the beam, indicating that the beam measured here is fundamental-mode- dominated.

[0099] FIG. 15 shows a numerically-generated beam profile 1510 of a fundamental mode of XLMA fiber and experimentally-measured beam profile 1520 from an embodiment of regenerative fiber amplifier 100. Beam profile 1520 is a near-field beam profile. White circles indicate core-cladding boundaries. The scaling in the experimental image is obtained by using the camera pixel dimensions and the magnification of the imaging system. Beam profile 1520 matches the dimensions of beam profile 1510, as both have a full-width at half-maximum diameter of approximately 71 pm.

[0100] Fundamental mode operation of large-core multimode fiber should enable laser performance well-beyond the limits of single-mode fibers. We demonstrate this by using the multimode fiber regenerative amplifier to amplify chirped pulses. The seed pulses are stretched with a chirped volume Bragg grating (VBG) to ~ 200 ps before being amplified. The same VBG is used to compress the pulses, and an additional standard grating compressor removes the uncompensated chirp from the oscillator and amplifier. A full schematic of this system is shown in FIG. 16.

[0101] FIG. 16 is a schematic of a regenerative fiber amplifier 1600, which is an example of regenerative fiber amplifier 100. Regenerative fiber amplifier 1600 includes an optical fiber 1644, which an example of doped optical fiber 144 and is a multimode fiber that operates in the fundamental mode. Fiber 1644 may be an extra large mode area (XLMA) fiber. FIG. 16 also electronics 1650, a pulse stretcher 1660 a pulse compressor 1670, and an optical isolator 1680, any of which may be part of regenerative fiber amplifier 1600.

[0102] Electro-optic control over the regenerative cavity of regenerative fiber amplifier 1600 is implemented by an electro-optic modulator 1642, quarter-wave plate 1643 and polarizing beam splitter 1646 of amplifier 1600. EOM 1642 may include a Pockels cell. EOM 1642 is driven by an amplifier 1656 which is triggered by a computer- controlled pulse-delay generator 1654 of electronics 1650.

[0103] Pulse delay generator 1654 is triggered by a signal from a photodiode 1652 of electronics 1650 that detects the mode-locked pulse train from a parasitic reflection within the fiber oscillator cavity. The regenerative amplifier cavity is constructed to image the fiber end faces to the cavity end mirrors (M), and vice versa. This is achieved with 4-f telescopes on either side of fiber 1644, indicated with focal lengths for each lens. Dichroic mirrors (DM) on either side of fiber 1644 couple the pump and strip the residual pump light from the signal.

[0104] The amplifier output is separated from the incoming pulse train, and the oscillator is isolated from the amplifier using a Faraday rotator (FR). A chirped volume Bragg stretches and compresses the seed pulse. A small amount of GDD due to the oscillator and amplifier fibers is compensated by an additional grating compressor. Regenerative fiber amplifier 1600 may include a compressor prior to the regenerative amplifier, which would pre-compensate this residual chirp. This pre-compensation would have negligible effect on the stretched pulse duration but significant improvement on the efficiency of de-chirping.

[0105] The results of the experiment in FIG. 12 show that obtaining fundamental mode operation does not require alignment of the seed pulse to the fundamental mode. However, to obtain the maximum efficiency and pulse quality, the seed pulse may be coupled to the fundamental mode of doped optical fiber 144. With this seed alignment, changing the number of round trips has negligible effect on the beam profile, which remains near pure fundamental mode with varying round trips, in contrast to the behavior in FIG. 12. [0106] FIG. 17 summarizes performance of an embodiment of regenerative fiber amplifier 100 operating at 10 kHz and six round trips (twelve total trips through the multimode fiber). FIG. 17 includes a spectral density plot 1710, a mode plot 1720, and a temporal profile 1730 of an amplified pulse, which is an example of amplified pulse 126. The amplifier achieves over 55 dB gain, amplifying 100 pj pulses to 55 pj. Despite this large gain, the spectral signal-noise contrast is excellent (over 30 dB as shown in spectral density plot 1710), in contrast to the near-zero signal-noise contrast shown at the same repetition rate in FIG. 3. Without regenerative amplification, the same level of gain would require several single-pass fiber amplifier stages. The regenerative configuration also enables strong amplification of seed pulses with very low average powers (~ 1 pW). Seeding the same amplifier with this average power and without regenerative feedback (in double-pass configuration) results in negligible gain and signal-noise contrast due to ASE (as shown in FIG. 3).

[0107] Mode plot 1720 includes a heat map 1722, with centered cross-sections 1724 and 1726 showing output beam intensity. Curve 1732 is a FROG-measured output pulse. Dashed curve 1734 indicates the transform-limited duration corresponding to spectral density plot 1710. Insets 1736 and 1738 show measured and retrieved FROG traces, respectively.

[0108] The quality of the temporal profile, shown in temporal profile 1730, is another indication of evolution in a single transverse mode. The compressed pulse is close to transform-limited in duration and has a temporal Strehl ratio of 74%. Evolution in multiple transverse modes would lead to pulses with a large deviation from the transform-limited duration owing to modal dispersion.

[0109] Single-mode operation of multimode fiber will underpin scaling of the performance reported above to much-higher levels. The fundamental mode area of XLMA fiber is already comparable with the mode areas that may be attained with rodtype photonic-crystal fibers (PCF) that are designed for single-mode operation. The mechanism for single-mode operation demonstrated here - regenerative feedback - does not rely on special fiber design, so it may be possible to surpass the fundamental mode diameter of the fiber employed here (71 pm) using this technique with larger- core, standard step-index fibers. We have amplified pulses to 100 pj pulse energy, limited by the properties of the Pockels cell, without degradation of the ASE contrast. The saturation energy of the fiber is ~ 1 mJ, and 10-ns pulses have been amplified to 100 mJ in a similar fiber. In embodiments, pulse energies well above 1 mJ will be achievable. The highest peak power obtained from a single-emitter fiber amplifier is 4 GW, in 2.2-mJ and 500-fs pulses. This system includes four gain stages including a PCF rod, three acousto-optic modulators, and a spatial light modulator for spectral phase control. Established scaling from the results above by stretched-pulse duration, mode area, and polarization would allow the regenerative fiber amplifier to generate 2-mJ and ~300-fs pulses, thus duplicating the performance of a highly-complex system in a single low-cost regenerative amplification stage.

3. Descriptions of Selected Embodiments

[0110] FIG. 18 is functional block diagram of a regenerative fiber amplifier 1800, which includes an optical cavity 1840. Amplifier 1800 and optical cavity 1840 are respective example of amplifier 100 and optical cavity 140. Optical cavity 1840 includes one or more optical switches 110 and doped optical fiber 144. Optical cavity 1840 may also include control elements 1860. Examples of control elements 1860 include optical elements that are at least one of dispersive, diffractive, or dissipative. Optical cavity 1840 may be configured in either a ring-type cavity 1940(1) or linear-type geometry 1940(2), as shown in FIG. 19, each of which is an example of optical cavity 140.

[0111] Doped optical fiber 144 may be optically pumped by an external light source. Pumping can occur via a fiberized wavelength division multiplexer, fiberized pump combiner, or with free-space alignment and wavelength- or polarizationdependent optics.

[0112] When correctly constructed, a low-energy pulse enters optical cavity 1840, is trapped in the cavity as it makes some number of round trips, and is eventually removed from cavity 1840 after being greatly amplified. A photodiode trace 2010 showing this amplification (taken from a parasitic reflection within a regenerative amplifier cavity) is shown in FIG. 20. The pulse makes six round trips through the cavity, and the energy increases during each round trip due to the fiber amplifier within.

[0113] The best way of making a regenerative fiber amplifier depends on the intended amplifier performance. Choice of fiber amplifier and control elements depend on the particular performance intended. Additional embodiments

[0114] Embodiments of regenerative fiber amplifier 100 may include fiber- integrated components, as shown in FIG. 21. FIG. 21 shows schematics of regenerative amplifiers 2100(1), 2100(2), 2100(3), and 2100(4), each of which is an example of regenerative fiber amplifier 100. Each regenerative amplifier 2100 has a linearly- configured optical cavity and includes switch-reflector unit 1180 introduced in FIG. 11. In FIG. 21, the initialisms are as follows: HWP, half-wave-plate; PBS, polarizing beamsplitter; FR, faraday rotator; PC, Pockels cell; QWP, quarter-wave plate; DM, dichroic mirror; PD, pump diode

[0115] Regenerative amplifier 2100(1) includes a fiber Bragg grating and fiber- integrated pump. The fiber Bragg grating reflects the signal light, and allows for fiberintegration of one side of the amplifier, and may also be configured to enhance dispersive or dissipative effects (adding group delay dispersion or acting as a spectral filter, e.g., to combat gain narrowing).

[0116] Regenerative amplifier 2100 may include a fiber integrated pump by use of a combiner or mode-field-adaptor, as in regenerative amplifier 2100(2). Regenerative amplifier 2100(3) includes an additional fiber Bragg grating that reflects any unabsorbed pump light back into the cavity, but does not affect the signal. Regenerative amplifier 2100(4) includes control elements 1860.

[0117] The use of fiber-Bragg-gratings (FBG) in linear-type regenerative amplifier cavities is especially helpful for making convenient, practical devices. The FBG first serves as a reflector for the signal, so helps to construct the optical cavity. Additionally, FBGs may be constructed to impart dispersive, diffractive, and dissipative effects, so can serve as a control element 1860. For example, an FBG might add dispersion, helping to realize the self-similar evolution as discussed above. As another example, the FBG might be written with a spectral filter that counter-acts the typical gain curve of the fiber gain medium in order to limit gain-narrowing. The FBG can also be written to include spatially diffractive effects in order to control multimode content.

Combinations of Features

[0118] Features described above, as well as those claimed below, may be combined in various ways without departing from the scope hereof. The following enumerated examples illustrate some possible, non-limiting combinations. [0119] Embodiment 1. A regenerative amplifier, comprising: a plurality of reflective elements forming an optical cavity having a plurality of optical-cavity modes; a doped optical fiber located within the optical cavity, the doped optical fiber having a plurality of waveguide modes; and an optical switch located within the optical cavity, the optical switch being controllable between first and second states, wherein: the optical switch, in the first state, transmits light exiting the doped optical fiber such that the light resonates within the optical cavity; and the optical switch, in the second state, one or both of (i) couples a seed pulse into the optical cavity and (ii) couples an amplified pulse out of the optical cavity; wherein an optical-cavity mode, of the plurality of optical-cavity modes, having the lowest loss and highest gain includes a mode of the plurality of waveguide modes. The mode may be the fundamental mode of the doped optical fiber.

[0120] Embodiment 2. The regenerative amplifier of embodiment 1, the doped optical fiber comprising a large-mode-area optical fiber, an extra-large-mode-area optical fiber, or a combination thereof.

[0121] Embodiment 3. The regenerative amplifier of either one of embodiments 1 or 2, the doped optical fiber being doped with one or more of ytterbium, erbium, neodymium, holmium, praseodymium, and thulium.

[0122] Embodiment 4. The regenerative amplifier of any one embodiments 1-3, further comprising a pump laser that pumps the doped optical fiber with pump light.

[0123] Embodiment 5. The regenerative amplifier of any one embodiments 1-4, wherein one or more of the plurality of reflective elements transmits the pump light.

[0124] Embodiment 6. The regenerative amplifier of either one of embodiments 4 or 5, further comprising a dichroic mirror located within the optical cavity, the dichroic mirror being that reflects the amplified pulse and transmit the pump light.

[0125] Embodiment 7. The regenerative amplifier of any one embodiments 4-6, further comprising first and second dichroic mirrors located within the optical cavity and near opposite ends of the doped optical fiber; wherein both of the first and second dichroic mirrors reflect the amplified pulse and transmit the pump light.

[0126] Embodiment 8. The regenerative amplifier of any one embodiments 1-7, the optical switch comprising a polarization rotator and wave plate located within the optical cavity. [0127] Embodiment 9. The regenerative amplifier of any one embodiments 1-8, the plurality of reflective elements forming a ring cavity.

[0128] Embodiment 10. The regenerative amplifier of embodiment 9, the ring cavity having a length such that a temporal duration of the seed pulse is less than a round-trip propagation time of the seed pulse through the ring cavity.

[0129] Embodiment 11. The regenerative amplifier of any one embodiments 1-10, the plurality of reflective elements forming a Fabry-Perot cavity.

[0130] Embodiment 12. The regenerative amplifier of embodiment 11, the Fabry- Perot cavity having a length such that a temporal duration of the seed pulse is less than one-half of a round-trip propagation time of the seed pulse through the Fabry-Perot cavity.

[0131] Embodiment 13. The regenerative amplifier of either one of embodiments 11 or 12, further comprising a lens system that images a facet of the doped optical fiber onto one of the plurality of reflective elements.

[0132] Embodiment 14. The regenerative amplifier of embodiment 13, the lens system comprising a 4f lens system.

[0133] Embodiment 15. The regenerative amplifier of any one embodiments 1-14, wherein: one of the plurality of reflective elements is a fiber Bragg grating having a first grating facet; and the first grating facet is directly affixed to a facet of the doped optical fiber.

[0134] Embodiment 16. The regenerative amplifier of embodiment 15, further comprising: a pump laser that emits pump light; and a passive optical fiber that couples the pump light to a second grating facet of the fiber Bragg grating; wherein the fiber Bragg grating transmits the pump light.

[0135] Embodiment 17. The regenerative amplifier of any one embodiments 1-16, further comprising a pulse stretcher that: stretches the seed pulse into a stretched pulse; and couples the stretched pulse into the optical cavity via the optical switch.

[0136] Embodiment 18. The regenerative amplifier of any one embodiments 1-17, further comprising a compressor that compresses the amplified pulse after the amplified pulse is coupled out of the optical cavity via the optical switch.

[0137] Embodiment 19. The regenerative amplifier of any one embodiments 1-18, further comprising, within the optical cavity, at least one of a spectrally-selective optical element, a temporally-dispersive optical element, and a saturable absorber. 1 [0138] Embodiment 20. A method for regenerative amplification includes controlling an optical switch to couple a seed pulse into an optical cavity that includes a doped optical fiber. The method also includes pumping the doped optical fiber with pump light such that the seed pulse is amplified into an amplified pulse within a mode of the doped optical fiber, the mode may be the fundamental mode of the doped optical fiber. The method also includes controlling the optical switch to couple the amplified pulse out of the optical cavity.

[0139] Changes may be made in the above methods and systems without departing from the scope of the present embodiments. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. Herein, and unless otherwise indicated the phrase “in embodiments” is equivalent to the phrase “in certain embodiments,” and does not refer to all embodiments.

[0140] Regarding instances of the terms “and/or” and “at least one of,” for example, in the cases of “A and/ or B,” “at least one ofA and B,” and “at least one of A or B,” such phrasing encompasses the selection of (i) A only, or (ii) B only, or (hi) both A and B. In the cases of “A, B, and/or C, ” “at least one of A, B, and C,” and “at least one of A, B, or C,” such phrasing encompasses the selection of (i) A only, or (ii) B only, or (iii) C only, or (iv) A and B only, or (v) A and C only, or (vi) B and C only, or (vii) each of A and B and C. This may be extended for as many items as are listed.

[0141] The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween.

Claims

CLAIMS We claim:

1. A regenerative amplifier, comprising: a plurality of reflective elements forming an optical cavity having a plurality of optical-cavity modes; a doped optical fiber located within the optical cavity, the doped optical fiber having a plurality of waveguide modes; and an optical switch located within the optical cavity, the optical switch being controllable between first and second states, wherein: the optical switch, in the first state, transmits light exiting the doped optical fiber such that the light resonates within the optical cavity; and the optical switch, in the second state, one or both of (i) couples a seed pulse into the optical cavity and (ii) couples an amplified pulse out of the optical cavity; wherein an optical-cavity mode, of the plurality of optical-cavity modes, having the lowest loss and highest gain includes a mode of the plurality of waveguide modes.

2. The regenerative amplifier of claim 1, the doped optical fiber comprising a large- mode-area optical fiber, an extra-large-mode-area optical fiber, or a combination thereof.

3. The regenerative amplifier of claim 1, the doped optical fiber being doped with one or more of ytterbium, erbium, neodymium, holmium, praseodymium, and thulium.

4. The regenerative amplifier of claim 1, further comprising a pump laser that pumps the doped optical fiber with pump light.

5. The regenerative amplifier of claim 1, the mode being the fundamental mode of the doped optical fiber.

6. The regenerative amplifier of claim 4, further comprising a dichroic mirror located within the optical cavity, the dichroic mirror being that reflects the amplified pulse and transmit the pump light.

7. The regenerative amplifier of claim 4, further comprising first and second dichroic mirrors located within the optical cavity and near opposite ends of the doped optical fiber; wherein both of the first and second dichroic mirrors reflect the amplified pulse and transmit the pump light.

8. The regenerative amplifier of claim 1, the optical switch comprising a polarization rotator and wave plate located within the optical cavity.

9. The regenerative amplifier of claim 1, the plurality of reflective elements forming a ring cavity.

10. The regenerative amplifier of claim 9, the ring cavity having a length such that a temporal duration of the seed pulse is less than a round-trip propagation time of the seed pulse through the ring cavity.

11. The regenerative amplifier of claim 1, the plurality of reflective elements forming a Fabry-Perot cavity.

12. The regenerative amplifier of claim 11, the Fabry-Perot cavity having a length such that a temporal duration of the seed pulse is less than one-half of a round-trip propagation time of the seed pulse through the Fabry-Perot cavity.

13. The regenerative amplifier of claim 11, further comprising a lens system that images a facet of the doped optical fiber onto one of the plurality of reflective elements.

14. The regenerative amplifier of claim 1, wherein: one of the plurality of reflective elements is a fiber Bragg grating having a first grating facet; and the first grating facet is directly affixed to a facet of the doped optical fiber.

15. The regenerative amplifier of claim 14, further comprising: a pump laser that emits pump light; and a passive optical fiber that couples the pump light to a second grating facet of the fiber Bragg grating; wherein the fiber Bragg grating transmits the pump light.

16. The regenerative amplifier of claim 1, further comprising a pulse stretcher that: stretches the seed pulse into a stretched pulse; and couples the stretched pulse into the optical cavity via the optical switch.

17. The regenerative amplifier of claim 1, further comprising a compressor that compresses the amplified pulse after the amplified pulse is coupled out of the optical cavity via the optical switch.

18. The regenerative amplifier of claim 1, further comprising, within the optical cavity, at least one of a spectrally-selective optical element, a temporally-dispersive optical element, and a saturable absorber.

19. A method for regenerative amplification, comprising: controlling an optical switch to couple a seed pulse into an optical cavity that includes a doped optical fiber; pumping the doped optical fiber with pump light such that the seed pulse is amplified into an amplified pulse within a fundamental mode of the doped optical fiber; and controlling the optical switch to couple the amplified pulse out of the optical cavity.

20. The method of claim 19, the mode being the fundamental mode of the doped optical fiber.