Systems with photonic integrated circuit and coupled resonator and related methods

Abstract

Photonic integrated circuits (PICs) interfaced with micro-scale resonators such as micro Fabry-Perot cavities. The PICs provide high frequency stability and low noise, and may be used in precision metrology, quantum computing, communication, and advanced sensing technology applications. PICs may include a first waveguide coupled to a light source, such as an on-chip laser, and a second waveguide outputting an indication of the resonator's resonant frequency, with the waveguides coupled by a directional coupler. The PICs may protect the light source from back reflection using destructive interference. Some PICs described are coupled to the resonator by a polarization- splitting grating coupler at two arms, and produce spatial separation of incident and reflected waves so that electrical feedback can be generated for use in Pound-Drever-Hall locking. Some PICs described are coupled to the resonator by a lens and use a reflector to generate resonant peaks useable as optical feedback for self-injection locking.

Description

[0001] Attorney Docket No.: Y0087.70172WQ00

[0002] SYSTEMS WITH PHOTONIC INTEGRATED CIRCUIT AND COUPLED

[0003] RESONATOR AND RELATED METHODS

[0004] CROSS-REFERENCE TO RELATED APPLICATIONS

[0005] This application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Application Serial No. 63 / 584,853, filed September 22, 2023, under attorney docket number Y0087.70172US01, and entitled “EFFICIENT COUPLING OF HIGH-Q FABRY PEROT RESONATORS TO PHOTONIC INTEGRATED CIRCUITS WITH BACKREFLECTION CANCELLATION AND SIGNAL REDIRECTION”, which is hereby incorporated herein by reference in its entirety.

[0006] This application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Application Serial No. 63 / 580,191, filed September 1, 2023, under attorney docket number Y0087.70172US00, and entitled “EFFICIENT COUPLING OF HIGH-Q FABRY PEROT RESONATORS TO PHOTONIC INTEGRATED CIRCUITS WITH BACKREFLECTION CANCELLATION AND SIGNAL REDIRECTION”, which is hereby incorporated herein by reference in its entirety.

[0007] FEDERALLY SPONSORED RESEARCH

[0008] This invention was made with government support under HR0011-22-2-0009 awarded by DARPA. The government has certain rights in the invention.

[0009] BACKGROUND

[0010] Photonic devices such as lasers may use frequency references.

[0011] SUMMARY

[0012] According to the disclosure there is provided a photonic integrated circuit, comprising: a first waveguide having an input port configured to be coupled to a light source; a second waveguide having an output port; a directional coupler coupling the first waveguide and the second waveguide; a micro-fabricated resonant cavity; and a grating coupling the first waveguide to the micro-fabricated resonant cavity and coupling the micro-fabricated resonant cavity to the second waveguide. Attorney Docket No.: Y0087.70172WQ00

[0013] In some embodiments, the directional coupler is configured to receive light from the input port and split the received light between the first waveguide and the second waveguide.

[0014] In some embodiments, the directional coupler is configured to induce a phase difference between light in the first waveguide and the second waveguide.

[0015] In some embodiments, the directional coupler is configured combine light from the first waveguide and the second waveguide and provide the combined light to the output port.

[0016] In some embodiments, the directional coupler is configured to combine light from the first waveguide and the second waveguide having a phase difference.

[0017] In some embodiments, the grating comprises a polarization- splitting grating coupler.

[0018] In some embodiments, wherein the polarization- splitting grating coupler is configured to: scatter light from the first waveguide having a first polarization to the micro-fabricated resonant cavity; and scatter light from the second waveguide having a second polarization to the microfabricated resonant cavity; and

[0019] In some embodiments, the polarization- splitting grating coupler is configured to: scatter light from the micro-fabricated resonant cavity having a first polarization to the first waveguide; and scatter light from the micro-fabricated resonant cavity having a second polarization to the second waveguide.

[0020] In some embodiments, the micro-fabricated resonant cavity comprises a Fabry-Perot resonator.

[0021] In some embodiments, the first waveguide and the second waveguide have a same path length.

[0022] In some embodiments, the light source is a laser.

[0023] In some embodiments, the output port is configured to provide an output signal representing a resonant frequency of the micro-fabricated resonant cavity.

[0024] According to the disclosure there is provided a photonic integrated circuit, comprising: a first waveguide having an input port configured to be coupled to a light source; a second waveguide having an output port; a directional coupler coupling the first waveguide and the second waveguide; a micro-fabricated resonant cavity coupled to the first waveguide; and a reflector coupled to the second waveguide.

[0025] In some embodiments, the directional coupler is configured to receive light from the input port and split the received light between the first waveguide and the second waveguide. Attorney Docket No.: Y0087.70172WQ00

[0026] In some embodiments, the directional coupler is configured combine light from the first waveguide and the second waveguide and provide the combined light to the output port.

[0027] In some embodiments, the photonic integrated circuit further comprises a control configured to adjust a light splitting ratio of the directional coupler.

[0028] In some embodiments, wherein the reflector comprises a loop mirror.

[0029] In some embodiments, the photonic integrated circuit further comprises a gradient-index lens coupling the first waveguide to the micro-fabricated resonant cavity.

[0030] In some embodiments, the micro-fabricated resonant cavity comprises a Fabry-Perot resonator.

[0031] In some embodiments, the photonic integrated circuit further comprises a control configured to adjust a phase of light in the first waveguide.

[0032] In some embodiments, the light source is a laser.

[0033] In some embodiments, the output port is configured to provide an output signal representing a resonant frequency of the micro-fabricated resonant cavity.

[0034] BRIEF DESCRIPTION OF DRAWINGS

[0035] FIG. 1 shows a poor man’s isolator in free space, according to some embodiments;

[0036] FIG. 2A shows a photonic integrated circuit , according to some embodiments;

[0037] FIG. 2B shows another photonic integrated circuit , according to some embodiments;

[0038] FIG. 3A shows detail views of the photonic integrated circuit, according to some embodiments;

[0039] FIG. 3B shows a transfer matrix schematic of the photonic integrated circuit, according to some embodiments;

[0040] FIG. 4A shows a side view of a polarization splitting grating coupler of a photonic integrated circuit, according to some embodiments;

[0041] FIG. 4B shows a top view of the polarization splitting grating coupler, according to some embodiments;

[0042] FIG. 4C shows a top view of scattering on the polarization splitting grating coupler, according to some embodiments;

[0043] FIG. 5A shows coupling efficiency of a polarization splitting grating coupler, according to some embodiments; Attorney Docket No.: Y0087.70172WQ00

[0044] FIG. 5B shows crosstalk of a polarization splitting grating coupler, according to some embodiments;

[0045] FIG. 5C shows performance of a set of polarization splitting grating couplers, according to some embodiments;

[0046] FIGs. 6A-6B shows performance of another polarization splitting grating coupler, according to some embodiments;

[0047] FIG. 7A shows a measurement apparatus for a polarization splitting grating coupler, according to some embodiments;

[0048] FIG. 7B shows a micro Fabry-Perot resonator array, according to some embodiments;

[0049] FIG. 7C shows a micro Fabry-Perot resonator, according to some embodiments;

[0050] FIG. 7D shows a GRIN lens and micro Fabry-Perot resonator assembly, according to some embodiments;

[0051] FIGs. 8A-8B show performance of a fiber mirror and fiber brag grating cavity assembly, according to some embodiments;

[0052] FIG. 8C shows performance of a GRIN lens and micro Fabry-Perot resonator assemblies, according to some embodiments;

[0053] FIGs. 9A-9B show a photonic integrated circuit and micro Fabry-Perot resonator assembly, according to some embodiments

[0054] FIGs. 10A-10B show a photonic integrated circuit, according to some embodiments;

[0055] FIG. 10C shows a measurement apparatus for a photonic integrated circuit, according to some embodiments;

[0056] FIG. 11 A- 11C show performance of a photonic integrated circuit, according to some embodiments;

[0057] FIG. 12A-12B show additional performance of a photonic integrated circuit, according to some embodiments;

[0058] FIG. 13A-13B show further performance of a photonic integrated circuit, according to some embodiments;

[0059] FIG. 14A-14C show photonic integrated circuits, according to some embodiments;

[0060] FIG. 15A show performance of a photonic integrated circuit, according to some embodiments; Attorney Docket No.: Y0087.70172WQ00

[0061] FIG. 15B shows a measurement apparatus for a photonic integrated circuit, according to some embodiments;

[0062] FIG. 16A-16B show photonic integrated circuits, according to some embodiments;

[0063] FIG. 16C shows performance of resonators, according to some embodiments;

[0064] FIG. 17A-17B shows a micro Fabry-Perot resonator array and micro Fabry-Perot resonators, according to some embodiments; and

[0065] FIG. 17C shows performance of a micro Fabry-Perot resonator, according to some embodiments.

[0066] DETAILED DESCRIPTION OF INVENTION

[0067] Provided are photonic integrated circuits (PICs) interfaced with micro-scale resonators such as micro Fabry-Perot cavities. The photonic integrated circuits provide high frequency stability and low noise, and may be used in precision metrology, quantum computing, communication, and advanced sensing technology applications. Photonic integrated circuits may include a first waveguide coupled to a light source, such as an on-chip laser, and a second waveguide outputting an indication of the resonator’s resonant frequency, with the waveguides coupled by a directional coupler. The photonic integrated circuits may protect the light source from back reflection using destructive interference. Some photonic integrated circuits described are coupled to the resonator by a polarization-splitting grating coupler at two arms, and produce spatial separation of incident and reflected waves so that electrical feedback can be generated for use in Pound-Drever-Hall locking. Some photonic integrated circuits described are coupled to the resonator by a lens and use a reflector to generate resonant peaks useable as optical feedback for self-injection locking.

[0068] There is provided a poor man’s isolator integrated with the semiconductor substrate. The poor man’s isolator may comprise a polarization splitting grating configured to scatter TE mode light in a first waveguide arm to p-polarized light, scatter light from a second waveguide arm into s-polarized light, and route light to the first or second waveguide arm, based on the polarization of the light, an on-chip phase shifter configured to adds a phase difference to light in the first and the two waveguide arms, and an on-chip beam splitter configured to route light in the first and second waveguide arms to a first or second port based on phase of the light. Attorney Docket No.: Y0087.70172WQ00

[0069] According to aspects of the disclosure there is provided an apparatus disposed on a semiconductor substrate, comprising a poor man’s isolator integrated with the semiconductor substrate. In some embodiments, the poor man’s isolator comprises a polarization splitting grating configured to scatter TE mode light in a first waveguide arm to p-polarized light, scatter light from a second waveguide arm into s-polarized light, and route light to the first or second waveguide arm, based on the polarization of the light, an on-chip phase shifter configured to adds a phase difference to light in the first and the two waveguide arms, and an on-chip beam splitter configured to route light in the first and second waveguide arms to a first or second port based on phase of the light.

[0070] In some embodiments, the poor man’s isolator integrated with the semiconductor substrate is configured to provide at least about 58% efficiency. In some embodiments, the poor man’s isolator integrated with the semiconductor substrate is configured to provide at least about 58% efficiency at about 1550 nm with about 25 nm bandwidth. In some embodiments, the poor man’s isolator integrated with the semiconductor substrate is configured to provide at least about 2.4 dB insertion loss. In some embodiments, the poor man’s isolator integrated with the semiconductor substrate is configured to provide at least about 17.7 dB of back reflection suppression. According to the disclosure there is provided a system incorporating an integrated poor man’s isolator. Systems described herein may incorporate inverse design strategies to realize a polarization splitting grating coupler with about 58% efficiency, and thereby provide an integrated poor man’s isolator exhibiting about 2.4 dB insertion loss and about 17.7 dB of back reflection suppression.

[0071] According to various embodiments, on-chip isolators are important building blocks in integrated photonic circuits, where they may be used to suppress unwanted backscattering. The inventors have recognized that isolators may be difficult to integrate on photonic chips and that the required magneto-optic materials may be incompatible with CMOS foundries. Conventional alternatives that do not rely on the magneto-optic effect and instead use a principle called dynamic modulation are disadvantageous because they may consume at least about tens of milliwatts of power.

[0072] In some embodiments, systems may use a simple substitute for the hard-to-make isolator. For example, the substitute may be used in implementation where the optical element to be isolated meets the follow requirements: (1) the element has polarization independent response; Attorney Docket No.: Y0087.70172WQ00 and (2) the element has deterministic reflection. Such an isolator may be referred to as a poor man’s isolator (PMI). Poor man’s isolators may be implemented in various free-space optical setups, as shown in FIG. 1. FIG. 1 shows an exemplary canonical implementation of a poor man’s isolator apparatus in free space, according to one embodiment. The poor man’s isolator 100 includes a light source 102 (which may be a laser), a polarization beam splitter 104, a quarter wave plate 106, and an optical element 108. In some embodiments, a poor man’s isolator may isolate the input port from reflections by rerouting the reflected signal to a second port. Information embedded in the reflection from an optical element under test may therefore be detected.

[0073] The inventors have recognized that conventional systems do not incorporate an on-chip version of a poor man’s isolator. The inventors have further recognized that access to an on-chip poor man’s isolator, provides the integration of integrated photonic circuits and high-quality reflective optical elements. For example, a system may be provided with heterogeneously integration of polarization independent micro-Fabry-Perot cavities with integrated photonic circuits, providing ultra- stable reference cavities on-chip.

[0074] The disclosure provides an on-chip poor man’s isolator on silicon-on-insulator (SOI) platform. In some embodiments, the poor man’s isolator may be coupled to an external fiber Bragg grating (FBG) to demonstrate the operating principle of a system. In some embodiments, a system may utilize the fact that two polarization modes in a SMF-28 fiber are degenerate. In some embodiments, to get access to two polarization modes in a fiber, a system may implement a polarization splitting grating (PSG) on chip. To minimize coupling loss from chip to fiber, systems may use the so-called photonic inverse design algorithm to optimize the complex 2-D grating structure. As provided herein, optimized polarization splitting grating may provide about 58% peak efficiency, without metal reflector underneath, and may result in an about 2.4 dB insertion loss for an on-chip poor man’s isolator. The system may also achieve and about 17.7 dB of reflection suppression with into the input port with optical element that possesses about 100% reflectivity.

[0075] In some embodiments, the mechanism of a poor man’s isolator as used in free-space optics is illustrated in FIG. 1. The input light al with polarization may transmit through a p- polarization beam splitter (PBS). After passing through a quarter wave plate (QWP), the p- polarization may be converted to circularly polarized light resulting from a <p = TT / 2 phase Attorney Docket No.: Y0087.70172WQ00 difference that is imprinted on two orthogonal polarizations. Where the optical element produces same response for two orthogonal polarization modes in free-space, the light may remain circularly polarized after reflection. A subsequent second pass through the quarter wave plate may then convert the circularly polarized light into s-polarized light a ( = TT) . The s-polarized light beam may be reflected by the polarization beam splitter and exit through a second port. The system thus suppresses unwanted reflection back into the input and instead reroutes the light to a second accessible port.

[0076] An on-chip poor man’s isolator may be constructed by integrating various on-chip elements as illustrated by FIG. 2B. FIG. 2B shows an exemplary schematic of a photonic integrated circuit comprising on-chip poor man’s isolator, as well as an inset of an exemplary SEM image of a polarization splitting grating, according to one embodiment. As shown in FIG. 2B, a photonic integrated circuit 100b may comprise an input port 202b, an output port 204b, a first waveguide 206b, a second waveguide 208b, a beam splitter 210b, a polarization splitting grating coupler 212b coupling to an optical element 214b, and a phase shifter 216b. The dashed region labeled PSG may comprise a polarization splitting grating coupler 212b. The polarization splitting grating may scatter TE mode light in left waveguide arm of the first waveguide 206b to p-polarized light in free space towards optical element 214b, whereas it may scatter light entering the grating from the bottom arm of the second waveguide 208b into s-polarized light. Input from free space (e.g., the optical element 214b) to the polarization splitting grating may also be routed to either of the two waveguide arms, depending on the polarization of the impinging light field. The dashed region labeled “quarter wave plate” may comprise an on-chip phase shifter 216b. Just like the quarter wave plate in free space it adds a phase difference a <p to light propagating in the two waveguide arms. The dashed region labeled “PBS” may comprise an on-chip 50:50 beam splitter 210b. Similar to the free space polarization beam splitter, it may also route light to different ports (input port 202b and output port 204b) based on a of the light in two arms. With these building blocks, a system may be tuned using the phase shifter such that b2 may be increased or maximized while bl is decreased or nulled.

[0077] FIG. 6A shows exemplary results of experiment and simulation for a polarization splitting grating, with an inset of exemplary poor man’s isolator- fiber Bragg grating measurement setup, and FIG. 6B shows exemplary experimental results for a poor man’s isolator-fiber Bragg grating. Attorney Docket No.: Y0087.70172WQ00

[0078] To measure the performance of an on-chip poor man’s isolator, the inverse designed polarization splitting grating may first be characterize, as is shown in plot 602 of FIG. 6A. In FIG. 6A, the higher curve at the peak near 1550 nm is the measurement, and the lower curve at the peak near 1550 nm is the simulation. Systems may provide about 58% efficiency at 1550 nm with 25 nm bandwidth. The polarization splitting grating may be formed to be mirror symmetric along diagonal line, as shown in the FIG. 2B inset, such that there is substantially identical efficiency for both arms. With this efficient polarization splitting grating, systems may couple fiber Bragg grating to the chip to demonstrate poor man’s isolator, as is shown in FIG. 6A. In FIG. 6A, the curve with the peak around 1549 nm is b2 and the curve without a peak around 1549 nm is bl. In some embodiments, fiber Bragg grating response may be provided in b2 with about 4.75 dB attenuation, where it goes though poor man’s isolator twice. In some embodiments, systems may also provide about 17.7 dB reflection suppression for bl, as shown in plot 604 of FIG. 6B. Since there is direct reflection from the silicon chip itself, we observe higher noise floor for bl, which limits our reflection suppression measurement.

[0079] Accordingly, provided is an on-chip poor man’s isolator with about 2.4 dB insertion loss and about 17.7 dB reflection suppression. As a simple substitute for isolator, the on-chip poor man’s isolator is easy to fabricate and may not use external dynamic modulation. Systems described herein provide for heterogeneous integration between integrated photonic circuits and high-quality reflective optical elements.

[0080] High Q Fabry Perot (FP) resonators may be used for on-chip component stabilization. However, due to the reflective response of Fabry Perot cavity, conventional systems may face challenges integrating such configurations to photonic integrated circuits (PIC) without back- reflection that can damage on-chip lasers or other components. Further, conventional on-chip isolators or circulators that can protect components from back-reflection are generally either power consuming or CMOS incompatible. Provided herein is a system integrating a Fabry Perot cavity to photonic integrated circuits without on-chip isolators.

[0081] Systems provided herein address challenges faced in conventional isolators, such as back-reflection cancellation and signal redirection of Fabry-Perot cavities. Systems provided herein may integrate a poor man’s isolator, such as used in free space optics. Systems described herein implement a poor man’s isolator on a chip, which has not previously been achieved, utilizing novel on-chip circuits. Attorney Docket No.: Y0087.70172WQ00

[0082] Systems provided by the disclosure may leverage a degenerate response of Fabry Perot cavities for two polarizations. Systems herein may be formed having on-chip circuits that effectively interfere with and cancel back-reflection, while redirecting the reflective signal towards the detector path. Systems herein provide a back-reflection suppression ratio of over about 9 dB to the rerouted signal. In some embodiments, this ratio may be associated with imperfection of on-chip 50 / 50 splitter.

[0083] In some embodiments, systems may have improved or optimized coupling between photonic integrated circuits and Fabry Perot cavities, by employing an inverse design approach for developing a polarization-splitting grating coupler. Such systems may provide efficient coupling between a chip and a cavity, further minimizing losses. This enables systems to provide a low insertion loss of about 5.8 dB from the photonic integrated circuits to the cavity.

[0084] Systems described herein may be enhance with additional features. For example, some systems may integrate tunable couplers. Tunable couplers may provide dynamic control of signal redirection, and may provide for back-reflection suppression ratio of up to about 50 dB. Such systems provide even higher performance and more precise control in integrated photonic circuits utilizing Fabry Perot cavities.

[0085] According to the disclosure, systems provide efficiently coupled photonic integrated circuits with Fabry Perot cavity without the need for on-chip circulators, not previously achieved. Systems herein may greatly suppress unwanted back-reflection to protect on-chip components and reroute the useful reflective signal for detection.

[0086] The disclosure provides a simple substitute for on-chip circulator to integrate Fabry Perot cavity to photonic integrated circuits. According to aspects of the disclosure, systems herein may be formed using standard CMOS foundry fabrication process, and provide photonic integrated circuits a stable Fabry Perot cavity that conventional on-chip cavity does not achieve.

[0087] The system described herein provide significantly lower fabrication cost, compared with conventional stable reference cavities for photonic integrated circuits. By eliminating the need for on-chip isolators and offering efficient back-reflection suppression, the systems described herein provide more cost-effective photonic integrated circuits reference cavities.

[0088] Moreover, the compact and stabilized photonic integrated circuits provided herein may be used in various industries such as radio frequency, atomic physics, and optical communications. These industries benefit from the compact size and stability of the integrated Attorney Docket No.: Y0087.70172WQ00 systems provided herein, and may incorporate the improved performance and reliability described herein in their respective applications.

[0089] According to aspects of the disclosure, there is provided systems having low-cost fabrication processes and offering enhanced functionality and performance in critical industries. The compact and stabilized photonic integrated circuits provide innovation driving economic benefits for industries relying on precise and stable optical systems.

[0090] According to aspects of the disclosure, a Coherent Heterodyne Robust Optical Microwave Emitter (CHROME) is provided. Provided is a system-on-a-chip configured to produces ultra- low phase noise microwave signals covering a frequency range about 1-40 GHz. Schematics of one such system are shown in FIGs. 1 and 2A-2B, according to some embodiments. The system described herein reduces risk by using mature, high-performance III- V and silicon photonic technology in the telecom bands to implement OFD using a simplified method that that obviates the need for octave-span comb generation. According to some embodiments, there is provided 2-point OFD, which lowers system complexity and power. For conventional systems, one practical problem in realization of spectrally pure microwave sources based on a monolithic platform is associated with the thermorefractive noise of the high-Q cavities. In the instant disclosure, to circumvent this problem provided is a micro-Fabry-Perot cavity hybridly integrated on a chip. By integrating the system, a Coherent Heterodyne Robust Optical Microwave Emitter (CHROME) may be provided, representing a dramatic reduction in SWAP for high performance microwave signal sources, compared with conventional systems. CHROME may also reduce cost using scalable manufacturing methods. The increased performance and reduced cost of CHROME, among other favorable attributes, provide particular benefits to airborne and spaceborne radar systems, and also provide enhancements ground-based systems.

[0091] According to the disclosure, there is provided an apparatus disposed on a semiconductor substrate, comprising: a photonic circuit disposed on the semiconductor substrate; and a polarization- splitting grating disposed on the semiconductor substrate, the polarization- splitting grating configured to couple the photonic circuit with a Fabry-Perot resonator.

[0092] Aspects of the disclosure provide systems and methods for efficiently coupling high-Q Fabry-Perot resonators to photonic integrated circuits with reflection cancellation. Benefits of Fabry-Perot resonators as frequency-stable reference cavities and as an efficient interface Attorney Docket No.: Y0087.70172WQ00 between atoms and photons make them an important resource in various emerging photonic technologies. To bring these performance benefits to next-generation communications, computation, and timekeeping systems, the inventors have recognized systems and methods for integrating compact Fabry-Perot resonators with photonic integrated circuits. Described herein are reflection cancellation circuits that utilize numerically optimized multi-port polarizationsplitting grating couplers to efficiently interface high-finesse Fabry-Perot resonators with a silicon photonic circuit. The circuit interfaces produce spatial separation of the incident and reflected waves, which is used for on-chip Pound-Drever-Hall frequency locking. The interfaces also suppress unwanted back reflections from the Fabry-Perot resonator. Described herein is a polarization- splitting grating coupler having at least 55% coupling efficiency. Such a design provides an insertion loss of 5.8 dB for the circuit interface and more than 9 dB of back reflection suppression. Furthermore, the system interfaces with various reflective off-chip devices.

[0093] High-finesse Fabry-Perot cavities provide high performance, providing high frequency stability, quality factors, and power handling, making them important to a wide range of applications. Among other applications, they may be used for next-generation quantum communications, computation, and timekeeping systems, and the inventors have recognized that it will be important to bring these performance advantages to compact, integrated platforms. Using new wafer-scale fabrication techniques, arrays of high-finesse (>1M) Fabry-Perot resonators may be fabricated, which may be used to create sub-Hz linewidth lasers and low- noise oscillators. The inventors have recognized that to harness these performance advantages in next-generation integrated photonic circuits, it is important to efficiently interface Fabry-Perot cavities with photonic circuits.

[0094] In various embodiments, structures for integrating Fabry-Perot resonators may depend on the intended use case. For example, when a Fabry-Perot resonator is used as a stable frequency reference for high-performance laser systems or optical clocks, the frequency of the cavity may typically be measured using the Pound-Drever-Hall (PDH) locking technique. In this case, laser light reflected from the resonator is to be separated from the incident wave and detected with high efficiency to obtain a low noise error signal for feedback stabilization of the laser frequency. Therefore, an on-chip PDH locking system uses an integration strategy that maps incident and reflected waves to distinct ports of an optical system, which permits direct detection Attorney Docket No.: Y0087.70172WQ00 of the reflected wave. This same photonic interface can provide further benefits by also protecting the laser from the frequency-destabilizing effects of back-scattered light by suppressing back reflections from the Fabry-Perot resonator.

[0095] An optical circulator may be one structure for this coupling, as it maps incident and reflected waves to distinct optical ports while offering some protection from back reflection. However, the fabrication of isolators and circulators on photonic chips poses a significant challenge due to the incompatibility of requisite magneto-optic materials with CMOS foundries. To address this challenge, a variety of non-magnetic isolators and circulators have been demonstrated, which use time modulation to produce non-reciprocal response. However, since these non-magnetic isolators and circulators are complex and can consume a substantial amount of power, they are not suitable for certain applications.

[0096] Accordingly, the inventors have recognized new strategies for passive reflection cancellation, in order to eliminate the need for isolators and circulators in various systems, providing simpler and more power-efficient integrated photonic circuits. One such system, referred to as the poor man’s isolator, includes a quarter- wave plate and a polarizing beam splitter to separate the incident and reflected optical waves. This system, pictured in FIG. 1, is frequently used instead of an optical circulator to implement PDH locking, since it offers lower losses and smaller back reflections. As described herein, photonic circuits implementing such systems provide practical and efficient interfaces between Fabry-Perot cavities and other free- space systems.

[0097] Described herein is a reflection cancellation circuit to efficiently interface high-finesse Fabry-Perot resonators with a silicon photonic circuit. This system, operating similar to a poor man’s isolator, is comprised of an interferometer that interfaces to two separate ports of an optimized polarization splitting grating coupler (PSGC) device. Light entering Port 1 of the interferometer is reflected from a fiber-coupled Fabry-Perot resonator before exiting Port 2 of the interferometer, yielding spatial separation of the incident and reflected waves as used for on- chip PDH locking. With the improved 2D grating structure described herein, peak fiber-to-chip coupling efficiency may be 55%, yielding 5.8 dB of loss in a double-pass configuration of the on-chip interface. Interferometric cancellation of reflections produced by the system may yield >9 dB of back-reflection suppression, in order to protect an on-chip laser source from unwanted back reflections. Since the degree of back-reflection cancellation may be only by the imprecision Attorney Docket No.: Y0087.70172WQ00 of the splitting ratio of a directional coupler, much higher (>30dB) back-reflection suppression ratios may be provided by adjusting the PSGC.

[0098] A photonic integrated circuit is illustrated in FIG. 2A. The reflection cancellation circuit interfaces a high-finesse Fabry-Perot resonator with a silicon photonic circuit, as illustrated in FIG. 1, and as described above. The operating principle of photonic circuit interface of FIG. 2A is similar to the free-space implementation of the poor man’s isolator shown in FIG. 1. In the free-space implementation of FIG. 1, p-polarized light entering Port 1 passes through the Polarizing Beam Splitter (PBS) and is subsequently conversion into left-handed circularly polarized light after it traverses the Quarter Wave Plate (QWP). Upon reflection from the Fabry- Perot resonator, this left-handed circularly polarized wave is converted to right handed circularly polarized wave. After traversing the QWP a second time, the right-handed circular polarized wave is converted to an s-polarized wave and is subsequently reflected by the PBS to exit Port 2 of the system. Hence, the system protects the laser source from back reflections while yielding spatial separation of the reflected wave as used for on-chip PDH locking. While the figures illustrate a Fabry-Perot resonator in this system, this scheme is applicable to any component with a polarization-independent reflection response.

[0099] FIG. 2A shows a photonic integrated circuit , according to some embodiments. As illustrated in FIG. 2A, photonic integrated circuit 200a may comprise an input port 202a, an output port 204a, a first waveguide 206a, a second waveguide 208a, a directional coupler 210a, and a polarization splitting grating coupler 212a coupling to an optical element 214a (which may be a micro Fabry-Perot resonator). The circuit interface of FIG. 2A is similar to a poor man’s isolator, and incorporates a polarization splitting grating coupler (PSGC) 212a. The circuit implementation of the poor man’s isolator system is shown in FIG. 2A, and includes a balanced interferometer that incorporates an optimized polarization- splitting grating coupler (PSGC) device. Similar to the free-space polarizing beamsplitter, the PSGC maps orthogonally polarized waves into separate output waveguide arms 206a and 208a. The 1 input arm of the PSGC couples to p-polarized free-space beams that are emitted perpendicular to the grating coupler, and the 2 input arm of the PSGC couples to s-polarized free-space beams that are emitted perpendicular to the grating coupler, as shown in FIG. 3A. FIG. 3A shows a schematic of a PSGC. Light input from Arm 1 will be scattered into p-polarized light in free space and that from Arm 2 will be scattered into s-polarized light in free space. Light entering Port 1 of this Attorney Docket No.: Y0087.70172WQ00 interferometer is split between two waveguides by a 50 / 50 directional coupler 210a before coupling to the PSGC 212a. Since the directional coupler 210a may induce a n / 2 phase difference between the two waveguides (each having identical path lengths), left-handed circularly polarized light is emitted from the PSGC 212a. Upon reflection from the Fabry-Perot resonator 214a (which may have a polarization-independent reflection response), the incident right-handed circular polarization is converted into a left-handed circular polarized wave before entering the PSGC 212a for a second time. This left-handed circular polarized wave is projected into orthogonal linear polarizations by the PSGCc212a, such that the waves exiting the PSGC now have a -n / 2 phase difference. This phase difference causes these two reflected waves to combine within the 50 / 50 directional couplerc210a, such that all of the reflected light exits Port

[0100] 2 of the interferometer. Hence, this circuit interface yields spatial separation of the incident and reflected waves (as required for on-chip PDH locking) while also producing interferometric cancellation of unwanted back-reflections from port 1.

[0101] FIG. 3B shows a transfer matrix schematic of the system. Transfer matrix formalism may be used to illustrate and analyze the response of this circuit interface. By mapping the bidirectional two-port system of FIG. 2A onto an equivalent unidirectional two-port system of FIG. 3B, with a first side 252 and second side 254 of the unidirectional two-port system shown in the figure, it may be appreciated that 2x2 transfer matrices may be used to analyze the system i' response. Denoting the incident waves as and the out-going waves as the system -^2- response by propagating the input waves through transfer matrices associated with each component of the system, as follows in Equation 1.

[0102] Ri 0

[0103] Here, 1, and MDevice o R2. are transfer matrices that describe the response of the directional coupler, differential phase delay, and PSGC device, respectively. Here, j and r = 1 — / z2are splitting coefficient of the directional coupler, <p is the phase imbalance between two waveguide segments, a is the coupling coefficient for PSGC, and Rt, R2are complex reflection coefficients for the external device (e.g., Fabry-Perot resonator) for s- and p-polarized light. Attorney Docket No.: Y0087.70172WQ00

[0104] This model demonstrates the reflection cancellation scheme. When light is only injected into port 1 (i.e., a2 = 0), it can be seen that the reflected wave amplitudes b = from the above transfer matrix model. From these expressions, it may be observed that / q may be nulled even in cases when RrR2. However, the inventors have recognized that systems may employ a use case when the reflection response is identical for both polarizations. Assuming that R^ = R2in the case of 50% power splitting ratio (r = g = 1 / V2), it may be appreciated that it is possible to null b while directing all of the output light b2in the case when 0 = 0. However, the back reflection

[0105] | i>2|24 z2(l- z2) . . . . . suppression ratio, |— | = |2 1S scnsitlvc 10 t'lcsplitting coefficient . For example, if g deviates from 1 / 2 by 14% due to fabrication errors, the back reflection suppression ratio will decrease to lOdB from perfect cancellation. Hence, tight control of the power splitting ratio may be used to obtain a high degree of back reflection cancellation.

[0106] According to some embodiments, the circuit interface is formed by fabricating a silicon photonic circuit from a Silicon-On-Insulator (SOI) wafer having a 250nm thick silicon layer and a 3 micron silica under cladding. E-beam lithography may be used and a reactive-ion etch (etch depth of 80nm) may be used to define both waveguide and grating structures, as seen in FIG. 4A-4B. FIGs. 4A shows a side view of a layered structure of the PSGC, with a single mode optical fiber positioned perpendicularly to the PSGC. The assembly includes a photonic integrated circuit 400a with a first Si layer 402, a SiO2 layer 404, a second Si layer 406, a PSGC 408a, as well as an optical fiber 420 aligned with the PSGC 408a, the optical fiber 420 having cladding 422 and fiber 424. FIG. 4B shows a top view SEM image of a photonic integrated circuit 400a having a PSGC 442, a first waveguide 444, and a second waveguide 446. The pattern of PSGC 442 may be symmetrical over the white line. FTo accurately define the desired structure during e-beam exposure, proximity effect correction may be used, and through dose tests using Hydrogen silsesquioxane (HSQ), an e-beam dose of 1050 pC / cm2may be used to provide improved performance. The PSGC device is an important component of the system, as the efficiency of circuit interfaces may be based on the performance of this grating coupler.

[0107] To improve the efficiency of the PSGC, an inverse design algorithm may be used, such as by employing a LUMOPT package with Lumerical FDTD software. Through the design of the grating coupler, the parameter space of numerical optimization may be reduced by imposing Attorney Docket No.: Y0087.70172WQ00 a mirror symmetry plane, indicated by the diagonal white line in FIG. 4B. In some embodiments, the LUMOPT package is modified in order to impose such mirror symmetry. This symmetry plane causes the grating coupler to produce the same scattering response when excited from either input port. The PSGC structure, as shown in FIGs. 4A-4C may be designed for vertical coupling to SMF-28, with a Gaussian beam waist radius of 4.5pm. FIG. 4C shows a Finite-Difference Time-Domain (FDTD) simulation showing a scattered field of the PSGC 442 3um above the Si device layer, prompted by an incident waveguide mode from bottom port, with light pattern 448. The scattering in FIG. 4C is a Gaussian field profile produced by the PSGC device layer when illuminated by a TE-like guided optical mode.

[0108] The fabricated PSGC may provide improved performance. To evaluate the optical performance of the fabricated PSGC structures, a cleaved optical fiber (SMF-28) may be vertically aligned with the PSGC to enable fiber-to-chip coupling efficiency and cross-talk measurements. FIG. 5A shows a plot 502 of empirical measurement of the coupling efficiency and crosstalk of the PSGC, where efficiency is characterized as the transmission from Arm 1 to the fiber, while crosstalk is defined as the transfer from Arm 1 to Arm 2, with FIG. 5B showing a zoomed in plot 504 on of the crosstalk data presented in FIG. 5A. The optical measurements seen in FIGs. 5A-5B, provide a fiber-to-chip coupling efficiency of 55% (2.6 dB) at a wavelength of 1550nm, over a 23 nm bandwidth. The crosstalk, defined as the direct coupling from Arm 1 to Arm 2, displays a contrast exceeding 60dB at 1550nm. FIG. 5C shows a scatter plot 506 indicating the performance among ten distinct PSGCs fabricated on a same chip. FIG. 5C shows the measured peak efficiency and 3dB bandwidth of 10 gratings fabricated on the same chip, revealing high efficiency (>50%) and broad operational bandwidth (>20nm) for the majority of fabricated gratings. Deposited mirror underneath a PSGC also further increases the efficiency to nearly 100%, avoiding light scattered into substrate.

[0109] The improved PSGC device may be used with the reflection cancellation circuit. In some embodiments, this system may be used to interface an off-chip Fabry-Perot resonator with the circuit. FIG. 7A shows a measurement apparatus for an on-chip poor man’s isolator. In the measurement setup for the characterization of PMI, DUT signifies device under test and PD indicates photo detector. FIG. 7A shows a measurement apparatus 700 comprising the photonic integrated circuit 200a, as well as a light source 702, a circulator 704, first and second polarization controllers 706 and 708, a device under test 710, and a photodetector 712. FIG. 7A Attorney Docket No.: Y0087.70172WQ00 shows a schematic of the experimental apparatus that may be used to assess the performance of the reflection cancellation circuit. The fiber circulator facilitates the measurement of system reflection, enabling the characterization of the back-reflection suppression ratio. A segment of SMF-28 fiber as a fiber umbilical may be used to flexibly interface the grating coupler to different reflective devices. This fiber umbilical contains a polarization controller (PC2) that compensates for any polarization distortion occurring within the fiber. The state of the polarization controller is chosen to ensure that the fiber umbilical produces Jones matrix of identity (i.e., so that it does not alter the polarization state). Hence, the fiber umbilical is a convenient way to couple to different devices to provide performance evaluations of this circuit interface in various scenarios. FIG. 7B shows a micro Fabry-Perot array 720 comprising micro Fabry-Perot resonators 722. FIG. 7C a detail section view of the array 720 and a micro Fabry- Perot resonator 722 that includes first and second reflection surfaces 724 and 726 and cavity 728. FIG. 7D shows an assembly 740 having a micro Fabry-Perot resonator 722 coupled with a gradient- index (GRIN) lens 742 and an optical fiber 744, where the lens is a collimator assembled to match the micro Fabry-Perot cavity mode.

[0110] FIGs. 8A-8B show measurement results with fiber mirror (FM) and fiber brag grating cavity (FBGC) as DUT. A commercial fiber mirror (FM) may be used as a reference device to examine the performance of the reflection cancellation circuit. The reflection and transmission response produced by the fiber mirror are shown in plot 802 of FIG. 8A. Power transmission from Port 1 to Port 2, denoted as |S1212shows a signal attenuation of -5.8 dB. Since the light exiting Port 2 passes through the grating coupler twice, with 2.6 dB of loss per pass, and the fiber mirror has a reflection loss of 0.5 dB, the total transmission loss of 5.8 dB is in good agreement with the anticipated transmission loss of 5.7 dB. Measurements of the reflection response from Port 1, denoted as |S1X|2show a back-reflection of -14.8 dB from a fiber mirror with near-unity back reflection efficiency. Since the reflection efficiency, is 9 dB lower than the transmission efficiency, |S1212|, these measurements show a back reflection suppression ratio of 9 dB, demonstrating the operation of the reflection cancellation circuit.

[0111] Now using the Fiber Bragg Grating cavity (FBGc) in place of the fiber mirror, the manner in which the reflection response of this Fabry-Perot-like resonator is imprinted on the response of this multi-port system may be seen. In some embodiments, the FBGc may be a commercial fiber Bragg defect cavity (Teraxion XX), and may comprise two fiber-Bragg grating Attorney Docket No.: Y0087.70172WQ00 mirrors that produce a standing-wave optical resonator. Such a cavity may produce a single resonance at 1550 nms having a linewidth of 85MHz and Q-factor of 2.3 million. Plot 804 of FIG. 8B displays the reflection, |S |2, and transmission, |S1212, measurements produced when this FBGc is coupled to the circuit. It may be appreciated that the reflection response of the resonator is clearly imprinted on the transmission response, |S1212, while the back-reflection is suppressed by lOdB in comparison to the transmission.

[0112] These reflection and transmission measurements may also be appreciated when a Fiber Bragg Grating cavity (FBGc) with a linewidth (Q-factor) of 85MHz (2.3 million) is employed, as depicted in FIG. 8B. The cavity resonance is discernible in the transmission signal, while the back reflection signal is suppressed by lOdB in comparison to transmission. As an illustration of the integration of a micro-Fabry-Perot cavity with the chip, the fiber may also be connected to a GRIN lens collimator, which couples to the micro Fabry-Perot cavity. This micro Fabry-Perot cavity is one of an array of resonators created using a scalable reflow-based fabrication process, having an optical linewidth of 60kHz, per independent cavity ring-down spectroscopy measurements. By sweeping the laser across the cavity resonance, with a linewidth of 60kHz, independently characterized by ring-down measurements, the resonance signal may be shown with a 7dB loss and a back reflection suppression ratio of lOdB. The oscillatory signal may be caused by beating of the ring-down signal and laser. Here the extra loss compared with fiber devices may be due to collimator cavity alignment. FIG. 8C shows plot 806 of measurement results with fiber-GRIN-micro Fabry-Perot as DUT.

[0113] Further advancements in the insertion loss are realized by applying a coated mirror to the backside of PSGC. For the improvement of the back reflection suppression ratio, the incorporation of a tunable coupler and phase shifter can provide a higher suppression ratio.

[0114] This reflection cancellation circuit is a versatile interface for any off-chip device that has a polarization-independent reflection response. This type of system may be used to couple with vapor cells as a frequency reference for integrated circuits. Furthermore, its application can be extended to reflectors that exhibit polarization-dependent reflection response by substituting the 50 / 50 directional coupler and balanced passive delay with a tunable coupler and tunable phase shifter. Even when the reflection response is not identical for both polarizations (RxA R2), o R i provided = - — — - the reflected wave energy can be directed into Port 2, thereby ensuring Attorney Docket No.: Y0087.70172WQ00 a null back reflection for Port 1. This provides the circuits described herein with broad scope of application, extending use of these circuits to more general case of diffuse scattering, as is often obtained in applications such as Lidar.

[0115] Further packaging with micro Fabry-Perot and PIC from fiber umbilical provides higher- level integration, as is shown in FIGs. 9A-9B. FIGs. 9A-9B show schematics of co-packaged micro Fabry-Perot with PIC. FIG. 9A shows an assembly 900 having a photonic integrated circuit 400b with a small PSGC 408b, coupled with a GRIN lens 742 to help with mode matching and coupling to micro Fabry-Perot resonator 722. FIG, 9B shows an assembly 920 having a photonic integrated circuit 400c with a numerically optimized large PSGC 408c to match a mode of micro Fabry-Perot resonator 722 directly. With the PSGC described herein, a GRIN lens may be used aligned to the PIC to help match the mode for micro Fabry-Perot. Furthermore, the inverse design method of the PSGC may be used with a larger beam spot size to directly couple to micro Fabry-Perot, without the need of GRIN lens, as shown in FIG, 9B.

[0116] Provided herein are various implementations of an on-chip PMI with a SOI platform. These implementations include an integrated directional coupler and a PSGC. The PSGC, an important component of the system, achieves a peak efficiency of at least 55% without using an underlying metal reflector, providing a substantially reduced insertion loss of 5.8 dB for on-chip PMI for FM and FBGC systems.

[0117] Employing a micro Fabry-Perot cavity fiber umbilical, provides an insertion loss of 7 dB. In various embodiments, a back reflection suppression ratio may exceed 9 dB, and may be related to the design of the 50 / 50 directional coupler. Hence, much higher (>30dB) back- reflection suppression ratios may be provided with different directional coupler designs. For example, a tunable directional coupler and an active phase shifter may provide much higher back reflection suppression while also extending the application range of the on-chip PMI to objects that exhibit polarization dependence.

[0118] Passive reflection cancellation schemes of the type provided herein may be used to eliminate the need for isolators and circulators in many applications, providing simpler and more power-efficient integrated photonic circuits. Accordingly, the systems described herein provide for heterogeneous integration between integrated photonic circuits and high-finesse Fabry-Perot resonators. Such systems may enable next-generation quantum communications, computation, and time-keeping systems, among other systems. Attorney Docket No.: Y0087.70172WQ00

[0119] Aspects of the disclosure relate to harnessing micro-Fabry-Perot reference cavities in photonic integrated circuits. According to some embodiments, there are provided compact photonic systems that provide offer high frequency stability and low noise. Such features are of increasing importance to applications in precision metrology, quantum computing, communication, advanced sensing technologies, among other applications. However, on-chip resonators comprised of dielectrics may not match the frequency stability and noise characteristics of Fabry-Perot cavities, whose electromagnetic modes live almost entirely in vacuum. Described herein are systems and methods for interfacing micro-fabricated Fabry-Perot cavities with photonic integrated circuits thereby providing compact, high-performance integrated systems. The systems and methods described herein provide self-injection locking of an on-chip laser to a millimeter-scale vacuum-gap Fabry-Perot using a circuit interface that transforms the reflected cavity response to enable efficient feedback to the laser. According to some embodiment, such a system may provide a phase noise of -97 dBc / Hz at 10 kHz offset frequency, a fractional frequency stability of 5xl0'13at 10 ms, a 150 Hz 1 / K integral linewidth, and a 35 mHz fundamental linewidth. Also described herein are integrated systems that utilize a vertical emission grating coupler and a back-reflection cancellation circuit to realize a fully copackaged module that effectively redirects the reflected signals and isolates back-reflections (e.g., with a 10 dB suppression ratio). The systems described herein enhance the precision and functionality of RF photonic systems, providing improved performance in various photonic applications.

[0120] The systems described herein provide for mass producible, micro-fabricated Fabry-Perot (pFP) reference cavities with photonic integrated circuits (PICs) that enable next-generation high-performance integrated systems. By storing the electromagnetic energy almost entirely in vacuum, such pFP vacuum gap reference cavities virtually eliminate thermo-refractive noise that limits the performance of waveguide-based resonators, providing compact lasers and oscillators with unmatched performance. The integrated systems described herein address key challenges of pFP back-reflections and transform the pFP reflection response to enable on-chip self-injection locked lasers with improved performance and signal redirection with back-reflection suppression for on-chip Pound-Drever-Hall (PDH) locking. These integrated systems further provide ultra- high performance (Q-factors > 4 billion) and low-noise oscillators to any number of integrated photonic platforms. Attorney Docket No.: Y0087.70172WQ00

[0121] To realize ultra-low noise lasers, oscillators, and sensors, conventional systems typically require a reference cavity that has high optical Q-factors (> Ibillion) and very low phase noise. To date, the field of integrated photonics has used waveguide-based resonators to create reference cavities. Thermo-refractive noise, caused by temperature fluctuations within dielectric media, is the dominant source of frequency instability and phase-noise within such waveguidebased resonators. Conventionally, thermo-refractive frequency noise within such dielectric reference cavities is reduced by dramatically expanding the mode volume of the resonator. This is why the dilute nitride waveguides with their fiber-like mode field diameters and low losses have enabled compelling performance. However, the strategy for managing thermo-refractive noise has its limits. For example, bending losses limit the degree to which the waveguide mode area can be increased. Moreover, the resonator length is fundamentally limited by the waveguide propagation losses, further limiting the attainable mode volumes. These factors, combined with practical aspects of photonic system design, prevent waveguide-based resonators from pushing waveguide-based oscillators far beyond their current levels of performance. To address these challenges, the disclosure provides an integrated system including a vacuum-gap reference cavities integrated with photonic circuits.

[0122] Vacuum-gap FP reference cavities provide excellent performance as frequency stable resonators, as their unique design may virtually eliminate thermo-refractive noise, thereby offering unrivaled phase noise and frequency stability. However, conventionally, such ultra-high performance has only been accessible in a laboratory setting due to the large sizes of such cavities (>10k cc) and the complex vacuum system (~50k cc) that are required to operate them. Further, due to the lack of isolators and circulator in integrated photonics, the mirror-like reflection of FP cavity can be problematic. To address these challenges, systems described herein provide a mm-scale vacuum-gap reference cavity (< 0.6 cc) that eliminates the need for complex and bulky vacuum systems, permitting direct integration with photonic circuits. Such cavities may be used with the on-chip interface circuits described herein to transform the mirrorlike reflection either into resonant feedback for laser locking or into complete redirection for detection. Accordingly, the systems described herein provide for the integration of pFP reference cavities with ultra-high Q-factor modes (> 4 billion) and ultra-low noise performance to photonic integrated circuits, greatly expanding the capabilities of integrated photonics. Attorney Docket No.: Y0087.70172WQ00

[0123] According to the disclosure, there is provided direct self-injection locking of an on-chip laser to a co-integrated pFP cavity using an interface circuit. According to some embodiments, the stabilized laser achieves high performance metrics including a phase noise of -97 dBc / Hz at 10 kHz offset frequency, a fractional frequency stability of 5 x 10'13at 10 ms, a 150 Hz l / jr integral linewidth, and a 35 mHz fundamental linewidth, thus providing a high level of stable laser performance into PICs. Additionally, the disclosure provides a complementary integrated system that includes a vertical emission grating coupler and a back-reflection cancellation circuit, achieving signal redirection with 10 dB suppression ratio. This system may be used in various RF photonic systems, such as fully integrated photonic microwave oscillators and can also be utilized for other RF photonic signal processing, such as RF filtering.

[0124] The systems described herein integrating pFP cavities and PICs provide ultra-stable integrated lasers and oscillators, providing substantial improvements in phase noise and frequency stability over conventional dielectric resonators. Combined with the wafer- level pFP fabrication approaches described herein, these systems provide portable, low-cost, and high- performance microwave-photonic systems. The systems address the challenge of frequency stability and noise in compact integrated photonic systems, which is crucial for advancements in precision metrology, quantum computing, communication, and advanced sensing technologies.

[0125] Systems described herein may eliminate wide-band mirror-like reflection from a micro Fabry-Perot cavity, which can cause laser destabilization. To do so, an interface circuit may be used to transform the reflection response. This interface may include a loop mirror and a phase shifter configured to destructively interfere with the mirror reflection from the micro Fabry- Perot cavity. Photodetectors (PD) in both the reflection port and the transmission port may be utilized to characterize the frequency response of the system while sweeping the laser across the micro Fabry-Perot cavity resonance. When the phase of the loop mirror and the micro Fabry- Perot cavity constructively interfere at the reflection port, the reflection provides a typical resonance dip response, as shown in plot 1302 of FIG. 13A. FIG. 13A illustrates reflection and transmission response for the constructive phase in the reflection port of loop mirror and micro Fabry-Perot cavity. By adjusting the phase of the interferometer with controls such as an on-chip heater or piezo control of the micro Fabry-Perot cavity position, destructive interference at the reflection port is instead provided. As illustrated in plot 1304 of FIG. 12B, this provides the suppression of the wide-band mirror-like response and the appearance of a resonant leakage Attorney Docket No.: Y0087.70172WQ00 peak in the reflection port. FIG. 13B illustrates reflection and transmission response for the destructive phase in the reflection port of loop mirror and micro Fabry-Perot cavity.

[0126] Fabry-Perot (FP) resonators have many unique properties that make them useful for applications ranging from ultra-stable lasers, optical clocks, microwave oscillators, to quantum networks, among other application. Since Fabry-Perot cavities host electromagnetic modes that live almost entirely in vacuum, Fabry-Perot cavities may provide greatly reduced frequency instabilities relative to dielectric resonators. To enable next-generation quantum communications, computation, and timekeeping technologies, the systems and methods described herein provide the performance advantages of Fabry-Perot resonators in compact, integrated platforms. As described herein, as part of these integrated technologies, techniques for wafer-scale fabrication of vacuum-gap micro-Fabry-Perot cavities may be used to produce compact reference cavities with ultrahigh Q-factors (e.g., > 109) and excellent frequency stability. However, the inventors have recognized that in order to harness these performance advantages in next generation integrated photonic systems, new systems and methods may be used to interface micro Fabry-Perot reference cavities with photonic integrated circuits (PICs).

[0127] To provide micro Fabry-Perot cavities for on-chip frequency references, systems described herein may provide efficient access to the resonator modes, and may use and methods to transform the cavity response to various applications. For instance, electrical feedback can be used to actively stabilize a laser to the modes of a Fabry-Perot cavity by detecting the reflection response using Pound-Drever-Hall (PDH)-based feedback control. These systems may protect the on-chip laser from back-reflections and efficient signal redirection for detection. Described herein are systems and methods that address the challenge of protecting the laser, using a reflection cancellation circuit with similar architecture to a poor man’s isolator.

[0128] Using systems and methods described herein, the frequency stability of a micro Fabry- Perot reference cavity can be transferred to a laser oscillator using optical feedback through selfinjection locking. These systems and methods may eliminate or reduce complex feedback control of other systems while producing noise suppression at higher bandwidths using a simpler system architecture. Such efficient and stable self-injection locking may use new configurations to shape and control the response of the micro Fabry-Perot cavity to provide resonant feedback with integrated laser. Accordingly, the circuit interfaces described herein may be used in ultra- Attorney Docket No.: Y0087.70172WQ00 high-performance lasers and oscillators, as they provide the performance advantages of vacuumgap reference cavities to integrated photonics systems.

[0129] Described herein are systems and methods for cointegration of vacuum-gap micro Fabry- Perot reference cavities with photonic integrated circuits to provide compact and ultrahigh performance lasers and oscillators. To harness micro Fabry-Perot cavities for self-injection locking, the systems and methods described herein use a circuit interface that transforms the reflection response of a micro Fabry-Perot to produce desired resonant feedback. Using such systems and methods, there is provided self-injection locking of a waveguide-integrated laser to an in-vacuum bonded micro Fabry-Perot reference cavity. The cavity may be fabricated using a wafer-scale process. By providing self-injection locking of the DFB laser to the micro Fabry- Perot reference cavity, the systems and method described herein may provide, for example, a single side-band phase noise of -97 dBc / Hz at 10 kHz offset frequency, 5 x 10'13fractional frequency stability at 10 ms, with a 150 Hz l / jr integral line width and a 35 mHz fundamental linewidth, corresponding to greater performance than conventional systems and methods for providing of self-injection locked laser within waveguide-integrated system. To harness the frequency stability of micro Fabry-Perot reference cavities using PDH-locking schemes, described herein is an alternative approach for fully integrating a micro Fabry-Perot cavity using a complementary circuit interface. The integrated micro Fabry-Perot may provide an isolator- free circuit interface for PDH locking, consisting of a circuit-based two-port interferometer that cancels unwanted back-reflections while mapping the cavity’s reflection response to a separate optical port. The systems and methods described herein use reference cavities within integrated circuits open new avenues for ultra-high performance portable photonic microwave systems, integrated optical gyroscopes, and enhanced quantum systems, among other applications, with the continued advancement of such micro Fabry-Perot reference cavity technologies.

[0130] Integration of high-performance vacuum-gap micro Fabry-Perot reference cavities with waveguide-based PIC platforms presents several challenges. For example, when directly probed, a Fabry-Perot reference cavity may reflect laser light back into source, which is generally unfavorable for stable laser operation. Described herein are general on-chip interferometric systems and methods that address this problem. Such systems and methods may either reshape the spectral response of the Fabry-Perot reference cavity reflection that enables on-chip laser self-injection locking, or may almost completely or completely redirect the reflection signal Attorney Docket No.: Y0087.70172WQ00 without using a circulator. A second challenge is the large difference in size between the modes supported by waveguides and Fabry-Perot reference cavities, where the latter are usually an order of magnitude larger. Systems and methods described herein overcome these challenges with two complementary approaches that use edge and surface couplers to efficiently interface and access millimeter-scale reference cavity modes from micron-scale waveguide modes in two steps. According to some embodiments, an inverse (e.g., FIG. 16A) taper or grating coupler (e.g., FIG. 16B) is first used to expand the waveguide mode to several microns. FIG. 16A-16B show integration of a micro Fabry-Perot cavity with PICs, illustrating a schematic of a mode- matched packaging approach from PIC to micro Fabry-Perot with FIG. 16A showing an end- fire coupler, and FIG. 16B showing a grating coupler. FIG. 16A shows a photonic integrated circuit 1600 with a waveguide 1602, an edge-coupled GRIN lens 1604, and a micro Fabry-Perot resonator 1606. FIG. 16B shows a photonic integrated circuit 1620 with a waveguide 1622, a grating coupler-coupled GRIN lens 1624, and a micro Fabry-Perot resonator 1626.

[0131] A micro-optic gradient-index (GRIN) lens may then be used to expand and collimate the beam to a mode field diameter of 240 pm, as used for efficient mode-matching with the micro Fabry-Perot cavity modes. An exemplary vacuum-gap micro Fabry-Perot reference cavity used for systems and methods described herein is shown in FIG. 17A. FIG. 17A shows a resonator array 1700 comprising resonators 1702. As shown in FIG. 17A, the array may be a wafer-level in-vacuum bonded cavity array, and micro Fabry-Perot cavities may be diced from the array on, for example, 2-inch wafers. Such a reference cavity may be formed using a wafer-scale fabrication process. A chemically assisted reflow process may be used to produce an array of concave micro-mirrors (e.g., with 35 cm radius of curvature) on a super-polished glass wafer (e.g., of size 2-inches). Through optical-contact bonding of the concave and flat mirror wafers onto a matched spacer, a micro Fabry-Perot cavity array may be constructed that can be diced into individual cavities (e.g., as in FIG. 17A). To reduce or eliminate unwanted sources of noise and frequency drift, the mirror and spacer may be fabricated from ultra-low expansion glass, and the cavity assembly may be bonded in a vacuum environment. FIG. 17B shows a schematic illustration of the in-vacuum bonded micro Fabry-Perot cavity, with ROC indicating radius of curvature. As shown in FIG. 17B, a micro Fabry-Perot cavity 1720 may comprise first and second reflective surfaces 1722 and 1724 as well as a cavity 1726. According to some embodiments, such a plano-concave micro Fabry-Perot reference cavity may have compact Attorney Docket No.: Y0087.70172WQ00 dimensions of 9x9x7 mm, small volume less than 0.6 mL and Gaussian mode field diameter of 240 pm. In some embodiments, the optical quality factors of these cavity modes may be 4.26 x 109according to optical ring-down spectroscopy (e.g., as shown in FIG 17C), corresponding to a cavity linewidth of 45 kHz and a finesse of 8.25 x 105. FIG. 17C shows a plot 1742 illustrating optical ring-down measurement of micro Fabry-Perot cavity yielding quality factor of 4.26 billion. In some embodiments, such vacuum-gap micro Fabry-Perot reference cavities may produce excellent phase noise and frequency stability. The fabricated micro Fabry-Perot cavity having a hermetically sealed vacuum gap may offer not only an unparalleled noise performance free from the limitations of thermo-refractive noise in dielectric cavities (as shown in FIG. 16C) but may also eliminate the need for a vacuum enclosure. Hence, the integration of such high- performance micro Fabry-Perot cavities may bring these benefits to PIC platforms to enable next-generation compact lasers, oscillators, and sensors. FIG. 16C shows a plot 1642 with illustrating a survey of resonator thermal noise limit at 10 kHz and quality factor for on-chip ring cavity, WGM cavity and vacuum Fabry-Perot cavity. Cavities described herein may have > 104 times smaller form factor than other devices plotted in FIG. 16C and may not require vacuum enclosure.

[0132] Systems and methods described herein may include a chip-based spectrum reshape circuit and micro Fabry-Perot reference cavity to demonstrate two applications for optical feedback and electrical feedback. According to some embodiments, there are provided systems performing direct self-injection locking of an on-chip laser to a micro Fabry-Perot reference cavity. Such methods use passive optical feedback to enhance laser stability directly with the micro Fabry-Perot cavity. According to some embodiments, using a grating coupler systems and methods may perform micro Fabry-Perot signal redirection and back-reflection cancellation within a co-packaged device. This configuration facilitates the effective use of the micro Fabry- Perot cavity for electrical feedback in a more general RF photonic platform.

[0133] According to aspects of the disclosure, there are provided systems and methods that use a photonic interface for self-injection locking. Through self-injection locking (SIL), optical feedback can be used to lock a laser frequency to an external cavity, causing the laser to inherit the noise characteristics of the cavity. Various systems may use silicon nitride ring resonators to self-injection lock chip-scale semiconductor lasers to improve their phase noise characteristics. Some conventional approaches may rely on Rayleigh back-scattering to produce resonant Attorney Docket No.: Y0087.70172WQ00 feedback necessary for self-injection locking. However, the thermo-refractive noise and scattering losses in such conventional approaches limit the achievable quality factors and noise characteristics of such waveguide-based resonators. The systems described herein solve the problems of such conventional approaches by using vacuum-gap micro Fabry-Perot reference cavities, to reduce or practically eliminate thermos -refractive noise, thereby providing systems with lasers that have greatly improved phase noise and frequency stability. Such systems and methods using self-injection locking of integrated lasers may utilize the approaches described herein for interfacing micro Fabry-Perot cavities with photonic integrated circuits to produce resonant feedback.

[0134] Some conventional approaches for producing resonant feedback may rely on circulators to redirect the transmission response of the Fabry-Perot cavity into the laser. However, such strategies present challenges, as they are difficult to implement using photonic integrated circuits, due to isolators and circulators not being widely available. Moreover, it would be difficult to access both ports of the micro Fabry-Perot cavity using a single chip. Alternatively, some conventional systems may produce resonant feedback by partial excitation of higher order modes using a tilted cavity configuration. However, this approach presents challenges due to the requirement of a more complex alignment procedure, and it results in excess coupling losses that greatly reduce the efficiency of laser feedback.

[0135] Described herein is a circuit interface configured to transforms the reflection response of a micro Fabry-Perot cavity to produce resonant feedback used for self-injection locking. In reflection, the cavity modes of a Fabry-Perot resonator appear as anti-resonances (dips) atop a high reflectivity background. Such anti-resonances are unsuitable for self-injection locking. These antiresonances result from interference between light that is resonantly scattered by the cavity modes and a broadband reflection produced by the mirrors. To utilize a micro Fabry-Perot for self-injection locking, it is systems and methods described herein reduce or eliminate the high reflectivity background, leaving only resonant scattering (or leakage field) to produce feedback. The high reflectivity background is to be eliminated because broadband mirror reflections can produce parasitic resonances that destabilize the laser. Using the systems and methods described herein, the wideband mirror reflection can be eliminated, leaving only resonant backscatter from the cavity modes, and efficient resonant feedback is provided. In these Attorney Docket No.: Y0087.70172WQ00 configurations, a sudden phase shift produced by resonant backscattering about the cavity resonance provides an improved or optimal feedback mechanism for self-injection locking.

[0136] FIG. 10A shows a photonic circuit with an on-chip laser directly self-injection locked to co-packaged micro Fabry-Perot cavity, with a schematic illustration of the on-chip circuit design that provides the self-injection locking to co-packaged micro Fabry-Perot cavity. FIG. 10A shows a photonic integrated circuit 1000, with an input port 1002, an output port 1004, a first waveguide 1006, a second waveguide 1008, a tunable directional coupler 1010, a GRIN lens 1012 coupled to an optical element 1014 (which may be a micro Fabry-Perot resonator), a reflector 1016 (which may be a loop mirror), a light source 1018 (which may be an on-chip laser), as well as first and second phase controls 1020 and 1022, (which may be heaters).

[0137] According to aspects of the disclosure a circuit interface configured to produce resonant feedback into a waveguide-based DFB laser is illustrated in FIG. 10A. An on-chip directional coupler 1010 divides the incoming light, directing a portion of light into a reflector 1016 which is an on-chip loop-mirror that introduces an additional broadband mirror reflection. The remaining light travels to the chip facet, where it is collimated by a GRIN lens 1012 to match the mode of the co-packaged Fabry-Perot cavity 1014. These two reflections interfere upon recombination at the directional coupler 1010. With the correct phase <p2, the loop-mirror reflection destructively interferes with the Fabry-Perot cavity reflection, cancelling the broadband mirror reflections and preserving only the resonant backscattered light. This results in a resonant (Lorenzian) feedback spectrum, facilitating self-injection locking by adjusting the feedback phase FIG. 10B shows a photograph of the photonic circuit 1000 comprising the DFB laser self-injection locked to micro Fabry-Perot cavity through interface chip.

[0138] In some embodiments, a GRIN lens of the system may be configured to expand and collimate a beam of light emitted from the waveguide end-facet to match the micro Fabry-Perot cavity mode. To perform this mode transformation using our circuit interface, the system may have an inverse taper at the output facet of a ShN4 waveguide, producing a mode diameter of approximately 3 pm. A GRIN lens with an effective focal length of 0.46 mm may then expand this 3 pm to 240 pm, matching the mode field diameter of the micro Fabry-Perot cavity, providing coupling losses as low as 1.5 dB. Hence, this simple and compact photonic interfacing technique, shown in FIG. 10B, offers a practical means of co-packaging the micro Fabry-Perot Attorney Docket No.: Y0087.70172WQ00 cavity with PICs, to enable high performance oscillators and lasers for next-generation photonic systems.

[0139] A circuit interface, such as illustrated in FIG 11C, may be used to control the optical feedback parameters of this system, in order to obtain a stable self-injection locking. FIG. 10C shows a schematic of experimental setup for noise measurement. Black lines indicate electrical control, and red lines indicates optical circuits, where PD indicates photodetector, ESA indicates electrical spectrum analyzer, and AOM indicates acousto-optical modulator. The output of SIL laser either beats with another stable laser or performs self-heterodyne with 800 m delay line for the ESA to measure phase noise. FIG. 10C shows a measurement apparatus 1050 comprising the photonic integrated circuit 1000, as well as current and temperature measurements 1052 and 1054, first and second piezos 1056 and 1058, photodetector 1060, and stable laser circuit 1062.

[0140] The interface circuit includes integrated heaters that allow for adjustment of the coupler splitting ratio, the feedback phase (p-^, and the interferometer phase <p2. Piezo actuators on both the DFB laser and the micro Fabry-Perot cavity may also be used for fine-tuning and <p2by modulating their separation from the photonic circuit. When and <p2are adjusted to produce a self-injection locked state, the frequency of laser emission becomes resonant with the micro Fabry-Perot cavity, producing a dramatic increase in the light intensity emitted by the micro Fabry-Perot cavity. Light transmitted from the micro Fabry-Perot cavity is collected through free space and monitored with a photodetector to observe the onset of the self-injection locking process. The output from the SIL laser is then coupled into the fiber-based apparatus of FIG. 10C for phase noise measurements.

[0141] According to some embodiments, two complementary techniques may be used to quantify the phase noise of the self-injection-locked laser. To measure the phase noise at low offset frequencies, the beat note between the integrated SIL laser and another frequency- stabilized reference laser may be analyzed using a phase noise analyzer, as shown in FIG. 10C. The stable laser may include a fiber laser that is PDH-locked to a large table-top Fabry-Perot reference cavity that is known to have low phase noise at low offset frequency (e.g., 0 dBc / Hz at 1 Hz offset frequency). However, since the PDH feedback loop introduces excess noise, seen as a servo bump at offset frequencies above 10 kHz, a complementary measurement method may be used to analyze the phase noise of SIL laser at higher offset frequencies. For example, a fiber interferometer with 800 m delay shown in FIG 10C may be used to perform self-heterodyne Attorney Docket No.: Y0087.70172WQ00 measurements. This complementary approach is ideal for phase noise measurements at high offset frequencies since the fiber interferometer is essentially free of technical noise for frequencies above 5 kHz. Combining these two techniques, a complete picture of phase noise spectrum of the SIL laser from 1Hz to 1MHz may be obtained, as seen in FIG. 11 A.

[0142] FIG. 11 A shows plot 1102 of phase noise spectrum for SIL and free running laser. Free running laser phase noise may be measured using self-heterodyne. The shaded region indicates the noise is limited by the measurement noise floor. The measurements of FIG. 11 A show a dramatic reduction in the phase noise of the DFB laser when it is injection locked to the micro Fabry-Perot cavity. Self-injection locking is seen to reduce the phase noise of the DFB laser by eight, seven, and six orders of magnitude at offset frequencies of 1 kHz, 10 kHz, and 100 kHz, corresponding to phase noise levels of -65 dBc / Hz, -97 dBc / Hz, and -122 dBc / Hz, respectively. Further analysis of the phase noise spectrum shows a fundamental linewidth of 35 mHz and a l / 7t integral linewidth of 150 Hz. The reduction in laser linewidth produced by self-injection locking is further shown in the direct RF beat note spectrum between the SIL laser and a stable reference laser, as shown in FIG. 1 IB. FIG. 1 IB shows plots 1104 for an RF beat note spectrum of the SIL laser and a stable laser revels linewidth compression when locked, and plot 1106 showing a zoom in of plot 1104. As shown in FIG. 1 IB, a free running beat note is taken with 91 kHz RBW, and locked beat note is taken with 3 kHz RBW.

[0143] It should be appreciated that the linewidth in FIG. 1 IB may be constrained by the resolution bandwidth (RBW) of the electronic spectrum analyzer. Note that these measurements may be performed with a relatively large resolution bandwidth (>3 kHz) to ensure a stable beat note spectrum within the acquisition time. The Allan deviation, which may be indicative of fractional frequency stability for different averaging times, is seen in FIG. 11C, showing 5 x 10"13at 10 ms averaging time. FIG. 11C shows plot 1108 of an Allan deviation of the SIL laser measured from frequency counter with and without linear drift removal. After removing linear drift of 109Hz / s, the system exhibits a fractional frequency stability better than 5 x 10'12from 1 ms to 50 s averaging times.

[0144] It should be appreciated that these measurements correspond to record-level improvements in phase noise over conventional systems. The measurements described above may be obtained without active temperature stabilization of the cavity, illustrating the temperature insensitivity and robustness of such in-vacuum bonded micro Fabry-Perot reference Attorney Docket No.: Y0087.70172WQ00 cavities. Deviations from the thermal noise limit at low offset frequencies may be attributed to mechanical noise from the translation stages used to position the cavity and DFB laser. Hence, the low offset phase noise and frequency drift may be even further improved for a system that is fully co-packaged.

[0145] The dynamics of the self-injection locking are also analyzed, by slowly modulating the DFB laser current to observe shifts in the RF beat note spectrum with a stable reference laser, as depicted in FIG. 12A. FIG. 12A-12B show locking range and dynamics of the SIL laser. In FIG. 12A, plot 1202 shows an RF beat note spectrum of the SIL laser and a stable laser with a sweeping current on the DFB laser yields a 265 MHz locking range. In FIG. 12B, plot 1204 shows a theoretical locking curve, where the SIL laser entering and exiting the locked state are due to relaxation oscillation of the DFB laser, and the off-resonance curve deviates from free running due to the residual broadband mirror reflection. This system enters and exits the SIL state at points b to b’ and f to f’, respectively, demonstrating a locking range of 265 MHz. Comparison with a theoretical model of the self-inj ection locking process suggests that the onset of self-injection locking occurs earlier than expected; this is likely due to laser relaxation oscillations produced by semiconductor gain medium. The asymmetric feature for two directions of SIL is due to the fact that the feedback phase is non-zero. It should also be appreciated that away from the micro Fabry-Perot resonance, the relationship between output frequency and DFB laser frequency may diverge from the identity line, indicating that mirror reflections are not entirely cancelled, leaving a small amount of residual broadband feedback. This feedback remains sufficiently weak to avoid destabilizing the laser, it appears to have little impact on the performance of the SIL laser.

[0146] Aspects of the disclosure provide a photonic interface for electrical control. Beyond selfinjection locking, circuit interfaces described herein provide efficient interrogation of micro Fabry-Perot cavity modes can enable complementary applications involving on-chip frequency metrology and microwave photonic signal processing. For example, PDH-locking provides a versatile means of harnessing reference cavities with many practical advantages. Since PDH- locking can be implemented with low incident optical powers (~10 pW) relative to self-injection locking (>1 mW), photothermal noise is greatly reduced, permitting systems and methods described herein to more readily reach the thermal noise limit, as shown in FIG. 11 A. Additionally, PDH-locking enables frequency tunability and lower phase noise at low offset Attorney Docket No.: Y0087.70172WQ00 frequencies, making it useful for the most demanding applications requiring precise frequency control. Alternatively, such ultra-high Q-factor micro Fabry-Perot cavities can be used for microwave-photonic filtering and signal processing. Applications such as PDH-locking and micro wave photonic signal processing may use a photonic interface for efficient interrogation of micro Fabry-Perot cavities while protecting on-chip lasers from strong feedback and reflections. Optical circulators are often used for redirecting reflected light for such applications in conventional systems, but circulators and isolators are not yet widely available in integrated photonics due to the incompatibility of magnetic media with CMOS fabrication processes.

[0147] Further described herein are reflection cancellation circuits that use configurations similar to poor man’s isolator into a circuit architecture. Such systems and methods may interface and integrate a micro Fabry-Perot cavity using a silicon photonic circuit fabricated from a silicon-on-insulator platform. This circuit may include a two-port interferometer that connects to an inverse-designed two-port polarization- splitting grating coupler (PSGC). By fine- tuning the on-chip phase shifter, this vertical-emission PSGC efficiently couples circularly polarized light into the micro Fabry-Perot cavity, providing interrogation of the reflection response of the cavity. Making use of the fact that the chirality of circularly polarized light is reversed upon the reflection from micro Fabry-Perot cavity, this circuit achieves a function very similar to that of a circulator. FIG. 14A shows a co-packaged micro Fabry-Perot for electrical feedback, with the schematic illustrating a co-packaged micro Fabry-Perot cavity, which provides signal redirection and back-reflection isolation. FIG. 14A shows a photonic circuit 200c comprising an input port 202c, an output port 204c, a first waveguide 206c, a second waveguide 208c, a directional coupler 210c, a control 218c, and a polarization splitting grating coupler 212c, which is coupled to an optical element 214c (which may be a micro Fabry-Perot resonator) using a GRIN lens 216c. FIG. 14B shows a cross section of a co-packaged micro Fabry-Perot cavity, further illustrating a spacer 220c between the polarization splitting grating coupler 212c and the optical element 214c. FIG. 14C shows a photograph of such a photonic integrated circuit 200c with a side view of the co-packaged module and photonic integrated circuit.

[0148] Efficient coupling into the micro Fabry-Perot may be provided using a GRIN lens to expand the beam produced by PSGC. The PSGC may be configured to produce vertical emission of a 10.4 pm mode field diameter. This beam may be expanded to produce a collimated Attorney Docket No.: Y0087.70172WQ00

[0149] 240 pm mode field diameter at the input micro Fabry-Perot cavity using a GRIN lens with an effective focal length of 0.94 mm. The GRIN lens and micro Fabry-Perot cavity may then be cointegrated with PIC using a custom spacer that provides mechanical stability for the bonded assembly, as is shown in FIG. 14B. Using this integration method, light can be coupled from the silicon circuit into the micro Fabry-Perot cavity with an efficiency of -2.8 dB. A fiber array may be bonded the chip-integrated micro Fabry-Perot module to interrogate the response of this multi-port photonic interface.

[0150] FIG. 15A shows plot 1522 with data showing signal redirection and characterizing back- reflection isolation ratio. FIG. 15A shows the optical reflection from Port A and the transmission to Port B as a function of laser detuning from the cavity resonance. As seen in 15C, this circuit maps the micro Fabry-Perot cavity reflection response to Port B while simultaneously suppressing back-reflections from Port A. The relative magnitude of the transmission and reflection reveal 10 dB back-reflection suppression, to aid in protecting an on-chip laser from unwanted feedback. Such a fully integrated module is readily suitable for an on-chip PDH locking system, as shown in FIG. 15B. FIG. 15B shows an outlook for an on-chip PDH locking system, with PM indicating phase modulator, PD indicating photodetector, LD indicating laser diode, and EIC indicating electric integrated circuits. As shown in FIG. 15B, a measurement apparatus 1500 includes photonic integrated circuit 200c, as well as a laser diode 1502, a stable light output 1504, a phase modulator 1506, a photodiode 1508, and electric integrated circuits 1510.

[0151] Together with many other applications such as photonic RF filtering and microwave oscillators, the co-integration of vacuum-gap micro Fabry-Perot cavities paves the way for a next-generation of compact, high-performance RF photonic systems.

[0152] According to some embodiments, systems described herein may integrate high- performance vacuum-gap micro Fabry-Perot reference cavities with photonic integrated circuits, providing both electrical and optical feedback for next-generation lasers, oscillators, and sensors. Using circuit interfaces described herein to transform the response of the micro Fabry-Perot resonator, the systems and methods according to the disclosure may provide the resonant optical feedback that is used to self-injection lock a waveguide-based laser with the reference cavity. According to some embodiments, these systems and methods may for produce an integrated laser with a fundamental linewidth of 35 mHz and an integrated l / jr linewidth of 150 Hz, Attorney Docket No.: Y0087.70172WQ00 corresponding to record- level performance. Phase noise measurements represent a 19 dB improvement in phase noise at 1 kHz offset frequency, and a 17 dB improvement in phase noise at 10 kHz offset frequency, relative to some conventional approaches using 1.4 m spiral waveguide resonators. Since the electromagnetic energy is stored almost entirely in vacuum, this vacuum-gap micro Fabry-Perot cavity may overcome numerous limitations imposed by dielectric-induced thermo-refractive noise. Moving from stage controlled pieces to fully packaged and on-chip electric-optical controlled system, low-offset frequency noise can be further improved and long-term locking robustness can be extended from several hours to longer durations. Such low phase noise levels make this system highly suitable for photonic microwave oscillators through use of optical frequency division, potentially eliminating the need for more complex PDH locking schemes.

[0153] According to aspects of the disclosure, the reflection response of such vacuum-gap micro Fabry-Perot cavities can be interrogated using a circuit interface, to provide on-chip PDH- locking and microwave photonic signal processing. Co-integration of the cavity with a silicon photonic circuit is provided by attaching the cavity to a multi-port vertical-emission grating coupler. Using this grating interface, the cavity is placed within an optical interferometer that cancels unwanted back reflections, eliminating the need for on-chip circulators and isolators. This same interferometer maps the reflection response to a separate optical port, providing efficient interrogation of the reflection response used for PDH-locking and microwave photonic signal processing. Hence, the interfacing methods described herein provide access to an ultranarrow linewidth and stable reference cavity that becomes a versatile resource for advanced microwave-photonic filtering, on-chip PDH locking, and sensing applications.

[0154] The cointegration of such high-performance vacuum-gap reference cavities with photonic circuits presents numerous advantages. By storing electro-magnetic field mostly in vacuum, the limitations associated with thermo-refractive noise are mitigated, and high performance is provided across various photonic integrated systems. Additionally, with sealed vacuum and athermal material, these cavities significantly reduce environmental constraints, thereby broadening the operating conditions. Furthermore, such reference cavities can achieve substantially higher performance with larger mode volumes, increased cavity lengths, and improved packaging. Hence, systems and methods described herein provide a crucial Attorney Docket No.: Y0087.70172WQ00 capabilities for use in next-generation integrated lasers, oscillators, and sensors, among other systems.

[0155] Also, various inventive concepts may be embodied as one or more processes, of which examples are provided. The acts performed as part of each process may be ordered in any suitable way. Accordingly, embodiments may be constructed in which acts are performed in an order different than illustrated, which may include performing some acts simultaneously, even though shown as sequential acts in illustrative embodiments.

[0156] Various aspects of the embodiments described above may be used alone, in combination, or in a variety of arrangements not specifically discussed in the embodiments described in the foregoing and is therefore not limited in its application to the details and arrangement of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments.

[0157] All definitions, as defined and used herein, should be understood to control over dictionary definitions, definitions in documents incorporated by reference, and / or ordinary meanings of the defined terms.

[0158] The indefinite articles “a” and “an,” as used herein in the specification and in the claims, unless clearly indicated to the contrary, should be understood to mean “at least one.”

[0159] The phrase “and / or,” as used herein in the specification and in the claims, should be understood to mean “either or both” of the elements so conjoined, i.e., elements that are conjunctively present in some cases and disjunctively present in other cases. Multiple elements listed with “and / or” should be construed in the same fashion, i.e., “one or more” of the elements so conjoined. Other elements may optionally be present other than the elements specifically identified by the “and / or” clause, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, a reference to “A and / or B,” when used in conjunction with open-ended language such as “comprising” can refer, in one embodiment, to A only (optionally including elements other than B); in another embodiment, to B only (optionally including elements other than A); in yet another embodiment, to both A and B (optionally including other elements); etc.

[0160] As used herein in the specification and in the claims, the phrase “at least one,” in reference to a list of one or more elements, should be understood to mean at least one element Attorney Docket No.: Y0087.70172WQ00 selected from any one or more of the elements in the list of elements, but not necessarily including at least one of each and every element specifically listed within the list of elements and not excluding any combinations of elements in the list of elements. This definition also allows that elements may optionally be present other than the elements specifically identified within the list of elements to which the phrase “at least one” refers, whether related or unrelated to those elements specifically identified. Thus, as a non-limiting example, “at least one of A and B” (or, equivalently, “at least one of A or B,” or, equivalently “at least one of A and / or B”) can refer, in one embodiment, to at least one, optionally including more than one, A, with no B present (and optionally including elements other than B); in another embodiment, to at least one, optionally including more than one, B, with no A present (and optionally including elements other than A); in yet another embodiment, to at least one, optionally including more than one, A, and at least one, optionally including more than one, B (and optionally including other elements); etc.

[0161] Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.

[0162] In the claims, as well as in the specification above, all transitional phrases such as “comprising,” “including,” “carrying,” “having,” “containing,” “involving,” “holding,” “composed of,” and the like are to be understood to be open-ended, i.e., to mean including but not limited to. Only the transitional phrases “consisting of’ and “consisting essentially of’ shall be closed or semi-closed transitional phrases, respectively.

[0163] The terms “approximately,” “about,” and “substantially” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, within ±2% of a target value in some embodiments. The terms “approximately,” “about,” and “substantially” may include the target value.

[0164] Having thus described several aspects of at least one embodiment, it is to be appreciated that various alterations, modifications, and improvements will readily occur to those skilled in the art. Such alterations, modifications, and improvements are intended to be part of this Attorney Docket No.: Y0087.70172WO00 disclosure and are intended to be within the spirit and scope of the principles described herein.

[0165] Accordingly, the foregoing description and drawings are by way of example only.

Claims

Attorney Docket No.: Y0087.70172WQ00CLAIMSWhat is claimed is:

1. A photonic integrated circuit, comprising: a first waveguide having an input port configured to be coupled to a light source; a second waveguide having an output port; a directional coupler coupling the first waveguide and the second waveguide; a micro-fabricated resonant cavity; and a grating coupling the first waveguide to the micro-fabricated resonant cavity and coupling the micro-fabricated resonant cavity to the second waveguide.

2. The photonic integrated circuit of claim 1, wherein the directional coupler is configured to receive light from the input port and split the received light between the first waveguide and the second waveguide.

3. The photonic integrated circuit of claim 2, wherein the directional coupler is configured to induce a phase difference between light in the first waveguide and the second waveguide.

4. The photonic integrated circuit of claim 1, wherein the directional coupler is configured combine light from the first waveguide and the second waveguide and provide the combined light to the output port.

5. The photonic integrated circuit of claim 4, wherein the directional coupler is configured to combine light from the first waveguide and the second waveguide having a phase difference.

6. The photonic integrated circuit of claim 1, wherein the grating comprises a polarizationsplitting grating coupler.

7. The photonic integrated circuit of claim 6, wherein the polarization- splitting grating coupler is configured to:Attorney Docket No.: Y0087.70172WQ00 scatter light from the first waveguide having a first polarization to the micro-fabricated resonant cavity; and scatter light from the second waveguide having a second polarization to the microfabricated resonant cavity; and8. The photonic integrated circuit of claim 6, wherein the polarization- splitting grating coupler is configured to: scatter light from the micro-fabricated resonant cavity having a first polarization to the first waveguide; and scatter light from the micro-fabricated resonant cavity having a second polarization to the second waveguide.

9. The photonic integrated circuit of claim 1, wherein the micro-fabricated resonant cavity comprises a Fabry-Perot resonator.

10. The photonic integrated circuit of claim 1, wherein the first waveguide and the second waveguide have a same path length.

11. The photonic integrated circuit of claim 1, wherein the light source is a laser.

12. The photonic integrated circuit of claim 1, wherein the output port is configured to provide an output signal representing a resonant frequency of the micro-fabricated resonant cavity.

13. A photonic integrated circuit, comprising: a first waveguide having an input port configured to be coupled to a light source; a second waveguide having an output port; a directional coupler coupling the first waveguide and the second waveguide; a micro-fabricated resonant cavity coupled to the first waveguide; and a reflector coupled to the second waveguide.Attorney Docket No.: Y0087.70172WQ0014. The photonic integrated circuit of claim 13, wherein the directional coupler is configured to receive light from the input port and split the received light between the first waveguide and the second waveguide.

15. The photonic integrated circuit of claim 13, wherein the directional coupler is configured combine light from the first waveguide and the second waveguide and provide the combined light to the output port.

16. The photonic integrated circuit of claim 13, further comprising a control configured to adjust a light splitting ratio of the directional coupler.

17. The photonic integrated circuit of claim 13, wherein the reflector comprises a loop mirror.

18. The photonic integrated circuit of claim 13, further comprising a gradient- index lens coupling the first waveguide to the micro-fabricated resonant cavity.

19. The photonic integrated circuit of claim 13, wherein the micro-fabricated resonant cavity comprises a Fabry-Perot resonator.

20. The photonic integrated circuit of claim 13, further comprising a control configured to adjust a phase of light in the first waveguide.

21. The photonic integrated circuit of claim 13, wherein the light source is a laser.

22. The photonic integrated circuit of claim 13, wherein the output port is configured to provide an output signal representing a resonant frequency of the micro-fabricated resonant cavity.

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