Universal frequency synthesizer

Abstract

To enable an increase in repetition rates of a passively mode-locked laser by a factor of up to 1000 up to a frequency range of 1 to 40GHz while maintaining comb characteristics of a harmonically mode-locked (HML) frequency comb laser.SOLUTION: The HML laser may include a reference cavity having a beam splitter that is common mode to the reference cavity and the main cavity, and is further configured to generate an output for the HML optical frequency comb. The bulk as well as the fiber reference cavities can be implemented with ultra-low expansion thermal expansion materials that enable the use of HML lasers as precision frequency references and frequency synthesizers for the microwave, millimeter wave, and optical frequency domains. HML dual-frequency combs with minimal differential noise between the two combs can reference both combs to the same reference cavity.SELECTED DRAWING: Figure 2A

Description

[Technical Field]

[0001] [Priority claim] This application claims the benefit of priority to U.S. Provisional Application No. 63 / 675,432, filed July 25, 2024, which is incorporated herein by reference in its entirety.

[0002] This application relates generally to ultra-high stability frequency synthesizers and pulse sources. [Background technology]

[0003] Frequency synthesizers and highly stable ultrashort pulse sources are ubiquitous in many areas of optical technology. Particularly attractive are systems based on frequency combs, which allow the generated frequency or pulses to be locked to a well-defined frequency grid. Application areas include, but are not limited to, sensing, machining, metrology, microwave generation, terrestrial and satellite communications, and quantum computing, to name a few. For example, in free-space optical communications, it is beneficial to use pulse sources with GHz-level repetition rates of 100 fs to reduce the effects of atmospheric speckle in long-distance signal transmission.

[0004] To date, seven main methods for ultrashort pulse generation are used in industry: 1) mode-locked fiber and solid-state lasers, 2) gain-switched and mode-locked diode lasers, 3) electro-optic modulator (EOM)-based pulse sources, 4) four-wave mixing (FWM)-guided fiber pulse sources, 5) cavity soliton-based sources, 6) microresonators (MRs), and fiber microresonators (FMRs). Such pulse sources may also be capable of operating as frequency combs, meaning they can have well-defined mode spectra in frequency space. To date, only mode-locked sources and microresonators (MRs) can operate as frequency combs without resorting to prohibitively complex system configurations. In many application areas, external short-pulse sources used for FMRs are undesirable, solid-state-based sources are generally considered too inflexible and bulky for use in frequency combs, and MR-based frequency combs are currently still very difficult to construct due to their high intrinsic repetition rates, typically exceeding 40 GHz, making measurement and control of their carrier-envelope offset frequency challenging. These considerations have led to fiber frequency combs dominating the frequency comb application space. Summary of the Invention [Problem to be solved by the invention]

[0005] In some embodiments, an apparatus includes a harmonically mode-locked (HML) laser including a main cavity having a first cavity round-trip time T and a reference cavity having a second cavity round-trip time T / N, where N is an integer. The main cavity and the reference cavity are coupled to each other. The apparatus further includes at least one optical beam splitter in the reference cavity. The at least one optical beam splitter is configured to generate a common mode substantially shared between the main cavity and the reference cavity and generate an output for the optical frequency comb.

[0006] In some embodiments, the apparatus includes a first cavity having a first cavity round trip time T and a second cavity having a second cavity round trip time T / N, where N is an integer. The first cavity and the second cavity are coupled to each other. The apparatus further includes at least one optical beam splitter within the second cavity. The at least one optical beam splitter is configured to generate a common mode substantially shared between the first cavity and the second cavity and generate an output for the optical frequency comb.

[0007] In some embodiments, the optical cavity comprises a first cavity mirror and a second cavity mirror. The first cavity mirror and the second cavity mirror are concentric about a major axis. The optical cavity further comprises an input beam impinging on the first cavity mirror at a first angular offset from the major axis. The optical cavity further comprises an output beam transmitting through the first cavity mirror at a second angular offset from the major axis. The second angular offset is substantially equal to the negative of the first angular offset, and the optical cavity is configured as an optical reference for a mode-locked laser.

[0008] In some embodiments, an apparatus comprises a harmonically mode-locked (HML) laser comprising a main cavity having a first cavity round-trip time T and a reference cavity having a second cavity round-trip time T / N, where N is an integer. The main cavity and the reference cavity are coupled to each other, and the harmonically mode-locked laser operates at a repetition rate N / T. The apparatus further comprises at least one optical beam splitter within the reference cavity. The at least one optical beam splitter is configured to generate a common mode that is substantially shared between the main cavity and the reference cavity, and the harmonically mode-locked laser has a repetition rate that is phase-locked to an external microwave reference.

[0009] In some embodiments, a harmonically modelocked (HML) fiber laser system is configured using an external reference cavity, which provides coherent feedback to pulses within the main fiber laser cavity, including an actuator to ensure long-term stability.

[0010] In some embodiments, the dual comb system comprises two harmonically mode-locked lasers, the two harmonically mode-locked lasers comprising a common reference cavity.

[0011] In some embodiments, the optical parametric oscillator comprises a mode-locked pump laser oscillating at a pump laser wavelength. The mode-locked pump laser comprises a first cavity having a first cavity round-trip time T and a second cavity having a second cavity round-trip time T / N, where N is an integer. The first and second cavities are optically coupled to each other, and the second cavity further comprises a nonlinear crystal. The second cavity is configured to generate an output at a wavelength different from the pump laser wavelength.

[0012] In some embodiments, the HML fiber laser system can also be configured with a nested reference cavity located within the main fiber laser cavity and can also include one or more actuators to ensure long-term stability.

[0013] In some embodiments, the HML fiber laser system can operate as a low-noise, high-repetition-rate frequency comb by having the mode spacing of the reference cavity that is a multiple of the cavity mode spacing of the main fiber laser cavity.

[0014] In some embodiments, the HML fiber laser system can be used as a low noise microwave source via detection of the HML repetition rate with a photodetector.

[0015] In some embodiments, the HML fiber laser system can be used as a low-noise mm source by filtering two of the HML comb modes and interfering them on a photodetector.

[0016] In some embodiments, the HML fiber laser system can be used as a low-noise frequency synthesizer by filtering the individual comb modes with appropriate optical bandpass filters. [Brief explanation of the drawings]

[0017] [Figure 1A] FIG. 1A shows a schematic diagram of an example of a harmonically modelocked pulse train in the time domain. [Figure 1B] FIG. 1B shows a schematic example of a harmonically modelocked pulse train in the spectral domain. [Figure 2A] FIG. 2A schematically illustrates the operating principle of an exemplary HML fiber laser with repetition rate doubling via an integrated reference cavity according to some embodiments described herein. [Figure 2B] FIG. 2B schematically illustrates the pulse evolution of a single pulse injected into an external reference cavity used as part of an exemplary HML fiber laser with repetition rate multiplication via an external reference cavity according to some embodiments described herein. [Figure 3A] FIG. 3A schematically illustrates an exemplary HML fiber laser with relative cavity length stabilization between the external reference cavity and the main fiber cavity, as well as fbeat and fceo stabilization according to some embodiments described herein. [Figure 3B] FIG. 3B schematically illustrates an exemplary HML fiber laser with relative cavity length stabilization between the external reference cavity and the main fiber cavity, as well as fbeat and fceo stabilization according to some embodiments described herein. [Figure 3C]FIG. 3C is a flow diagram of an example method for phase-locking fceo and fbeat for an example HML fiber laser according to some embodiments described herein. [Figure 4A] FIG. 4A depicts an actual measurement of the RF spectrum of the output of an exemplary HML fiber laser according to some embodiments described herein when interfered with a cw laser as recorded with a photodetector. [Figure 4B] FIG. 4B depicts actual measurements of the optical spectrum of the output of the exemplary HML fiber laser referenced in FIG. 4A under different conditions. [Figure 4C] FIG. 4C depicts actual measurements of phase noise power spectral density (left axis) and integrated phase noise (right axis) versus fbeat for an exemplary HML fiber laser according to some embodiments described herein. [Figure 5] FIG. 5 schematically illustrates another exemplary HML fiber laser with repetition rate stabilization via an external reference cavity, according to certain embodiments described herein. [Figure 6] FIG. 6 schematically illustrates another exemplary HML fiber laser with repetition rate stabilization via an external reference cavity, according to certain embodiments described herein. [Figure 7A] FIG. 7A schematically illustrates an example of a bulk bidirectional reference cavity operable in transmission of an exemplary HML fiber laser with repetition rate stabilization through the reference cavity, according to some embodiments described herein. [Figure 7B] FIG. 7B schematically illustrates an example of an all-fiber bidirectional reference cavity operable in transmission of an exemplary HML fiber laser with repetition rate stabilization through the reference cavity, according to some embodiments described herein. [Figure 8] FIG. 8 schematically illustrates another exemplary fiber reference cavity operable in transmission of an exemplary HML fiber laser configured as a figure-eight laser with repetition rate stabilization via the reference cavity, according to some embodiments described herein. [Figure 9A] FIG. 9A schematically illustrates an example of an ultra-high stability bidirectional fiber-based reference cavity operable in transmission with an exemplary HML fiber laser with repetition rate stabilization through the reference cavity, according to some embodiments described herein. [Figure 9B] FIG. 9B schematically illustrates an example of an ultra-high stability bidirectional bulk reference cavity operable in transmission with an exemplary HML fiber laser with repetition rate stabilization through the reference cavity according to some embodiments described herein. [Figure 9C] FIG. 9C schematically illustrates an example of a monolithic bulk reference cavity operable in transmission with an exemplary HML fiber laser with repetition rate stabilization through the reference cavity according to some embodiments described herein. [Figure 9D] FIG. 9D schematically illustrates an exemplary HML fiber laser with relative cavity length stabilization between an external fiber reference and the main fiber cavity, as well as an actuator, according to certain embodiments described herein. [Figure 9E] FIG. 9E schematically illustrates an exemplary HML fiber laser with relative cavity length stabilization between an external fiber reference and the main fiber cavity, as well as an actuator, according to certain embodiments described herein. [Figure 10A] FIG. 10A schematically illustrates an example of a bulk reference cavity operable as a frequency reference for repetition rate stabilization of an exemplary HML laser via a reference cavity, according to some embodiments described herein. [Figure 10B] FIG. 10B schematically illustrates an example of a bulk reference cavity operable as a frequency reference for repetition rate stabilization of an exemplary HML laser via a reference cavity, according to some embodiments described herein. [Figure 10C]FIG. 10C schematically illustrates an example of a bulk reference cavity operable as a frequency reference for repetition rate stabilization of an exemplary HML laser via a reference cavity, according to some embodiments described herein. [Figure 10D] FIG. 10D schematically illustrates an example of a bulk reference cavity operable as a frequency reference for repetition rate stabilization of an exemplary HML laser via a reference cavity, according to some embodiments described herein. [Figure 10E] FIG. 10E schematically illustrates an exemplary HML fiber laser comprising a V-cavity operably connected to a nonlinear amplifying loop mirror to facilitate HML and serve as a frequency reference for repetition rate stabilization of the HML fiber laser, according to some embodiments described herein. [Figure 10F] FIG. 10F schematically illustrates another exemplary HML fiber laser comprising a monolithic V-cavity integrated with an electro-optic modulator operably connected to a nonlinear amplifying loop mirror to facilitate HML, according to some embodiments described herein. [Figure 10G] FIG. 10G schematically illustrates an exemplary monolithic V-cavity integrated with a lithium niobate-based electro-optic modulator according to certain embodiments described herein. [Figure 11] FIG. 11 illustrates schematically an exemplary HML frequency reference as used for ultra-low phase noise microwave generation, according to some embodiments described herein. [Figure 12] FIG. 12 schematically illustrates an exemplary HML frequency reference used for ultra-low phase noise microwave generation or as a frequency synthesizer, according to certain embodiments described herein. [Figure 13] FIG. 13 illustrates a schematic diagram of an exemplary HML fiber laser configured for frequency downconversion according to some embodiments described herein. [Figure 14]FIG. 14 schematically illustrates an exemplary system of two HML fiber lasers configured with a common reference cavity for dual-comb operation, according to certain embodiments described herein. [Figure 15] FIG. 15 schematically illustrates an example configuration of two common-cavity HML fiber lasers for dual-comb operation according to some embodiments described herein. [Figure 16] FIG. 16 illustrates a schematic diagram of an exemplary HML fiber laser configured as an optical parametric oscillator according to some embodiments described herein. DETAILED DESCRIPTION OF THE INVENTION

[0018] Despite its dominance in industry, fiber frequency combs still have several limitations that negatively affect their applicability. One of the most serious limitations is the relatively long length of the fiber gain medium used to construct mode-locked fiber lasers. This makes it extremely difficult to operate fiber frequency combs operating with mode spacings Δf > 250 MHz, since the length L of the gain medium determines the maximum mode spacing by the well-known formula (for a ring cavity mode-locked with the fundamental cavity round-trip time): Δf=c / (n idx ×L) (1) where c is the speed of light and n idx is the fiber refractive index. Much research has been done to increase the repetition rate of fiber laser sources via harmonically modelocked (HML) fiber lasers (see, e.g., U.S. Patent 5,414,725 (Fermann et al.)) or to work on other compact repetition rate pulse sources based on EOMs (e.g., U.S. Patent 7,239,442 (Kourogi et al.)), but to date such sources suffer from significant frequency noise that makes their operation as frequency combs impossible, or at least very difficult.

[0019] Regarding the application of mode-locked fiber lasers to frequency synthesizers, frequency combs also have severe limitations, and typically an external cw laser locked to a bulky, ultra-high-Q reference cavity is used to transfer the stability of the reference cavity to the fiber comb repetition rate, providing a low-noise microwave output (via comb repetition rate detection) or reducing the phase noise of individual comb lines. Such a system is described, for example, in X. Xie, Nature Photonics, vol. 11, pp. 44-47 (2017).

[0020] Therefore, there is a need for compact, highly coherent pulse sources and frequency synthesizers with pulse repetition rates in the range of 250 MHz to 40 GHz, where most of the applicability of ultrafast pulse sources lies.

[0021] Some embodiments described herein provide compact, highly robust, ultra-low noise HML fiber lasers and frequency synthesizers that can further technological developments in sensing, machining, metrology, microwave generation, terrestrial and satellite communications, as well as quantum computing and other applications.

[0022] Harmonically mode-locked (HML) fiber lasers have been the subject of much investigation (see, e.g., U.S. Patents 5,212,711 (Harvey et al.), '725 (Fermann et al.), U.S. Patent 6,738,408 (Abedin et al.), and more recently X. Cao et al., "GHz Figure-9 Er-Doped Optical Frequency Comb Based on Nested Fiber Ring Resonators," Laser Photonics Rev. vol. 17, 230057 (2023)). Both Harvey and Cao used a Fabry-Perot-based subcavity as a repetition rate multiplier and obtained stable operation for a subcavity with an optical round-trip cavity length L or equivalent cavity round-trip time t = L / c. t=L / c=1 / (f0×N)=T / N (2) where f0 is the fundamental repetition rate, T is the fundamental round-trip time of the mode-locked fiber laser, and N is an integer satisfying N ≥ 1. A limitation of previously disclosed HML fiber lasers is that they either contain an internal subcavity or, at most, only one actuator for repetition rate control to match the subcavity length to the main cavity. No additional actuators were included for stabilizing the beat signal (obtained when the mode-locked laser output is interfered with an external reference laser) or the carrier-envelope offset frequency. Therefore, the construction of a frequency synthesizer based on HML was not considered.

[0023] In contrast, frequency synthesizers have been built based on both mode-locked fiber lasers operating at a fundamental repetition rate, as described in T. Schibli et al., "Phase-locked widely tunable optical single-frequency generator based on a femtosecond comb," Opt. Lett., vol. 30, pp. 2323–2325 (2005) and D.T. Spencer et al., "An Integrated-Photonics Optical-Frequency Synthesizer," Nature, vol. 557, pp. 81–85 (2018). The term frequency synthesizer is generally used in industry and science to describe a source capable of generating a well-characterized single-frequency output with a predetermined frequency. Ideally, the predetermined frequency would also be tunable over a selectable frequency range. Until now, the use of HML for frequency synthesizers has been precluded by the inability to stabilize the optical frequency of the optical mode spectrum, resulting in a large level of frequency noise. Rather, only the overall repetition rate or mode spacing of such a source has been stabilized.

[0024] This is further illustrated in Figures 1A and 1B. Figure 1A shows a pulse repetition rate of 1 / f rep, a conventional HML fiber pulse train in the time domain with pulses separated by, e.g., f rep The HML frequency comb is stabilized using a conventional technique that uses only one actuator to adjust the repetition rate mismatch between the subcavity and the HML frequency comb with N × f. Figure 1B shows the optical spectrum of the HML frequency comb in the frequency domain, f rep plus at least one optical comb mode f opt =f ceo +N×f rep The absolute optical frequency of is also precisely stabilized, where f ceo is the carrier envelope offset frequency, and N is an integer. Similar to a standard fundamental mode-locked frequency comb, f opt The stabilization of f ceo and measuring or stabilizing the frequency f cw Beat frequency f using an external cw laser reference with beat Similar to a standard fundamental mode-locked frequency comb, the measurement or stabilization of f beat is f, assuming that the beat between cw lasers with nearest neighbor comb modes is measured, as shown in Figure 1B. beat =f ceo +N×f rep -f cw f for a harmonically mode-locked laser is given by ceo and f beat Simultaneous measurement or stabilization of both has not been possible in any previously disclosed harmonically modelocked system. The reasons for this deficiency are many, including the prevalent excessive noise of harmonically modelocked lasers, inadequate cavity design, actuator, and actuator position, to name just a few.

[0025] Example of ultra-low noise HML laser A schematic diagram of an exemplary HML design 10 is shown in FIG. 2A. A mode-locked fiber laser 20, or a mode-locked solid-state laser or mode-locked diode laser, includes a gain medium with a mode-locking mechanism and merges with an integral reference cavity 30 via a beam splitter 32 and coupling optics 34. The mode-locking mechanism may include, for example, a Kerr-based fast saturable absorber based on a fiber loop mirror, a semiconductor saturable absorber, a carbon nanotube, or any other mode-locking mechanism. No optical isolator is used between the mode-locked laser 20 and the integral reference cavity 30, which is bounded by mirrors 36a and 36b. Therefore, the beam splitter 32 is inserted within the boundary of the reference cavity 30. The mirrors 36a and 36b can be curved with a radius of curvature, but flat mirrors (e.g., with an infinite radius of curvature) can also be used. Therefore, the reference cavity 30 can provide direct optical feedback to the mode-locked laser 20. The reference cavity 30 has a round-trip length L ref and the position of mirror 36b is determined by the cavity mode spacing Δf of reference cavity 30. ref and the cavity mode spacing of a mode-locked laser 20 operating at fundamental frequency f0 can be adjusted (e.g., translated) so that the following relationship between Δf ref =N*f0(3) Here, the fundamental cavity frequency is determined by the round trip time of the pulse traveling from mirror 36a through beam splitter 32 to mode-locked laser 20 and back.

[0026] The reference cavity 30 can provide coherent feedback to the mode-locked laser pulse train, as shown in Figure 2B, so that when the first pulse enters the reference cavity 30 from the mode-locked laser 20, that same pulse bounces around in the reference cavity 30, producing an output attenuated train of pulses, as shown in Figure 2B. This attenuated pulse train can be fed back into the main cavity 22 of the mode-locked laser 20, coherently seeding the growth of pulses separated by the reference cavity round trip time, which can produce a pulse train at a harmonic of the mode-locked laser 20. The beam splitter 32 splits the Δf ref = N*f0 (e.g., outside the cavity 30), can be preferentially filtered, but Δf ref =N*f0 can be preferentially injected back into the main cavity 22.

[0027] 2A, such a reference cavity 30 has at least one optical beam splitter 32 inserted within its boundaries, which directs pulses from the main cavity 22 into the reference cavity 30. By superimposing the optical beam in the reference cavity 30 with the beam coming from the main cavity 22 and reflected by the beam splitter 32, the beam from the main cavity 22 can be coherently superimposed in phase with the beam in the reference cavity 30 (e.g., the beam splitter 32 is configured such that the main cavity 22 and the reference cavity 30 share a substantially common spatial mode).

[0028] The beam splitter 32 can further direct the pulses inside the reference cavity 30 and the pulses from the main cavity 22 out of the optical system simultaneously (e.g., to generate output for an optical frequency comb) and can be reduced (e.g., minimized) for optimal coherent coupling between the main cavity 22 and the reference cavity 30. These two sets of pulses have good overlap and are out of phase, which reduces (e.g., minimizes) the output power from the system, as measured downstream of the beam splitter 32.

[0029] This, e.g., Fabry-Perot reference cavity 30, can act as a reflective end mirror for the main cavity 22. To optimize harmonic modelocking, the reflectivity of this mirror can be maximized when there is high power inside the reference cavity 30. Similarly, for a loop or ring-type reference cavity 30, harmonic modelocking can be optimized when there is high power inside the cavity 30, maximizing transmission through the loop.

[0030] 3A schematically illustrates an exemplary HML fiber laser 100 according to some embodiments described herein. The HML fiber laser 100 is based on a nonlinear amplifying mirror (see, for example, N. Kuse et al., “All polarization-maintaining Er fiber-based optical frequency combs with nonlinear amplifying loop mirror,” Opt. Expr., Vol. 24, Issue 3, pp. 3095-3102 (2016); U.S. Patent 9,819,141 (Fermann et al.)). The HML fiber laser 100 includes an electro-optic modulator (EOM) 102 within a reference cavity 30 bounded by first and second mirrors 36 a and 36 b. In some other implementations, the EOM 102 and the second mirror 36 b are not present. In the exemplary HML fiber laser 100 of FIG. 3A, a nonlinear amplifying loop mirror (NALM) 110 generates short mode-locked pulses (e.g., having pulse widths in the range of 50 fs to 1 ps) at the output, which are extracted via transmission through a beam splitter 32 (e.g., having a reflectivity in the range of 0.01% to 99%). The NALM 110 includes an optical coupler 112a with a coupling ratio of x / (1-x)% (e.g., 50 / 50%). The NALM 110 further includes a fiber amplifier 114, e.g., an erbium-doped fiber amplifier (EDFA) pumped by a laser diode via another coupler (not shown), a nonreciprocal phase bias element 116, and a piezoelectric transducer (PZT) 118 configured to provide relative cavity length control. The PZT 118 can be configured to stretch the fiber length (e.g., as a fiber stretcher); multiple fiber stretchers with different lengths can be implemented to provide fiber length actuation with different bandwidths. In some embodiments, the dispersion inside the HML fiber laser 100 is compensated by concatenating lengths of positive and negative dispersion fiber with small overall negative (or soliton-supporting) dispersion.

[0031] In some embodiments, the fundamental repetition rate of the HML fiber laser 100 can be in the range of 1 MHz to 250 MHz. The second mirror 36b is positioned over the length L of the reference cavity 30. ref To adjust , and according to equation (3), the exemplary HML fiber laser 100 of FIG. 3A can initiate harmonic modelocking from Q-switching instability at a repetition rate corresponding to the round-trip time of the reference cavity 30. Measurements of the RF spectrum of the laser system output (e.g., 1 MHz resolution bandwidth) are shown in FIG. 4A and detected with the first photodetector 120a. For these measurements, the beam splitter 32 had a 40% reflectivity, and the HML fiber laser 100 was pumped with approximately 1800 mW from two polarization-multiplexed single-mode diode lasers. The intermodal beat frequency shown in FIG. 4A is 1.272 GHz, which corresponds to the 12th harmonic of the fundamental repetition rate at 106 MHz. Beat frequencies of approximately 615 MHz and 658 MHz, corresponding to beats between the HML fiber laser 100 and an external narrow-linewidth laser 124 (e.g., detected with the second photodetector 120b), can also be seen. These f beat The signal-to-noise (S / N) ratio of the signal is approximately 50 dB at 1 MHz resolution, higher than what is typically achievable with previously disclosed mode-locked fiber frequency combs operating at the fundamental cavity round-trip time. In FIG. 4A, no spurious RF beats due to supermode noise are visible, indicating that the HML fiber laser 100 comprises a high-quality frequency comb. To achieve such a high-quality comb and high S / N ratio, the reflectivity of the beam splitter 32 can be greater than 15%. In some embodiments, an S / N ratio of greater than 25 dB at 1 MHz resolution (e.g., equivalent to 35 dB at 100 kHz resolution) can be achieved. Because an S / N ratio of greater than 35 dB at 100 kHz resolution can enable cycle-slip-free phase locking between laser systems, or in this example, between the comb and an external cw laser 124, such a high S / N ratio is sufficient for applications in precision metrology and optical clock technology.

[0032] Cavity length mismatch, fbeat and f ceo Exemplary control of In some embodiments, the HML fiber laser 100 is highly sensitive to cavity mismatch between the reference cavity 30 and the main cavity 22 (e.g., sensitivity in the λ to λ / 100 range). Increasing the optical feedback from the second mirror 36b can enhance wavelength sensitivity. Therefore, to control the cavity length mismatch, a feedback loop 130 (see, e.g., Figures 3A and 3B) can be implemented that uses the power level of the optical output spectrum. The upper curve in Figure 4B shows the optical output spectrum. When filtered through a spectral bandpass filter (e.g., 1590 nm), an error signal can be obtained to stabilize the relative cavity length. The signal level detected by the first photodetector 120a (which can sample the output extracted from the system via the second beam splitter 122) can then be directed to a loop filter that controls the cavity length of the main cavity 22 via fiber stretching by the PZT 118 inside the NALM 110. Simulations of pulse evolution in this HML fiber laser 100 show that the output pulse spectrum is sensitive to phase variations between the main cavity 22 and the reference cavity 30, which can be utilized in some embodiments for generating an error signal for cavity locking. A high-quality error signal can be generated with passive stability of the relative phase between the two cavities 20, 30 in the millisecond range or less, even in the presence of some Q-switching instability in the HML fiber laser 100. To improve performance, the spectral densities at two spectral locations can also be used as error signals.

[0033] The operation of the feedback loop 130 for adjusting the relative cavity lengths is further illustrated in Figure 4B. As explained above, the top curve in Figure 4B shows the harmonically mode-locked pulse spectrum when the two cavities 20, 30 are locked to each other. The middle curve in Figure 4B shows the harmonically mode-locked pulse spectrum when the two cavities 20, 30 are near the locking point, resulting in the intermittent generation of a stable pulse train and Q-switching. The bottom curve in Figure 4B shows the harmonically mode-locked pulse spectrum when the two cavities 22, 30 are further away from the locking point, resulting in Q-switching instability. Figure 4B shows that the spectral density of the locked system (e.g., at 1590 nm) can be approximately 10 dB higher compared to the spectral density during Q-switching. Even in the presence of Q-switching instability, the locking electronics can "capture" the spectral shape present during harmonic mode-locking and provide excellent control of the cavity length mismatch in the locked state.

[0034] The PZT 118 inside the NALM 110 as shown in Figures 3A and 3B can have a bandwidth in the range of 1 Hz to 1000 Hz, and in some other embodiments can include additional actuators such as intracavity waveguides or bulk electro-optic modulators. In some embodiments, high-speed PZT actuators are used at or near the first mirror 36a and / or second mirror 36b to increase the feedback bandwidth. Such embodiments are not shown separately.

[0035] f beat For control, the output from the HML fiber laser 100, for example, the output from the rejected output 113 from the NALM 110 as shown in FIGS. 3A and 3B, is directed through a third mirror 140 and interferes with a cw reference laser 124 to generate a beat signal f at a second photodetector 120b. beatThe cw laser may be combined with another beam splitter (not shown) to generate f. For example, another output extracted from output port 119 of second optical coupler 112b of NALM 110 or via second beam splitter 122 may also be used. beat The feedback loop 150 is f beat This can be accomplished using an electronic controller that compares the signal to a reference frequency (e.g., in the RF domain) and generates error signals for fast and slow control of the short cavity's cavity length. Fast control can be enabled via an EOM (e.g., a bulk intracavity electro-optic phase modulator), and slow control can be enabled via a PZT (not shown) that controls the position of the second mirror 36b. In certain embodiments, the position of the second mirror 36b controls only the reference cavity length and not the length of the main cavity 22. The f obtained for the exemplary HML fiber laser 100 of FIG. 3A is beat The residual phase noise spectral density (dBc / Hz) of the 0.25 rad f is further shown in Figure 4C, measured when integrated from the sideband frequencies of 6 MHz to 2 Hz. beat The phase noise of

[0036] In some embodiments, f ceo For control of the gain, an acousto-optic frequency shifter (AOM) 152 can be positioned downstream of the output from the HML fiber laser 100 and output a transmitted output 153. Alternatively, the intracavity gain or loss of the HML fiber laser 100 shown in FIG. 3A can be modulated. Gain control can be achieved via control of the pump power to the HML fiber laser 100, and loss control can be achieved by tilting one of the reference cavity mirrors 36a, 36b or by inserting an additional acousto- or electro-optic modulator (not shown) configured for amplitude modulation inside the reference cavity 30 (see, e.g., U.S. Patent 9,698,555 (Fermann et al.)).

[0037] The positions of the various actuators shown in FIG. 3A serve only as examples. In some embodiments, the length of the reference cavity 30 can also be controlled by controlling the position of the first mirror 36a instead of the second mirror 36b. In some embodiments, fast cavity length control can be enabled by inserting a high-speed phase modulator between the beam splitter 32 and the first mirror 36a or inside the fiber loop of the NALM 110. More than three actuators can also be implemented. Due to the good stability of the reference cavity 30, it is possible to avoid having actuators in the reference cavity 30 and use only one or two actuators to lock the main cavity 22 to the reference cavity 30. High-stability reference cavities are discussed herein with reference to FIGS. 7A, 7B, 9A-9E, and 10A-10D.

[0038] In some implementations, the f of a harmonically mode-locked fiber laser beat and f ceo The phase noise of (for example, as shown in Figure 2A) is beat and f ceo The stabilization of f also accounts for the mismatch of the relative cavity lengths between the main cavity 22 and the reference cavity 30 (e.g., the variation of f ceo When used to stabilize the f (which is due to the strong coupling of fluctuations), it can be reduced (e.g., minimized). ceo When stabilizing f, the relative cavity length mismatch can also be stabilized. Figure 3B shows that f can also be stabilized for cavity length stabilization according to some embodiments described herein. ceo3B is a schematic diagram of an exemplary HML fiber laser 100 that uses stabilization. The exemplary HML fiber laser 100 in FIG. 3B is very similar to the exemplary HML fiber laser 100 shown in FIG. 3A. In FIG. 3B, the exemplary HML fiber laser 100 includes a pump laser 142 and an f-2f interferometer 144 that generates an f-2f beat frequency in the RF region. The pump laser 142 is coupled to the NALM 110 via a wavelength division multiplexing (WDM) coupler 146. The f-2f interferometer 144 utilizes an output port 119 from the NALM 110, which is subsequently amplified via a series of optical amplifiers (not shown) to generate a supercontinuum output that is sufficiently wide for f-2f signal generation. The output of the f-2f interferometer 144 is ceo Through the feedback loop 152, f ceo It can be used to generate error signals for slow and fast control of the frequency, with slow control being enabled via control of the PZT 118 and fast control being enabled via control of the pump current to the pump laser 142.

[0039] FIG. 3C illustrates the f for the exemplary HML fiber laser 100 shown in FIG. 3B according to some embodiments described herein. ceo and f beat1 is a flow diagram of an exemplary method 160 for phase-locking of the f laser 142. In operation block 162, the method 160 may include setting the cavity lengths of the reference cavity 30 and the main cavity 22 to be approximately harmonics of each other. In operation block 164, the method 160 may further include adjusting the pump power so that sufficient pump power is available for the HML pulse train. In operation block 166, the method 160 may further include continuously scanning the cavity length of the main cavity 22 with the PZT 118 until the operating range of the f-2f interferometer 144 encompasses the desired lock point. In operation block 168, the method 160 may further include maintaining mode-locking by adjusting the PZT 118 until the temperature stabilizes, and then leaving the laser 142 passively mode-locked; if mode-locking is lost, the method 160 may include returning to operation block 166. In operation block 170, the method 160 may include adjusting the PZT 118 until the temperature stabilizes, and then leaving the laser 142 passively mode-locked. beat to the desired frequency, and if mode-locking is lost, method 160 may include returning to operation block 166. In operation block 172, method 160 may further include checking the frequency range for f-2f operation. In operation block 173, method 160 may further include adjusting the pump current baseline value or continuing to scan PZT 118 to find a better operating point in operation block 166 if the target f-2f frequency is not centered within the stability range. In operation block 174, method 160 returns to operation block 166. beat Check the position of f beat and returning to operation block 170 if f is not approximately equal to the desired frequency. ceo and f beat When is approximately equal to the desired frequency, f is controlled via feedback to the pump current (e.g., high-speed control) and PZT 118 (e.g., low-speed control). ceoEngage the lock and determine the position of the second mirror 36b (e.g., slow) and f via feedback to the EOM 102 (e.g., fast). beat It may further include engaging a control.

[0040] f ceo and f beat When f is phase-locked, long-term cavity length matching can also be implicitly guaranteed. The exemplary HML fiber laser 100 shown in FIG. 3B can also include a temperature control box (not shown) with additional vibration damping to avoid large perturbations of cavity length mismatch, which may prevent the actuator from responding fast enough. ceo and f beat Locking (see, e.g., exemplary method 160) of the f frequency can include four steps: 1) scanning the cavity length of the main cavity 22 with the PZT 118 to observe the f-2f signal; 2) the f-2f signal can be observed at a cavity length mismatch interval of λ, so continue scanning the PZT 118 until the observed f-2f frequency is approximately at the desired location; and 3) scanning the f frequency. beat 4) scanning the cavity length of the reference cavity 30 until the signal is also at approximately the desired frequency; ceo Rock and f beat Multiple iterations can be used to ensure that the HML fiber laser 100 is phase locked at the desired frequency.

[0041] f ceo or f beat Since there may be sufficient crosstalk between the actuators for control, the HML fiber laser 100 may be stabilized by various assignments of the actuators to the diagnostic signals. For example, f beat Switch the main cavity 22 to stabilize f ceo The reference cavity 30 may be switched in to stabilize the . The optimal allocation of actuators to diagnostic signals may vary depending on the actuator response and the type of noise found in a particular system.

[0042] For commercially viable systems, some embodiments are configured to reduce the pump power utilized for a particular laser configuration. The power for harmonic modelocking can be reduced, for example, by using a lower-doped fiber and a more efficient fiber amplifier. Another alternative for reducing power consumption is shown in FIG. 5, in which the x / 1-x (e.g., 50 / 50) optical coupler 112a in the NALM 110 of FIG. 3A is replaced with a polarizing beam splitter 210a. The nonlinear phase delay required to saturate the nonlinear reflectivity of the NALM 110 incorporating the polarizing beam splitter 210a can be substantially reduced, thereby reducing the power utilized for the HML fiber laser 100. A Faraday rotator 220 can also be inserted to compensate for polarization rotation within the NALM 110. As shown in FIG. 5, the additional insertion of a λ / 2 waveplate 222 and a λ / 4 waveplate 224 can enable tuning of the nonlinear saturation power of the NALM 110. ceo , f beat and relative cavity length control can then be performed similarly, and the rejected output 113 can be obtained from the polarizing beam splitter 210b. In FIG. 5, for simplicity, only one f beat An exemplary embodiment of a feedback loop 150 is shown.

[0043] The exemplary HML fiber laser 100 shown in FIGS. 3A, 3B, and 5 may be highly sensitive to any cavity mismatch between the reference cavity 30 and the main cavity 22, and precise cavity length control may be utilized. FIG. 6 schematically illustrates another exemplary HML fiber laser 100 (based on the exemplary HML fiber laser 100 of FIG. 3A) that is only weakly dependent on cavity length mismatch, according to some embodiments described herein. As shown in FIG. 6, the switch 230 (e.g., a mechanical shutter, an optical switch) can first be fully opened to induce an intermittent HML output with a spectrum similar to that shown by the central curve in FIG. 4B. The switch 230 can then be adjusted to substantially reduce feedback from the second mirror 36b (or decrease the Q factor of the reference cavity 30), generating an HML pulse train that is much less sensitive to cavity length mismatch than would be possible if the switch 230 were open. Exemplary switches may include at least one of a mechanical shutter, a MEMS mirror inserted between the beam splitter 32 and the second mirror 36b, an acousto-optic modulator, a polarizing beam splitter, and a rotatable λ / 4 wave plate. In some embodiments, the EOM phase modulator 240 may be modulated at approximately the desired repetition rate of the HML fiber laser 100, as shown in FIG. 6, which may be beneficial in initiating the HML output with a reduced (e.g., minimized) amount of supermode noise. In some embodiments, as shown in FIG. 6, the second photodetector 120b may derive a beat signal f from the interference of the signal from the NALM 110 derived from the coupler 112a and lens 126 with the signal from the cw reference laser 124 via the second beam splitter 128. beat is configured to generate

[0044] The intermittent HML-to-HML transitions may be random, and several shutter / switch cycles may be utilized to ensure the generation of an HML pulse train. However, switching the switch 230 between an open and a partially closed state can be performed at frequencies up to tens of Hz or tens of kHz, and thus, an HML pulse train can still be reliably generated in a very short time. Monitoring the RF power at the desired harmonic as well as the undesired subharmonic can then be used as a reliable indicator of whether HML output is obtainable with the partially closed switch 230. Once HML output is obtainable, in the absence of perturbations, the HML fiber laser 100 can continue to operate at the correct repetition rate and the EO modulator 240 can be turned off. With good thermal control (e.g., control of the system temperature to approximately 10 mK), the HML fiber laser 100 shown in FIG. 6 can be passively stable (e.g., control of the cavity length mismatch between the reference cavity 30 and the main cavity 22 is not used to ensure HML output). Such a passively stable HML system could be useful, for example, as a high-repetition-rate femtosecond pulse source for applications in free-space optical communications. For example, by mounting the second mirror 36b on a PZT, the repetition rate of the HML fiber laser 100 can be further locked to a microwave reference. For added stability, the optical spectrum from the HML fiber laser 100 can be further monitored and used for slow feedback to ensure the relative cavity lengths do not drift apart. In some embodiments, the feedback level from the second mirror 36b can remain fixed and reliable, resulting in self-starting HML operation. Alternatively, the reflectivity of the beam splitter 32 can be selected for optimal self-starting operation.

[0045] In some embodiments, f beatcan be controlled by a PZT 242 as well as an EO phase modulator 240 inside the NALM 110 fiber loop, as shown in Figure 6, allowing for a relatively simple system configuration. In some embodiments, the EO phase modulator 240 can serve two functions: 1) facilitating the initiation of pulses at the correct repetition rate, and 2) providing a fast f beat In some implementations, this allows for rapid adjustment of the cavity length 20 for control. f ceo You can also give them control.

[0046] While the HML fiber laser 100 of FIGS. 3A-3B, 5, and 6 are examples of different cavity configurations that can perform similar functions, other cavity configurations are also compatible with some implementations described herein. For example, FIG. 7A schematically illustrates an exemplary bidirectional sub-cavity 300 according to some embodiments described herein. The exemplary sub-cavity 300 can comprise bulk optical components that can be used for transmission, for example, as part of a ring cavity or within the loop section of the NALM 110 shown in FIGS. 3A-3B, 5, and 6. As shown in FIG. 7A, the sub-cavity 300 can be terminated by first and second retroreflectors 306a and 306b. The input port 302 of the NALM 110 can be directed toward a beam splitter 304, and after reflection from the first retroreflector 306a, the output 308 can be directed back into the NALM 110 after a second reflection from the beam splitter 304. The beam splitter 304 can have a reflectivity in the range of 0.01% to 99%. As explained with respect to FIGS. 2A-2B, the function of the beam splitter 304 is to reduce the reflectivity by Δf ref = N*f0 (e.g., outside the cavity 20 with the beam path labeled transmitted output), but filtering out pulse components that do not satisfy Δf ref= N*f0 are injected back into the main cavity 22. The sub-cavity 300 of Figure 7A is bidirectional and therefore can also be used by reversing the input / output direction towards the NALM 110.

[0047] FIG. 7B schematically illustrates another exemplary all-fiber subcavity 300 according to some embodiments described herein. The exemplary subcavity 300 in FIG. 7B is similar to that in FIG. 7A, except that the beam splitter 304 and retroreflectors 306a, 306b are replaced with a ring cavity 312 (e.g., a fiber loop) and two couplers 314a, 314b, each of which can have a coupling ratio ranging from 0.01% to 99%. The subcavity 300 shown in FIG. 7B can be used to generate pulse trains at repetition rates exceeding approximately 1 GHz and exceeding 10 GHz using a highly compact fiber loop (e.g., a fiber knot). Such high repetition rates can be achieved because increasing the intracavity power in the subcavity 300 can increase the nonlinear phase delay of the HML pulses. Because stable pulse operation in a passively mode-locked laser can be enabled by a minimum nonlinear phase delay for the pulses, the nonlinear subcavity 300 can facilitate the preservation of a large nonlinear phase delay at very high repetition rates, and the reflectivity of the NALM 110 can saturate at relatively small pulse energies. Even larger nonlinear phase delays can be obtained by using a microresonator instead of a fiber loop as the ring or subcavity. For example, a microresonator can replace the fiber ring cavity 312 shown in Figure 7B (e.g., the microresonator can be constructed using two bus waveguides instead of the linear fiber section shown in Figure 7B to couple light into and out of the microresonator).

[0048] The relative lengths between the exemplary sub-cavity 300 shown in Figures 7A and 7B and the main cavity (not shown) can be conveniently controlled using a feedback loop as discussed herein with respect to Figures 3A, 3B, and 5. For example, the spectral content of the system output can be used as an error signal, and an actuator (e.g., PZT, EO modulator) can be included in the sub-cavity 300 as shown in Figure 3A or in the main cavity 22 as shown in Figure 2A for precise length control.

[0049] With the subcavity 300 operable in transmission, a ring cavity or nonlinear loop mirror configured in a figure-eight (F8) configuration can also be used for HML. Figure 8 schematically illustrates an exemplary HML fiber laser 100 having an F8 laser (F8L) configuration according to some embodiments described herein. In some embodiments, the F8L configuration allows for minimization of the nonlinear phase delay used for saturation of the reflectivity of the NALM 110 (e.g., similar to that discussed herein with respect to Figure 5) and can be implemented to lower the pulse energy used for operation at very high repetition rates. The exemplary F8L configuration shown in Figure 8 includes the NALM 110 to the right of the four-port coupler 112a. Unidirectional propagation between coupler leads E1 and E2 can be ensured by an isolator 340. The coupler ratio x / (1-x) of the coupler 112a can range from 5 / 95% to 50 / 50%. The NALM 110 can include a nonreciprocal phase shifter (NRP) 250 configured to generate a linear phase bias between two counter-propagating pulses inside the NALM 110, an amplifier 260 positioned asymmetrically inside the NALM 110, and a subcavity 300 as described herein with respect to FIGS. 7A and 7B. The NALM 110 can be pumped by a pump laser 272 through a coupler 270 and can also include an additional PZT fiber stretcher and EO modulator for fiber length adjustment (not shown). The NALM 110 of the HML fiber laser 100 shown in FIG. 6 also includes the NRP 250, amplifier 260, coupler 270, and pump laser 272, as shown in FIG. 8.

[0050] 9A-9C schematically illustrate various exemplary subcavities 300 according to some embodiments disclosed herein. The subcavity 300 of FIG. 9A is substantially equivalent to the subcavity 300 of FIG. 7B and uses a nonlinear fiber cavity to generate an HML output. At least one of the two couplers 314a, 314b of the subcavity 300 of FIG. 9A can comprise a dual-fiber four-port coupler based on standard low-cost fiber components used in optical communications. In some embodiments, at least one of the two couplers 314a, 314b comprises a beam splitter 322 and two gradient index (GRIN) lenses 320a, 320b (e.g., approximately quarter-period GRIN lenses) on either side of the beam splitter 322. In some other embodiments, at least one of the two GRIN lenses 320a, 320b is replaced by a collimating lens (not shown). 9A, the first coupler 314a includes a first dual-core fiber 330a (e.g., a twin-core fiber) configured to be the input port 302 to the first coupler 314a from the NALM 110 and the transformer output from the first coupler 314a, a second dual-core fiber 330b (e.g., a twin-core fiber) configured to be the first port 340a and the second port 340b of the ring cavity 312, a third dual-core fiber 330c (e.g., a twin-core fiber) configured to be the third port 340c and the fourth port 340d of the ring cavity 312, and a fourth dual-core fiber 330d (e.g., a twin-core fiber) configured to be the output 308 back to the NALM 110. 9A, the core separation between the two cores is increased for illustrative purposes only. In practice, a section (e.g., a single section) of dual-core fiber can be used for the ring cavity 312, with the two cores spatially separated from each other.The dual-core fiber input and output can be spatially separated only upstream and downstream of the device, as shown in Figure 9A, for easy splicing to external fiber pigtails. In some embodiments, the ring cavity 312 for the second dual-core fiber 330b and the third dual-core fiber 330c can be replaced by a single twin-core fiber section.

[0051] The input from the NALM 110 may then be injected into the input port 302 of, for example, the dual-core fiber 330a and collimated by a quarter-period grin lens 320a. A beam splitter 322 may then direct the signal into the fiber ring cavity 312 via a second grin lens 320b, and the beam splitter 322 of the first coupler 314a may also direct the transmitted output out of the fiber ring cavity 312. The fiber ring cavity 312 may be bounded by the beam splitters 322 of the first coupler 314a and the second coupler 314b. The two grin lenses 320a, 320b of the second coupler 314b may perform a similar function compared to the two grin lenses 320a, 320b of the first coupler 314a. The output 308 from the fiber ring cavity 312 can be taken out of one of the fiber ends of the dual-core fiber 330d and returned to the NALM 110. The configuration of FIG. 9A can be configured to facilitate the use of very short lengths of fiber for the sub-cavity, suitable for repetition rates in the range of 1 GHz to 10 GHz.

[0052] FIG. 9B schematically illustrates another exemplary subcavity 300 according to some embodiments described herein. The subcavity 300 of FIG. 9B can be operated in a transmit mode substantially equivalent to the subcavity 300 illustrated in FIG. 7A. Instead of retroreflectors 306a and 306b, the subcavity 300 of FIG. 9B includes two beam splitters 350a and 350b and a total reflector 352. In FIG. 9B, the input port 302 of the NALM 110 is designated IL, the transmitted output is designated TO, and the output 308 returns to the NALM 110 as OL. The subcavity 300 may be bidirectional and then used within the loop section of the NALM 110 for the HML output. In bidirectional operation, port IL can also serve as a port directing backward pulses back to the NALM 110, and port OL can serve as a port receiving input from the backward pulses from the NALM 110. In some embodiments, the subcavity 300 shown in FIG. 9B can be made completely monolithic for maximum stability, as illustrated schematically by FIG. 9C. In some embodiments, the two beam splitters 350a, 350b and the total reflector 352 are replaced with a prism 360, whose outer surfaces provide reflective or partially reflective surfaces. In the exemplary subcavity 300 shown in FIG. 9C, the polarization of the input pulse can be selected to be S-oriented to increase the reflectivity of the prism surfaces. One surface of the prism 360 can be HR-coated, as shown, if only unidirectional operation is desired. For bidirectional operation, all surfaces can remain uncoated. Other geometries for the monolithic reference subcavity 300 can be used.

[0053] A highly monolithic cavity may offer maximum stability with limited flexibility. FIG. 9D schematically illustrates an exemplary HML fiber laser 100, in which a compromise between these two requirements is provided in accordance with some embodiments described herein. The reference cavity 30 is substantially equivalent to the reference cavity 30 shown in FIG. 3A, 3B, or 6 in that the reference cavity 30 comprises and is bounded by a first mirror 36 a and a second mirror 36 b. The beam splitter 32 comprises a fiber-based beam splitter, as compared to the beam splitter 32 of FIGS. 3A, 3B, and 6, which comprises a bulk-optic beam splitter. The first output 280a (e.g., equivalent to the transmitted output 153 in FIG. 3A) can couple light from the out-of-phase coupled cavity system, and the second output 280b (e.g., equivalent to the rejected output 113 in FIG. 3A) can couple rejected light from the NALM 110. Similar to FIG. 3A, the first output 280a or the second output 280b can further be used for feedback control, which is not shown in FIG. 9D. The reference cavity 30 in FIG. 9D is part of a fiber subassembly 370, which further includes a collimating lens 372 and a f ceo and f beat The fiber subassembly 370 includes a plurality of actuators 374 for control, including, for example, a first actuator 374a (e.g., an EOM) and a second actuator 374b (e.g., an EOM), as described herein with respect to FIG. 3A . The second mirror 36b can further be mounted on a PZT controller (not shown) for slow repetition rate control or slow control of the relative lengths of the main cavity 22 and the reference cavity 30. Operation at a fixed repetition rate can be achieved, for example, by controlling the reference cavity length via the second mirror 36b. The fiber subassembly 370 can be integrated into a very small form factor and constructed with minimal sensitivity to vibration. Furthermore, the thermal expansion coefficients of the main cavity 22 and the reference cavity 30 can be closely matched, resulting in a very stable system configuration.

[0054] FIG. 9E schematically illustrates another exemplary HML fiber laser 100 including a reference cavity 30 according to some embodiments described herein. The NALM 110 in FIG. 9E may be the same as that in FIG. 9D , except that instead of the transmissive beam splitter 32 in FIG. 9D , the reference cavity 30 includes a reflective collimator / beam splitter (CO / BS) assembly 373. Similar to FIG. 9D , a first output 280 a can couple out the out-of-phase components of the HML fiber laser 100, and a second output 280 b can output the rejected output from the NALM 110, which can also be used for feedback control (not shown in FIG. 9E ). Also, instead of an all-fiber reference cavity 30, the reference cavity 30 in FIG. 9E includes a combination of fiber and bulk optical components (e.g., fiber and free-space propagation is used). The CO / BS assembly 373 can be constructed from micro-optics and can collimate the beam from a fiber pigtail 376 attached to port E1 and reflect a small portion of that beam to the first mirror 36a. The reflectivity of the CO / BS assembly 373 can be in the range of 10% to 50%, although other values ​​are possible. The free-space beam is shown by the dashed line. The first mirror 36a can also be mounted on a mechanical stage for additional repetition rate adjustment. The beam transmitted through the CO / BS assembly 373 can then be directed to the second mirror 36b, which can be mounted on a PZT (not shown) and stage (not shown) for medium- and low-bandwidth repetition rate adjustment. The first actuator 374a and second actuator 374b can further be inserted for high-bandwidth repetition rate adjustment and high-bandwidth loss adjustment within the reference cavity 30, which can be used to adjust the high-bandwidth f of the HML fiber laser 100. ceoThis exemplary HML fiber laser 100 is highly compact and low-cost, and can provide a frequency comb operating at repetition rates of 1 GHz or greater. In some embodiments, the subassembly 282 includes an integrated reference cavity 30 (e.g., including the first and second mirrors 36a, 36b, the CO / BS assembly 373, and the first and second actuators 374a, 374b) in a relatively small package.

[0055] Although the exemplary HML fiber laser 100 of some embodiments includes a nonlinear amplifying loop mirror as the primary mode-locking mechanism, other mode-locking mechanisms may be used in some other embodiments, such as a standard loop mirror without an in-loop amplifier, or any type of saturable absorber (e.g., as described in U.S. Patent 7,088,756 (Fermann et al.), including carbon nanotubes, etc.).

[0056] In some embodiments, an HML fiber laser 100 as described herein is configured to be used as a precision frequency standard. Figures 10A-10C schematically illustrate an exemplary frequency reference 400 based on an HML fiber laser 100 (e.g., similar to those described herein with respect to Figures 2A-2B, 3A, 3B, and 5) according to some embodiments described herein. In Figures 10A-10C, the first and second mirrors 36a and 36b, and the beam splitter 32, are all mounted on a zero-thermal expansion substrate 410 (e.g., a spacer), which may comprise, for example, ULE®, available from Corning, Corning, NY, or Zerodur®, available from Schott North America, Inc., Rye Brook, NY. The reference cavity 30 shown in Figures 10A-10C can be connected to the main cavity 22 via a beam splitter 32, as described herein with respect to Figures 2A-2B, 3A, 3B, and 5, and transmitted light from the reference cavity 30 can also be obtained via the beam splitter 32. The use of a zero-thermal expansion material for the substrate 410 can improve the frequency stability of the HML fiber laser 100, enabling the generation of an ultra-stable full frequency comb with individual comb linewidths of less than 10 Hz, or even less than 1 Hz, without the need for an external reference cavity (e.g., an external reference cavity as used in conventional frequency comb technology). To ensure ultra-high frequency stability, the reference cavity 30 can be used as a frequency reference, and the main cavity 22 can be locked to the reference cavity 30 using an appropriate fiber stretcher and modulator within the main cavity 22.

[0057] For additional stability, other substrates (not shown) can be attached to the top and sidewalls of the first mirror 36a and second mirror 36b in FIG. 10A, leaving holes for the input and output light beams. The holes can also be covered with optical windows, and the reference cavity 30 can be evacuated for increased stability. As shown in FIGS. 10B and 10C, the substrate 410 can comprise a hollow block (e.g., containing ULE® or Zerodur®) configured to be used as an ultra-high stability spacer. For example, the first mirror 36a and second mirror 36b can be attached to the block via optical contact. The substrate 410 can also be designed with holes that allow for positioning and fixation of the beam splitter 32 within it. To avoid potential instability due to the beam splitter 32 being positioned between the first mirror 36a and the second mirror 36b, some embodiments can have the beam splitter 32 positioned around the periphery of the substrate 410 (e.g., a spacer block), as shown in FIG. 10C. The substrate 410 in Figure 10C may include a hollow section for beam propagation (e.g., as shown in Figure 10B). The first and second mirrors 36a, 36b and the beam splitter 32 may be attached to the substrate 410 via optical contact (e.g., for maximum stability). To increase the manufacturing tolerance of the L-shaped reference cavity 30 in Figure 10C (e.g., having an approximately 90-degree angle between the two beams in the reference cavity 30), at least one of the three mirrors (e.g., the first mirror 36a, the second mirror 36b, and the beam splitter 32) may be curved with a finite radius of curvature.

[0058] In some embodiments, a V-shaped reference cavity 30 can be used, where the angle between the two beams in the reference cavity 30 is less than 90 degrees. Ultrastable V-shaped cavities 30 have previously been used as frequency references, for example, to reduce the linewidth of cw lasers (see, e.g., N. Jobert et al., "High stability in near infrared spectroscopy: part 2, optomechanical analysis of an optically contacted V-shaped cavity," Appl. Phys. B. 128:56 (2022)).

[0059] However, conventional fabrication techniques used for the ultra-stable reference cavity 30 to produce a V-shaped ultra-stable cavity may not be applicable because conventional reference cavities typically use only two mirrors. Figure 10D schematically illustrates an exemplary V-shaped reference cavity 30 comprising a reflector 420 (e.g., a mirror) and a beam-splitting mirror 422 according to some embodiments described herein. Such a reference cavity 30 can be compatible with ultra-high stability cavity designs known in the prior art (see, e.g., YY Jiang et al., "Making optical atomic clocks more stable with 10-level laser stabilization," Nature Photonics, volume 5, pp. 158-161 (2011)) and can be fabricated at a relatively low cost.

[0060] As shown in FIG. 10D , both the reflector 420 and the beam-splitting mirror 422 can be concentric with one another, and the input (solid arrow) from the main laser cavity 20 can enter through the beam-splitting mirror 422 at an angle α / 2 from the main axis of the beam-splitting mirror 422 and strike the reflector 420 at an offset d from the main axis. The reflector 420 can then be configured to reflect the input beam back onto itself, and the beam transmitted by the beam-splitting mirror 422 can then return to the main cavity 22, and the beam reflected by the beam-splitting mirror 422 (dashed arrow) can return to the reflector 420 at an angle −α / 2 and strike the reflector 420 at an offset −d. The reflection from the reflector 420 can then reflect back onto itself or be directed back to the beam-splitting mirror 422, and the process can repeat. The beam transmitted at the beam-splitting mirror 422 can be a transmitted output beam, as described herein with respect to FIGS. 10A-10C . The two-mirror V-shaped cavity 30 shown in FIG. 10D can provide a reference cavity 30 with improved mechanical stability that can be used for ultrastable harmonic mode-locking. Furthermore, the two-mirror V-shaped cavity 30 can be used for other applications, such as improving the configuration of reference cavities used for line narrowing of cw diode lasers, as discussed by N. Jobert et al. In certain other embodiments of the two-mirror V-shaped cavity 30, one of the reflector 420 and the beam-splitting mirror 422 can be curved, while the other can be flat. Some such embodiments can use at least one mirror with a highly reflective (HR) coating around its periphery and partially transmissive in the central section. The reflector 420 and the beam-splitting mirror 422 can be optically contacted with a spacer material that has a central region removed to allow beam propagation in air or vacuum.

[0061] An ultra-stable reference cavity can also be constructed without an intra-cavity actuator; however, the main cavity 22 can be locked to the reference cavity 30 by including an actuator into the main cavity 22 or in the beam path between the main cavity 22 and the reference cavity 30. For example, if a high-bandwidth EO modulator is provided within the main cavity 22, the cavity length can be modulated at a frequency of several MHz, as described herein with respect to FIG. 6 , and detection of the output of the reference cavity 30 and mixing the output signal with the modulated signal can then generate an error signal for matching the length of the main cavity 22 to the reference cavity 30 (e.g., similar to the Pound-Drever-Hall cavity locking technique). In some embodiments, the f ceo can be controlled, for example, by controlling the pump power to a fiber amplifier that is part of the main cavity 22. Other configurations are possible.

[0062] The exemplary reference cavity 30 shown in FIGS. 10A-10C has a frequency of f beat or f ceo It may be configured for construction of an HML pulse source that does not utilize controls and uses standard silica substrates to save cost. To enable locking of the repetition rate of such a source to an external microwave reference, at least one of the first and second mirrors 36a and 36b and the beam splitter 32 may be mounted on a PZT for precise cavity length control.

[0063] As described herein with respect to FIG. 9E, some embodiments of the HML fiber laser 100 utilize f ceo10E is a schematic diagram of an exemplary HML fiber laser 100 according to some embodiments described herein. The HML fiber laser 100 includes a main cavity 440 (e.g., a nonlinear amplifying loop mirror) on the left side including an Er gain fiber 442, a coupler 444 (e.g., 50 / 50) coupled to a V-cavity 450 (e.g., including a first mirror 452a and a second mirror 452b) on the right side, and utilizes an imaging system (e.g., represented by a lens 454) to focus the output from the intracavity pigtail 456 onto the first partially reflective mirror 452a. ceo To facilitate locking, the output from the HML fiber laser 100 (e.g., extracted by a tap 458) can be directed to an f-2f interferometer (not shown). In some embodiments, at least one PZT fiber stretcher 446 is included for length control of the main cavity 440. PZT stretchers 446 with different operating bandwidths can be easily implemented. The HML fiber laser 100 of FIG. 10E further comprises a pump laser 448 and a wavelength division multiplexer (WDM) 449.

[0064] f ceo In some embodiments with locking (e.g., via control of pump current), the relative cavity length between the V-cavity 450 and the main cavity 440 can also be stabilized. As a result, the main cavity 440 is responsible for the stability of the V-cavity 450, allowing for the generation of output pulse trains with extremely stable repetition rates. For a V-cavity 450 comprising an ultra-low expansion material (e.g., ULE® or Zerodur® glass), repetition rate stability can be as high as 1×10 1 / s. ―15 The stability can be further optimized by inserting at least the V-cavity 450 into a vacuum chamber. The linewidth of the comb mode can be reduced by implementing a relatively high reflectivity (e.g., greater than 70%) for the first mirror 452a and reducing the frequency space to f ceocan be further reduced (e.g., minimized) by optimizing the location of the frequency. In some embodiments, the individual comb line widths are less than 1 kHz (e.g., less than 100 Hz; less than 10 Hz, substantially lower than is possible with standard frequency combs). In some embodiments, since the comb modes are essentially locked to the reference cavity 30, f beat No locking is utilized. The exemplary HML fiber laser 100 shown in Figure 10E is particularly attractive for ultra-low noise microwave generation, as described with respect to Figure 11.

[0065] In some embodiments, the V-cavity 450 shown in FIGS. 10D and 10E or the reference cavity 30 shown in FIGS. 3A and 3B may not be optimal for generating very high repetition rates, as some applications also utilize ultra-high bandwidth control of the cavity length. FIG. 10F schematically illustrates an exemplary HML fiber laser 100 in which the V-cavity 450 of FIG. 10E or the reference cavity 30 of FIGS. 3A and 3B is replaced with a monolithic V-cavity 470 (e.g., operatively integrated with an electro-optic modulator) according to some embodiments described herein. FIG. 10G schematically illustrates an exemplary monolithic V-cavity 470 according to some embodiments described herein. FIG. 10F schematically illustrates a top view of the monolithic V-cavity 470 of FIG. 10G. In some embodiments, the monolithic V-cavity 470 can be fabricated from a block of electro-optic material, such as a lithium niobate (LN) crystal. As shown in Figure 10G, the input polarization of the incident light and the optical axis of the electro-optic material can be parallel to each other. Electrodes (not shown) can be deposited on the top and bottom of the electro-optic material to enable electro-optic modulation by applying a voltage that creates an electric field in the same direction as the optical axis of the electro-optic material. As a result, rapid modulation of the optical path length within the electro-optic material can be generated, which allows for high bandwidth f ceo or f beatThis can be used for control (e.g., utilizing additional detectors and additional feedback loops as described with respect to FIG. 3B). The resulting operating bandwidth can be on the order of 1 MHz or even higher, which is in line with the f derived from the HML fiber laser 100. ceo or f beat The timing jitter and / or phase noise of the signal may be reduced (eg, minimized).

[0066] The optical beam path inside the monolithic V-cavity 470 can be similar to that of the V-reference cavity 30 in FIG. 10D or the V-cavity 450 in FIG. 10E. The front mirror can be flat, and the input from the main cavity 22 can enter the monolithic V-cavity 470 at an angle α / 2 from the surface normal. Refraction of the input beam at the crystal's front mirror surface is omitted here for simplicity. After reflection from the curved rear crystal surface of the monolithic V-cavity 470, the beam transmitted by the front surface can return to the main cavity 22, and the beam reflected from the front surface can return to the curved surface at an angle -α / 2 and impinge on the curved surface. The reflection from the curved rear surface can then reflect back onto itself or be directed back to the front surface, and the process can be repeated. FIG. 10G schematically shows a lithium niobate crystal with a flat front surface and a rear surface shaped as a cylindrical lens, which can be easy to fabricate. In some other embodiments, a spherical back facet and a spherical front facet may be used. The HML fiber laser 100 shown in Figure 10F may be particularly useful for generating very high repetition rates (e.g., in the range of 1 GHz to 10 GHz, or even higher), where inserting a separate electro-optic crystal for high-bandwidth cavity length modulation of the reference cavity 30 is difficult.

[0067] A frequency reference based on the HML fiber laser 100 as described herein can have many applications; for example, the output of the HML fiber laser 100 can be used for ultra-low noise microwave generation, as shown in FIG. 11 . The optical output of the HML fiber laser 100 can be a frequency reference directed to a high-saturation current photodetector 430 (e.g., a uni-traveling-carrier (UTC) photodiode) that converts the optical pulse train into a microwave signal at the pulse repetition rate and its harmonics. For example, to generate an ultra-low noise microwave signal at 10 GHz, an HML fiber laser 100 operating at 2.5 GHz can generate 10 GHz as a fourth harmonic of the pulse repetition rate. In contrast to previously disclosed RF sources based on passively mode-locked fiber frequency combs (e.g., operating at 250 MHz), some embodiments described herein do not utilize pulse train interleaving due to the much higher pulse repetition rate of the HML fiber comb. Additionally, because the HML fiber laser 100 can be its own frequency reference, some embodiments described herein do not utilize a cw laser locked to an ultra-high Q reference cavity. Some embodiments described herein achieve substantial improvements over previously disclosed systems (e.g., those described in X. Xie, Nature Photonics, vol. 11, pp. 44-47 (2017) or M. Kalubovilage et al., “X Band photonic microwaves with phase noise below −180 dBc / Hz using a free-running monolithic comb,” Optics Express, Vol. 30, Issue 7, pp. 11266-11274 (2022)).In some embodiments, the HML fiber laser 100 described herein provides excellent ultra-low noise performance with low frequency offset and compact system configuration, while reducing (e.g., minimizing) the use of optical amplification and pulse interleaving with their associated noise issues (e.g., as used in both the Xie et al. and Kalubovilage et al. systems).

[0068] In some embodiments, higher microwave frequencies can be generated by filtering harmonics of the pulse repetition rate or by filtering appropriate optical comb lines and interfering them on a photodetector. Figure 12 schematically illustrates an exemplary millimeter-wave source 500 based on the HML fiber laser 100 described herein. In some embodiments, the frequency reference output of the HML fiber laser 100 can be directed into a circulator 510 and split into two portions by a coupler 512. The two portions can then be used to injection-lock two different laser diodes 514a, 514b (e.g., two different distributed feedback (DFB)) lasers) to select and amplify the two different comb lines, which are then recombined and directed through the circulator 510, ultimately interfering on a photodetector 430, which can convert the beat signal into the millimeter-wave or THz frequency domain.

[0069] In some embodiments, the HML fiber laser 100 can act as a universal frequency synthesizer for ultra-low noise microwave and millimeter-wave frequencies. Optical frequency synthesis may equally be possible using a setup such as that shown in FIG. 12, in which only one laser diode may be used for frequency selection and amplification. Frequency tuning of the optical synthesizer can be performed using an actuator within the HML fiber laser 100. Operation of previously disclosed mode-locked fiber lasers as universal frequency synthesizers is much more challenging due to the small comb spacing and much lower power per mode. In some embodiments, the universal frequency synthesizers described herein offer improved performance compared to previously disclosed systems.

[0070] In some embodiments, frequency downconversion from the millimeter-wave frequency range (e.g., 100 GHz to 1 THz) to the microwave range may also be of interest. Such a frequency downconversion system is disclosed in U.S. Patent 11,409,185 (Kuse et al.), and the use of the HML fiber laser 100 described herein can be used for frequency downconversion. FIG. 13 schematically illustrates an exemplary system 600 for frequency downconversion based on the HML fiber laser 100 to convert millimeter-wave signals to microwave signals, according to some embodiments described herein.

[0071] The input to the downconverter can be obtained from two optical cw nodes 602 (e.g., laser wavelengths) separated by a desired frequency interval, for example, in the range of 100 GHz to several THz. To downconvert the millimeter-wave beatnote to the RF domain, the HML fiber laser 100 can operate at a repetition rate of approximately 1 GHz to several GHz. To phase-lock the HML fiber laser 100 to the millimeter-wave beatnote, for example, the photodetector 610 can detect the two beats of the two cw nodes with the closest adjacent comb lines from the HML fiber laser 100.

[0072] The two beats can be filtered in the RF domain by two RF bandpass filters (RFBPs) 612a, 612b. The two beats can then be mixed by a mixer 614 to generate a secondary beat signal. The mixer 614 can reduce or remove the carrier-envelope offset frequency of the HML fiber laser 100 from the secondary beat signal. The secondary beat signal can then be mixed with a local oscillator 616 (e.g., at a frequency of 10 MHz) by a mixer 615 to generate an error signal via a PID controller 618 that is fed back to a repetition rate controller within the HML fiber laser 100 (e.g., the PZT and EOM inside the reference cavity 30, as shown in FIG. 9E). The inter-modal beat frequency from the HML fiber laser 100 can be detected by a photodetector 619, generating an ultra-stable output at the repetition rate of the HML fiber laser 100. In some such embodiments, two wavelengths from two cw nodes separated by hundreds of GHz are used to stabilize the repetition rate of the HML fiber laser 100. Thus, the repetition rate of the HML fiber laser 100 can carry the differential phase noise of the two cw nodes with a frequency separation of hundreds of GHz. In other words, the frequency stability of the HML repetition rate can be the same (or nearly the same) as the stability of the differential frequency between two cw nodes separated by hundreds of GHz.

[0073] In some embodiments, the HML fiber laser 100 is used for dual-comb spectroscopy because the built-in reference cavity 30 can greatly improve the stability of the output pulse train. Additionally, operation at GHz repetition rates can improve the signal acquisition speed for dual-comb spectroscopy compared to conventional mode-locked fiber combs operating with mode spacing in the 100 MHz to 200 MHz range. In some embodiments, two HML fiber combs operating at slightly different repetition rates can be configured for efficient dual-comb spectroscopy. A dual-comb system is described in U.S. Patent 8,699,532 (Fermann et al.).

[0074] In some embodiments, the HML fiber laser 100 uses only one reference cavity 30 for dual-comb operation, which can reduce differential noise between the two HML combs through common-mode noise suppression. Figure 14 schematically illustrates an exemplary system 620 having two HML fiber combs (e.g., a first fiber comb 622a and a second fiber comb 622b) referenced to a common reference cavity 30, according to some embodiments described herein. For example, the two fiber combs 622a, 622b can be configured as described with respect to Figure 10E. The fiber combs 622a, 622b can be configured to operate on two different polarization axes, thus enabling simultaneous coupling of both combs 622a, 622b to the common reference cavity 30 via a polarizing beam splitter (PBS) 624. The reference cavity 30 (eg, V-cavity 450) may include birefringent optics (BO) 626 (eg, waveplates) to ensure operation of the two combs 622a, 622b at slightly different repetition rates.

[0075] In some embodiments, the HML fiber laser 100 can provide dual-comb operation with a common fiber cavity and a common reference cavity 30, which can further reduce differential noise between the two HML combs 622a, 622b through common-mode noise suppression. For example, dual-comb operation in a single fiber cavity was described in P.E. Collin Aldia, “Detection of carbon monoxide using a polarization multiplexed erbium dual-comb fiber laser,” Journal of Physics: Photonics, vol. 6, (2024) 045017. However, this system was susceptible to noise from non-common-mode fiber sections, and providing HML or common-mode noise suppression via an integrated reference cavity was not suggested.

[0076] FIG. 15 schematically illustrates an exemplary configuration 630 of two common HML fiber combs 622a, 622b referenced to a common reference cavity 30, according to some embodiments described herein. FIG. 15 is essentially a combination of the HML fiber laser 100 shown in FIG. 5 and the exemplary system 620 shown in FIG. 14. The configuration 630 includes two main fiber cavities operating along orthogonal polarization directions constructed from a single polarization-maintaining fiber loop 632. The fiber loop 632 also includes a fiber amplifier (not shown) for lasing. For simplicity, FIG. 15 illustrates the fiber loop 632 as a line connecting two pigtail ends 634a, 634b of the fiber loop 632 (e.g., illustration of a coupler, fiber amplifier, or fiber stretcher within the loop is omitted). As shown in FIG. 15, the pigtail ends are connected upstream of the pigtail ends 634a, 634b to form the fiber loop 632. The outputs of the two pigtail ends 634a, 634b may be collimated and directed to a polarization splitting subassembly (PSSA) 636. The PSSA 636 includes multiple polarizing beam splitters (PBSs) 638 and multiple mirrors 640. The first PBS 638a splits the two polarized waves propagating clockwise in the fiber loop 632 into their polarization components P1+ and P2+, and the second PBS 638b splits the two polarized waves propagating counterclockwise in the fiber loop 632 into their polarization components P1− and P2−. P1+ and P2− are then polarization-coupled via the fourth PBS 638d, and P2+ and P1− are then polarization-coupled via the third PBS 638c. By appropriately positioning the first PBS 638a, the first mirror 640a, the fourth mirror 640d, and the fourth PBS 638d, the optical path lengths of P1+ and P2− (e.g., from the fourth PBS 638d along the fiber loop 632 back to the fourth PBS 638d) can be made approximately equal. Thus, P1+ and P2− can nonlinearly interfere in the fifth PBS 638e using the first polarization control assembly 642a (see, e.g., FIG. 5 ) to induce short pulse formation.

[0077] Similarly, P2+ and P1− can be nonlinearly interfered to induce short pulse formation in orthogonal polarizations using a second polarization control assembly 642b, which includes another set of a Faraday rotator, a half-wave plate, a λ / 4 wave plate, and a polarizing beam splitter (not shown). In Figure 15, the optical paths of P1+ and P2− are shown by long-dashed lines, and the optical paths of P2+ and P1− are shown by dotted lines.

[0078] In some such embodiments, the exemplary configuration 630 can be simultaneously mode-locked along two different polarization directions with slightly different repetition rates. The PSSA 636 can be fabricated with micro-optical components, resulting in a very small form factor.

[0079] The PSSA 636 can generate two outputs, Output 1 and Output 2, which can be configured to have orthogonal polarizations. As described with respect to FIG. 14 (although not shown in FIG. 15), the two polarization directions can be combined via a beam splitter and coupled into a single reference cavity containing birefringent optics (BO) to generate two frequency combs operating at slightly different repetition rates for dual-comb spectroscopy. To ensure that the optical path lengths of the two different polarization directions coupled into the single reference cavity are appropriate harmonics of the optical path length within the reference cavity, additional delay stages (not shown) can be inserted between the third PBS 638c and the second polarization control assembly 642b, and between the fourth PBS 638d and the first polarization control assembly 642a. Because the exemplary configuration 630 can benefit from common-mode noise suppression in both the fiber loop 632 and the reference cavity 30, the exemplary configuration 630 can also utilize the differential f of the two combs 622a, 622b. ceo and f rep This can be utilized for dual-comb spectroscopy with minimal stabilization.

[0080] In some embodiments, output wavelengths from the HML fiber laser 100 that are different from the constraints of the gain material can be used (e.g., utilizing nonlinear wavelength conversion). In the HML fiber laser 100 disclosed herein, wavelength conversion can be conveniently performed when using the reference cavity 30 as an optical parametric oscillator (OPO). The HML fiber laser 100 can be configured as an OPO by adding a nonlinear crystal such as periodically poled lithium niobate, a curved mirror to establish a focal point inside the nonlinear crystal, and optical components to generate output from the OPO, and by selecting appropriate optical materials and coatings for the wavelengths of interest.

[0081] FIG. 16 schematically illustrates an exemplary HML fiber laser 100 configured as an OPO according to some embodiments described herein. The reference cavity beam splitter can be positioned to avoid passage through the substrate in the reference cavity. In the case of a nonlinear crystal made of lithium niobate, a fast actuator in the form of an EOM made of lithium niobate can also be added to the reference cavity. Such an EOM can transmit the same wavelengths as the nonlinear crystal. In some embodiments, stable operation can also be obtained without an EOM. In FIG. 16, the output coupler can be a coated end mirror configured to pass some of the converted light. Compared to other intracavity OPOs, some embodiments can allow for different OPO and main laser cavity lengths, higher intensity in the OPO cavity than in the main laser cavity, and can utilize a pump beam already resonating with the OPO cavity for harmonic modelocking.

[0082] Although various exemplary embodiments described herein may be based on erbium-doped fiber amplifiers, other fiber amplifier materials may equally be used in accordance with some embodiments described herein (e.g., fiber amplifiers comprising Yb, Tm, and Nd). In some embodiments, harmonically modelocked frequency combs as disclosed herein can also be constructed from bulk solid-state lasers or semiconductor diode lasers (e.g., solid-state or semiconductor gain media).

[0083] Exemplary, non-limiting experimental data is included herein to illustrate results achievable by various implementations of the systems and methods described herein. All data ranges shown or described herein, and all values ​​within such data ranges, are expressly included in this disclosure. The exemplary experiments, experimental data, tables, graphs, plots, figures, and process and / or operating parameters (e.g., values ​​and / or ranges) described herein are intended to be illustrative of the operating conditions of the disclosed systems and methods and are not intended to limit the range of operating conditions for various implementations of the methods and systems disclosed herein. In addition, the experiments, experimental data, computational data, tables, graphs, plots, figures, and other data disclosed herein demonstrate various regimes in which implementations of the disclosed systems and methods may effectively operate to produce one or more desired results. Such operating regimes and desired results are not limited solely to the particular values ​​of operating parameters, conditions, or results shown, for example, in a table, graph, plot, or figure, but also include suitable ranges that include or span these particular values. Thus, values ​​disclosed herein include ranges of values ​​between any of the values ​​listed or shown in a table, graph, plot, figure, etc. Additionally, values ​​disclosed herein include ranges of values ​​above or below any of the values ​​listed or shown in a table, graph, plot, diagram, etc., as may be demonstrated by other values ​​listed or shown in a table, graph, plot, diagram, etc. Also, while the data disclosed herein may establish one or more effective operating ranges and / or one or more desired results for particular embodiments, it is understood that not all embodiments need be operable within each such operating range or produce each such desired result. Moreover, other embodiments of the disclosed systems and methods may operate in other operating regimes and / or produce other results other than those shown and described with reference to the exemplary experiments, experimental data, tables, graphs, plots, diagrams, and other data herein.

[0084] The present invention has been described in several non-limiting embodiments. It should be understood that the embodiments are not mutually exclusive, and that elements described in connection with one embodiment can be combined with, rearranged from, or eliminated from other embodiments in a manner suitable to achieve the desired design objectives. No single feature or group of features is necessary or required in each embodiment.

[0085] For purposes of summarizing the invention, certain aspects, advantages, and novel features of the invention are described herein. It should be understood, however, that not necessarily all such advantages may be achieved in accordance with any particular embodiment. Thus, the invention may be embodied or performed to achieve one or more advantages without necessarily achieving other advantages that may be taught or suggested herein.

[0086] As used herein, a reference to “one embodiment” or “some embodiments” or “an embodiment” means that a particular element, feature, structure, or characteristic described in connection with an embodiment is included in at least one embodiment. The appearances of the phrase “in one embodiment” in various places in the specification do not necessarily all refer to the same embodiment. While commonly used terms are used to describe the systems and methods of particular embodiments for ease of understanding, these terms are used herein to have their broadest reasonable interpretation. Various aspects of the present disclosure are described in terms of illustrative examples and embodiments, but the disclosed examples and embodiments should not be construed as limiting. In particular, conditional language used herein, such as “can,” “could,” “might,” “may,” “e.g.,” etc., is intended to generally convey that some embodiments include certain features, elements, and / or steps, while other embodiments do not, unless specifically stated otherwise or understood otherwise within the context of use. Thus, such conditional language is not generally intended to imply that features, elements, and / or steps are in any way required by one or more embodiments, or that one or more embodiments necessarily include logic for determining whether those features, elements, and / or steps are included or should be performed in any particular embodiment, with or without user input or prompting.

[0087] As used herein, terms of degree, such as "approximately," "about," "generally," and "substantially," refer to a value, amount, or characteristic that is close to the stated value, amount, or characteristic that still performs a desired function or achieves a desired result. For example, the terms "approximately," "about," "generally," and "substantially" can refer to an amount that is within ±10%, ±5%, ±2%, ±1%, or ±0.1% of the stated amount. As another example, the terms "nearly parallel" and "substantially parallel" refer to a value, amount, or characteristic that is ±10 degrees, ±5 degrees, ±2 degrees, ±1 degree, or ±0.1 degrees away from exact parallelism, and the terms "nearly perpendicular" and "substantially perpendicular" refer to a value, amount, or characteristic that is ±10 degrees, ±5 degrees, ±2 degrees, ±1 degree, or ±0.1 degrees away from exact perpendicularity. Ranges disclosed herein also encompass any and all overlaps, subranges, and combinations thereof. Terms such as "up to," "at least," "greater than," "less than," "between," and the like, include the recited numbers. Furthermore, the articles "a" or "an" or "the" as used in this application and the appended claims should be construed to mean "one or more" or "at least one" unless otherwise specified.

[0088] As used herein, the terms "comprises," "comprising," "includes," "including," "has," "having," or any other variation thereof, are open-ended terms and are intended to encompass a non-exclusive inclusion. For example, a process, method, article, or apparatus that includes a list of elements is not necessarily limited to only those elements and may include other elements inherent to such process, method, article, or apparatus that are not explicitly listed. Furthermore, unless expressly stated to the contrary, "or" refers to neither inclusive nor exclusive. For example, condition A or condition B is satisfied by either A being true (or present) and B being false (or absent), or A being false (or absent) and B being true (or present), or both A and B being true (or present). As used herein, a phrase referring to "at least one of" a list of items refers to any combination of those items, including single members. As an example, "at least one of A, B, and C" is intended to encompass A, B, C, A and B, A and C, B and C, and A, B, and C. Connecting language such as "at least one of X, Y, and Z," unless otherwise specified, is understood otherwise in the context in which it is generally used to convey that an item, term, etc. may be at least one of X, Y, and Z. Thus, such connecting language is not generally intended to imply that some embodiments require that at least one of X, at least one of Y, and at least one of Z, respectively, be present.

[0089] Although methods and systems are discussed herein with respect to elements labeled with ordinal adjectives (e.g., first, second, etc.), the ordinal adjectives are only used as labels to distinguish one element from another (e.g., one signal from another, or one circuit from another), and the ordinal adjectives are not used to indicate the order of these elements or their sequence of use.

[0090] Thus, while only a few embodiments have been specifically described herein, it will be apparent that numerous modifications may be made without departing from the spirit and scope of the present invention. Furthermore, acronyms are used merely to enhance the readability of the specification and claims. It should be noted that these acronyms are not intended to reduce the generality of the terms used, and should not be construed to limit the scope of the claims to the embodiments described herein.

Claims

1. a harmonically mode-locked laser comprising a main cavity having a first cavity round trip time T and a reference cavity having a second cavity round trip time T / N, where N is an integer, and the main cavity and the reference cavity are coupled to one another; and at least one optical beam splitter in the reference cavity that generates a common mode that is substantially shared between the main cavity and the reference cavity and generates an output for an optical frequency comb.

2. 10. The apparatus of claim 1, further comprising phase locking to an external cw reference laser.

3. 3. The apparatus of claim 2, further comprising detecting a beat signal between the apparatus and the external cw reference laser with a signal-to-noise ratio greater than 35 dB at 100 kHz resolution.

4. 10. The apparatus of claim 1, wherein the reference cavity comprises a bulk reference cavity.

5. 10. The apparatus of claim 1, wherein the reference cavity comprises a fiber reference cavity.

6. 10. The apparatus of claim 1, wherein the reference cavity comprises a combination of fiber optic and bulk optic components.

7. 10. The device of claim 1, further comprising an electro-optic modulator.

8. 10. The apparatus of claim 1, further comprising at least one actuator for controlling cavity misalignment between the main cavity and the reference cavity.

9. 9. The apparatus of claim 8, wherein at least one of the actuators is driven by an error signal derived from the optical spectrum of the harmonically mode-locked laser.

10. At least one of the actuators is driven by the harmonically mode-locked laser. ｃｅｏ 9. The apparatus of claim 8, wherein the apparatus is driven by an error signal derived from the signal.

11. 10. The apparatus of claim 8, wherein the actuator facilitates a transition from Q-switching to harmonic modelocking.

12. 10. The apparatus of claim 1, wherein at least one of the optical beam splitters has a reflectivity greater than 15%.

13. 10. The apparatus of claim 1, wherein at least one of the optical beam splitters has a reflectivity of less than 10%.

14. 2. The apparatus of claim 1, wherein N is greater than 11.

15. 10. The apparatus of claim 1, wherein the harmonically modelocked laser operates at a repetition rate greater than 1 GHz.

16. 10. The apparatus of claim 1, wherein the reference cavity comprises an optical spacer based on an ultra-low thermal expansion material.

17. 10. The apparatus of claim 1, wherein the output comprises ultra-high stability microwaves.

18. 10. The apparatus of claim 1, wherein the output comprises an ultra-stable millimeter wave.

19. 10. The apparatus of claim 1 further configured as an optical frequency synthesizer.

20. 10. The apparatus of claim 1, wherein the reference cavity comprises a microresonator.

21. 10. The apparatus of claim 1, wherein the reference cavity comprises a fiber knot resonator.

22. a first cavity having a first cavity round trip time T and a second cavity having a second cavity round trip time T / N, where N is an integer, and the first cavity and the second cavity are coupled to one another; and at least one optical beam splitter in the second cavity that generates a common mode that is substantially shared between the first cavity and the second cavity and generates an output for an optical frequency comb.

23. 23. The apparatus of claim 22, wherein the first cavity or the second cavity comprises a bulk reference cavity.

24. 24. The apparatus of claim 23, wherein the bulk reference cavity is a monolithic bulk reference cavity.

25. 23. The apparatus of claim 22, further comprising at least one actuator that locks the repetition rate of the apparatus to an external microwave frequency reference.

26. 23. The apparatus of claim 22, wherein the apparatus is a frequency comb and comprises a fiber gain medium.

27. 23. The apparatus of claim 22, wherein the apparatus comprises a solid-state or semiconductor gain medium.

28. a first cavity mirror and a second cavity mirror concentric about a major axis; an input beam impinging on the first cavity mirror at a first angular offset from the major axis; an output beam transmitted through the first cavity mirror at a second angular offset from the major axis, the second angular offset being substantially equal to the negative of the first angular offset, the optical cavity being configured as an optical reference for a mode-locked laser.

29. 30. The optical cavity of claim 28, wherein the optical cavity is further configured as a reference for a harmonically modelocked laser.

30. 30. The optical cavity of claim 28, wherein one of the first cavity mirror and the second cavity mirror is curved and defines the major axis, and the other of the first cavity mirror and the second cavity mirror is substantially flat.

31. 30. The optical cavity of claim 28, wherein the first cavity mirror and the second cavity mirror are both curved.

32. a harmonically mode-locked laser comprising a main cavity having a first cavity round trip time T and a reference cavity having a second cavity round trip time T / N, where N is an integer, the main cavity and the reference cavity being coupled to one another, the laser operating at a repetition rate N / T; and at least one optical beam splitter in the reference cavity that generates a common mode substantially shared between the main cavity and the reference cavity, wherein the harmonically mode-locked laser has a repetition rate that is phase-locked to an external microwave reference.

33. 33. The apparatus of claim 32, wherein the reference cavity comprises both an optical beam propagating in free space and an optical beam propagating in fiber.

34. A dual comb system characterized by two harmonically mode-locked lasers with a common reference cavity.

35. 35. The dual-comb system of claim 34, further comprising two of the harmonically modelocked lasers propagating in a common fiber loop.

36. 1. An optical parametric oscillator comprising: a mode-locked pump laser oscillating at a pump laser wavelength, the mode-locked pump laser comprising: a first cavity having a first cavity round-trip time T; and a second cavity having a second cavity round-trip time T / N, where N is an integer; the first cavity and the second cavity being optically coupled to each other; the second cavity further comprising a nonlinear crystal; and the second cavity producing an output at a wavelength different from the pump laser wavelength.

37. two resonators having relative round trip times that are harmonics of each other; f ｃｅｏ or f ｂｅａｔ means for generating a signal; Said f ｃｅｏ or the f ｂｅａｔ means for generating an error signal derived from the signal; and at least one actuator driven by the error signal for differential cavity length control.

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