The present invention provides octave-spanning optical frequency combs. The octave-spanning optical frequency combs employ microresonators having improved stability using a smaller form factor. In some embodiments, the octave-spanning optical frequency combs are fabricated using aluminum nitride (AlN). AlN is a more robust Kerr material for generating octave-spanning soliton comb (e.g., 1.5 octaves or more).

BACKGROUND

Silicon Nitride (Si3N4) is a commonly used optical frequency comb microresonator material, but it is a challenging material to reproducibly fabricate and deterministically launch octave-spanning soliton combs. Furthermore, the properties of Si3N4impose physical limitations that require comb-locking to be performed off-chip, which not only introduces loss but also adds system complexity.

Optical frequency combs, originally developed from solid-state or fiber based mode-locked lasers, have evolved into photonic-chip-based sources that are compact, robust and power efficient. Among various chipscale schemes, microresonator Kerr frequency combs (“microcombs” hereafter) are of particular interest because of their high scalability for photonic integration. Indeed, substantial efforts have been made towards soliton mode-locking, allowing phase coherent microcombs on the one hand and unveiling rich soliton physics on the other hand. Specifically, octave-spanning soliton microcombs permit phase locking of the carrier-envelop offset (CEO) frequency (fceo) via well-known f−2f interferometry, and are prerequisite for chip-scale implementation of precision metrology, frequency synthesizers and optical clocks. To date, silicon nitride (Si3N4) nanophotonics has proved viable for octave soliton operations with a terahertz repetition rate (frep). Nevertheless, such a large frepis not amenable for direct photodetection and poses challenges to access the CEO frequency with a value up to frep. In the meantime, the lack of intrinsic quadratic x(2)nonlinearities in Si3N4films typically requires an external frequency doubler and off-chip optical circuitry for deriving the CEO frequency. These off-chip optical components compromise the scaling advantage of microcombs and significantly set back self-locked microcombs for portable applications.

Thus, there is a need in the art for improved optical frequency combs. This invention satisfies this unmet need.

SUMMARY

In one aspect, the present invention provides an octave-spanning optical frequency comb device, comprising: an optical pathway having at least one entry and at least one exit; at least one laser source positioned at the at least one entry; and at least one micro ring resonator positioned adjacent to the optical pathway between the at least one entry and the at least one exit, wherein the at least one micro ring resonator comprises aluminum nitride (AlN).

In one embodiment, the at least one laser source is a continuous wave (CW) laser. In one embodiment, the optical pathway further comprises a suppressed carrier single sideband modulator (SC-SSBM) positioned between the at least one laser source and the at least one micro ring resonator. In one embodiment, the optical pathway further comprises an amplifier positioned between the at least one laser source and the at least one micro ring resonator. In one embodiment, the filter is an erbium-doped fiber amplifier (EDFA). In one embodiment, the optical pathway further comprises a fiber polarization controller (FPC) positioned between the at least one laser source and the at least one micro ring resonator.

In one embodiment, the at least one micro ring resonator comprises an oxide cladding. In one embodiment, the oxide cladding is silicon oxide. In one embodiment, the at least one micro ring resonator comprises a ring width and a ring radius. In one embodiment, the ring width is between about 0.5 μm to about 100 μm. In one embodiment, the ring radius is between about 10 μm to about 1000 μm.

In one embodiment, the at least one micro ring resonator is fabricated by chemical vapor deposition of an AlN thin film on a substrate. In one embodiment, the chemical vapor deposition is metalorganic chemical vapor deposition (MOCVD). In one embodiment, the substrate is sapphire. In one embodiment, the AlN thin film comprises at least 0.5% thickness uniformity. In one embodiment, the AlN thin film comprises an annealing temperature of about 1700° C.

In one embodiment, the device comprises an intrinsic optical Q factor of at least 3,000,000. In one embodiment, the at least one micro ring resonator comprise a ring width of 2.5 μm, a ring radius of 60 μm, a repetition frequency frepof 362 GHz, and a comb span of 1.2 octave In one embodiment, the at least one micro ring resonator comprise a ring width of 3.3 μm, a ring radius of 100 μm, a repetition frequency frepof 216.5 GHz, and a comb span of 1.1 octave. In one embodiment, the comb span is at least 1.5 octaves. In one embodiment, the device further comprises an electro-optical comb for repetition comprising a waveguide in resonance with the at least one microring resonator, at least one frequency second harmonic generation doubler, and a racetrack resonator.

DETAILED DESCRIPTION

Definitions

DESCRIPTION

The present invention provides octave-spanning optical frequency combs. Frequency microcombs, successors to mode-locked laser and fiber combs, enable miniature rulers of light for applications including precision metrology, molecular fingerprinting, and exoplanet discoveries. To enable frequency ruling functions, microcombs must be stabilized by locking their carrier-envelop offset frequency. So far, the microcomb stabilization remains compounded by the elaborate optics external to the chip, thus evading its scaling benefit. To address this challenge, the present invention provides a nanophotonic chip solution based on aluminum nitride thin films, which simultaneously offer optical Kerr nonlinearity for generating octave soliton combs and Pockels nonlinearity for enabling heterodyne detection of the offset frequency. The agile dispersion control of crystalline III-Nitride photonics permits high-fidelity generation of solitons with features including 1.5-octave spectral span, dual dispersive waves, and sub-terahertz repetition rates down to 220 gigahertz. These attractive characteristics, aided by on-chip phase-matched aluminum nitride waveguides, allow the full determination of the offset frequency.

The octave-spanning optical frequency combs employ microresonators having improved stability using a smaller form factor. In some embodiments, the octave-spanning optical frequency combs are fabricated using aluminum nitride (AlN). AlN is a more robust Kerr material for generating octave-spanning soliton comb (e.g., 1.5 octaves or more). AlN is also a strong Pockels (x2) material offering on-chip doubling for carrier-envelope-offset frequency (fceo) locking. The X2effect of AlN permits on chip electro-optic modulation for repetition frequency (frep) locking. frepof AlN octave-spanning optical frequency combs can be as low as 216 GHz as opposed to 1 THz fceooffered by Si3N4. Direct photodetection of frepis also possible using AlN octave-spanning optical frequency combs. Additional materials contemplated herein include LiNbO3.

In some embodiments, octave-spanning optical frequency combs are fabricated using chemical vapor deposition to deposit single crystalline AlN thin films onto a substrate. In some embodiments, metalorganic chemical vapor deposition (MOCVD) is used for high throughput film growth. The substrate can comprise any suitable material, such as sapphire. The AlN thin film can be screened and its thickness mapped. Dispersion modeling can be performed using thickness data to achieve flattened anomalous dispersion over a broad bandwidth in devices of appropriate geometries. The fabrication methods can control the thin film nanometer thickness by epitaxial growth (with at least 0.5% thickness uniformity). AlN also permits high temperature annealing (up to 1700° C. as opposed to 1100° C. of Si3N4) for optimization of optical Q factor. Intrinsic optical Q factors of over 3,000,000 are routinely achievable (wherein loaded Q factors are over 1,000,000).

In some embodiments, the octave-spanning optical frequency combs are clad and protected with an oxide layer, such as silicon oxide. In some embodiments, the dispersive features can be tuned continuously up to at least 1.5-octave separation. In some embodiments, the microresonators have a ring shape with an overall ring radius and a ring thickness or width. In some embodiments, the microresonators can have any suitable geometry for self-locking. For example, microresonator width can range between about 0.5 μm wide to 100 μm wide microresonator rings. Microresonator radius can range between about 10 μm to about 1000 μm. In one embodiment, 2.5 μm wide microresonator rings are fabricated with a radius of 60 μm, frep=362 GHz, and a comb span of 1.2 octave; THz comb is not required. In one embodiment, 3.3 μm wide microresonator rings are fabricated with a radius of 100 μm, frep=216.5 GHz, and a comb span of 1.1 octave. In various embodiments, frepis directly detectable. For example, frepcan be directly detectable at frepbelow 500 GHz, below 200 GHz, or below 100 GHz. Phase modulators are optional or can be replaced with additional microring modulators with microheaters to increase efficiency. In one embodiment, fceodetection S/N=700 assuming 17000%/W efficiency, −30 dBm if power and −35 dBm 2f power.

Micro-comb self-locking was achieved without using off-chip doublers and phase modulators. Sustained operations were achieved due to the high stability of the AlN films. AlN has quadratic optical nonlinearity which allows self-locking of the comb by on-chip construction of 1f−2f interferometer to access carrier envelope frequency and on-chip implementation phase modulators to access free spectral ranges. In short, AlN provides a single chip solution to self-locked comb whereas Si3N4could not.

In some embodiments, the optical frequency combs of the present invention are applicable in enhanced precision optical clocks, spectroscopy sensing, extremely high speed and high bandwidth data transmission, and astrocomb applications.

III-Nitride semiconductors such as aluminum nitride (AlN) exhibit a non-centrosymmetric crystal structure, thereby possessing inherent optical X2) nonlinearity as well as Pockels electro-optic and piezoelectric properties. Apart from the advances in ultraviolet light emitting diodes and quantum emitters, AlN has also proved viable for low-loss nanophotonics in high efficiency second-harmonic generation (SHG) and high-fidelity Kerr and Pockels soliton mode-locking. Therefore, it is feasible to establish an on-chip f−2f interferometer provided that an octave AlN soliton microcomb is available. This solution is favored when compared with the heterogeneous integration approach, such as a device based on hybrid gallium arsenide (GaAs)/Si3N4waveguides. Despite that on-chip fceodetection was achieved from supercontinua driven by a femtosecond laser in non-resonant X2) nanophotonic waveguides made from AlN or lithium niobate (LN) thin films, resonator microcomb-based f−2f interferometry using nanophotonics remains elusive.

Disclosed is a high-fidelity generation of octave soliton microcombs and subsequent fceodetection using AlN-based nanophotonic chips. Thanks to mature epitaxial growth, AlN thin films with highly uniform thickness are available, thus permitting lithographic control of group velocity dispersion (GVD) for comb spectral extension via dispersive wave (DW) emissions. The octave soliton microcombs possess separated dual DWs and moderate frepof 433, 360 and 220 gigahertz, and are found to be reproducible from batch-to-batch fabrications. The results permit the capture of the f−2f beatnote through on-chip SHG in phase-matched AlN waveguides. This work establishes the great potential of non-centrosymmetric III-Nitride photonic platforms for portable self-locked microcomb sources.

FIG.1is a basic schematic representation of a single on-chip stabilized locked microcomb and its output. The device is an octave spanning soliton comb and provides on-chip f−2f interferometric locking of fceoand direct detection of fceo.

FIG.2is a schematic representation of octave-spanning optical frequency comb device100. The device design achieves a single-chip realization of a fceoand freplocked AlN microcomb. The device includes a laser source105, a micro-heater110, a micro ring resonator115(also referred to herein as a microring resonator and an octave soliton comb), a 1f−2f interferometer120, a phase modulator125, detectors130, and an optical pathway135having at least one entry and at least one exit.

In one embodiment the laser105is positioned at the at least one entry of the optical pathway135. In one embodiment, the micro ring resonator115is positioned adjacent to the optical pathway135between the at least one entry and the at least one exit. In one embodiment, the micro ring resonator115comprises aluminum nitride (AlN). In one embodiment, the micro ring resonator115comprises LiNbO3. In one embodiment, the laser source is a continuous wave (CW) laser. In one embodiment, the optical pathway135further comprises a suppressed carrier single sideband modulator (SC-SSBM) positioned between the at least one laser source105and the at least one micro ring resonator115.

In one embodiment, the device100further includes a filter. In one embodiment, the filter is an erbium-doped fiber amplifier (EDFA). In one embodiment, the optical pathway135further comprises a fiber polarization controller (FPC) positioned between the at least one laser source100and the at least one micro ring resonator115. In one embodiment, the at least one micro ring resonator115comprises an oxide cladding. In one embodiment, the oxide cladding is silicon oxide.

In one embodiment, the at least one micro ring resonator115comprises a ring width and a ring radius. In one embodiment, the ring width is between about 0.5 μm to about 100 μm. In one embodiment, the ring radius is between about 10 μm to about 1000 μm. In one embodiment, the at least one micro ring resonator115is fabricated by chemical vapor deposition of an AlN thin film on a substrate. In one embodiment, the chemical vapor deposition is metalorganic chemical vapor deposition (MOCVD). In one embodiment, the substrate is sapphire. In one embodiment, the AlN thin film comprises at least 0.5% thickness uniformity. In one embodiment, wherein the AlN thin film comprises an annealing temperature of about 1700° C.

In one embodiment, the device100comprises an intrinsic optical Q factor of at least 3,000,000. In one embodiment, the at least one micro ring resonator115comprises a ring width of 2.5 μm, a ring radius of 60 μm, a repetition frequency frepof 362 GHz, and a comb span of 1.2 octave. In one embodiment, the at least one micro ring resonator115comprises a ring width of 3.3 μm, a ring radius of 100 μm, a repetition frequency frepof 216.5 GHz, and a comb span of 1.1 octave. In one embodiment, the comb span is at least 1.5 octaves. In one embodiment, the device further comprises an electro-optical comb for repetition comprising a waveguide in resonance with the at least one microring resonator, at least one frequency second harmonic generation doubler, and a racetrack resonator.

If frepis pushed to below about 100 GHz, direct detection of frepis possible, and the phase modulator125can be eliminated. Additionally, the phase modulator125can be replaced with microring modulators with microheater integration for higher efficiency. In one embodiment, the detectors130are InGaAs detectors. In one embodiment the fceohas a S/N of about 700, assuming 17000%/W efficiency, −30 dBm 1f power, and −35 dBm 2f power.

FIG.3shows an illustration of f−2f interferometry using octave-spanning soliton microcombs and second-harmonic generators in a nanophotonic platform harboring simultaneous X(3)and X(2)susceptibilities. The offset frequency fceois accessible from the beatnotes of δ1and δ2, and fpis the pump laser frequency. The strategy is to leverage non-centrosymmetric photonic media for simultaneous integration of X(3)octave soliton microcombs and X(2)SHG doublers. For a proof-of-principle demonstration, an auxiliary laser (at faux) was adopted to obtain sufficient SHG power (at 2faux) from phase-matched optical waveguides. The use of the auxiliary laser can be eliminated by exploiting microring-based architecture to boost the SHG efficiency. By subsequently beating fauxand 2fauxwith the fnand f2ncomb lines at their corresponding beatnotes of δ1and δ2, thefceo signal reads:
fceo=δ2−2δ1(1)

In certain embodiments, AlN thin films were epitaxially grown on a c-plane sapphire substrate via metal-organic chemical vapor deposition.

FIG.4shows a sketch of a hexagonal AlN layer with lattice constants: a and c, epitaxially grown on a c-plane sapphire substrate, the unit cell of an AlN crystal, and photograph image of a 2-inch AlN wafer featuring a broad transparency window from ultraviolet to mid-infrared regimes. The AlN crystals exhibit a hexagonal wurtzite structure with a unit cell shown in the bottom, highlighting the non-centrosymmetry. Also shown is a 2 inch AlN-on-sapphire wafer featuring a broadband transparency and a favored film thickness, seeFIG.7, both of which are crucial factors to ensure octave GVD control. Great attention was also paid to the film crystal quality and surface roughness for low-loss photonic applications. The AlN nanophotonic chips were manufactured following electron-beam lithography, chlorine-based dry etching and silicon dioxide (SiO2) coating processes and were subsequently cleaved to expose waveguide facets. The intrinsic optical quality factors (Qint) of the AlN resonators were characterized to be ˜1-3 million depending on the waveguide geometries. The detailed film and device characterization is presented in the Experimental Results section.

Since wurtzite AlN manifests optical anisotropy for vertically or horizontally-polarized light, the waveguide structures were engineered for optimal operation of fundamental transverse magnetic (TM00) modes, which allows the harness of its largest X(2)susceptibility to ensure high-efficiency SHG. To expand microcomb spectra out of the anomalous GVD restriction, soliton-induced DW radiation was exploited by tailoring the resonator's integrated dispersion (Dint):

FIG.5shows an example process flow for manufacturing an AlN octave-spanning optical device100including a microring resonator115(octave soliton comb). Section A shows a MOCVD which provides high throughput growth. Section B is an example of the thin film produced by the MOCVD. Section C is a schematic representation of the cross section of the microcomb resonator. Sections D and E show images of example microcomb resonators. Section F shows a cross section image of an example microcomb resonator. By utilizing the process of epitaxial growth, the thickness can be controlled at a nanometer level with better that 0.5% thickness uniformity. High temperature annealing up to 1700° C., as opposed to 1100° C. for SiN, provides better optimization of optical Q. An intrinsic Q greater than 3,000,000 (loaded Q greater than 1,000,000) is easily achievable. Additionally, the devices100are not air cladded, but cladded with oxide instead, leading to longer expected lifetime.

FIG.6shows an example embodiment of the electro-optic comb device100for repetition. The sequence of events which leads to ultimately the self-referenced locking of an octave spanning soliton comb is as follows. First, input light enters the waveguide from the left edge of the chip which is in resonance with the first microring resonator605. A soliton comb is achieved from the microring resonator605and the carrier envelope offset frequency signal is generated by the cascade of frequency second harmonic generation doublers610. Finally, the repetition rate of the soliton comb is stabilized by the beat-note between an electro-optic frequency comb generated from the race-track resonator615. The basic working principle of the racetrack resonator electro-optic comb is that a microwave signal sent to the device through the electrodes620, will modulate the light that is in resonance of the racetrack resonator615. The modulation is possible due to the z-directional electric field (into and out of the plane of the figure) allowed by the design of the electrodes620, which is situated directly on top of the waveguide as well as next to the waveguides as shown in the enlarged display of the top section of the racetrack resonator. Since the resonators for soliton generation, carrier envelope offset frequency detection as well as repetition rate locking share the same bus waveguide, locking of an octave spanning soliton is made possible using one single compact device. To further demonstrate this configuration's compactness, multiple of these devices are shown inFIG.6.

EXPERIMENTAL EXAMPLES

The following description details example experimental data and structures of the present invention.FIG.7shows a spectroscopic ellipsometer mapping of the AlN film thickness of an example device100in a region of 4×9 mm2, showing a minor variation of 1000±5 nm denoted by the right color bar.

FIG.8shows example experimental data for octave soliton microcombs at hundreds of gigahertz repetition rates. The top panel ofFIG.8section A shows the integrated dispersion (Dint) of a 50 μm-radius AlN resonator (cross section: 1.0×2.3 μm2), where the anomalous and normal GVD regimes are shaded with light blue and orange colors respectively, and the insets show a zoom-in view of the measured (red dots) and simulated (blue curve) values and the resonator modal profile shown in the right. The bottom panel ofFIG.8section A shows a soliton microcomb spectra from the experiment (blue) and simulation (red) at an on-chip pump power of ˜390 mW. The resonator Qintis 1.6 million and the frepis estimated to be around 433 GHz.FIG.8section B shows a soliton microcomb spectrum from a 100 μm-radius AlN resonator (cross section: 1.0×3.5 μm2) with a decreased frepof ˜220 GHz. The applied pump power is ˜1 W at a resonator Qintof 3.0 million.

The GVD engineered AlN resonators are coated with a SiO2protection layer, making it less susceptible to the ambient compared with the air cladded Si3N4counterpart. An example of the resonator modal profile is shown in the inset ofFIG.8section A. The top panel ofFIG.8section A plots the Dintcurve from a 50 μm-radius AlN resonator through numerical simulation. In spite of the limited anomalous GVD window (light blue shade), octave microcomb operation is feasible via DW radiations at phase-matching conditions Dint=0, allowing for spectral extension into normal GVD regimes (light orange shade). Note that the occurrence of such dual DWs benefits from the optimal film thickness in the AlN system, while the DW separation is agilely adjustable over one octave through the control of resonator's dimensions. Around the telecom band, the Dintvalue (red dots) was characterized by calibrating the resonator's transmission with a fiber-based Mach-Zehnder interferometer. The experimental result matches well with the simulated one (inset ofFIG.8Section A) with an extracted D2/2π of ˜6.12 MHz.

Soliton mode-locking was then explored based on a rapid frequency scan scheme to address the abrupt intracavity thermal variation associated with transitions into soliton states. The soliton spectrum is recorded using two grating-based optical spectrum analyzers (OSAs, coverage of 350-1750 nm and 1500-3400 nm). The bottom panel ofFIG.8section A plots the soliton spectrum from a 50 μm-radius AlN resonator, featuring a moderate frepof 433 GHz and an observable spectral span of 1.05-2.4 μm, exceeding one optical octave. Meanwhile, soliton induced DW radiations occur at both ends of the spectrum, in agreement with the predicted Dintcurves. Note that the low-frequency DW location matches well with the Dint=0 position, while the high-frequency one exhibits an evident blue shift, which is ascribed to Raman-induced soliton red shifts relative to the pump frequency. This conclusion is supported by the soliton spectral simulation (red curve) when accounting for Raman effects, while the intact low-frequency DW might be a result of the cancellation of soliton recoils.

The single crystal nature of AlN thin films permits reproducible optical index in each manufacture run. This, in combination with their uniform film thickness control, leads to a high predictability for the dispersion engineering, making it feasible to predict octave soliton combs at various repetition rates. For instance, the GVD model indicates that octave spectra with repetition rates further decreased by two times are anticipated from 100 μm-radius AlN resonators at optimal widths of 3.3-3.5 μm.FIG.8Section B plots the recorded soliton comb spectrum at a resonator width of 3.5 μm, where a frepof ˜220 GHz and dual DWs separated by more than one octave are achieved simultaneously. Such a low frepis amenable for direct photodetection with state-of-the-art unitravelling-carrier photodiodes. A weak sharp spectrum occurred around 130 THz, which might arise from modified local GVD due to avoided mode crossing. In the nanophotonic platform, resonator geometries could be further predicted for achieving octave solitons with an electronically detectable frepof ˜109 GHz. Nonetheless, the strong competition between Kerr nonlinearities and stimulated Raman scattering (SRS) must be taken into account since the free spectrum range (FSR) of the resonator is already smaller than the ATO1phonon linewidth (˜138 GHz) in AlN crystals.

FIG.9shows example experimental data for octave soliton microcombs with agilely tunable spectra.FIG.9section A shows engineered Dintcurves of 60 μm-radius AlN resonators at varied widths of 2.3-2.5 μm revealed by the colored shadow regime.FIG.9section B shows corresponding soliton microcomb spectra at resonator widths of 2.3, 2.4, and 2.5 μm from the top to bottom panel, respectively. The frepis ˜360 GHz, while the vertical arrows in spectral wings indicate the emergence of DWs. Akin toFIG.8, high-frequency DWs here also exhibit an evident blue shift from the Dint=0 position. From a sech2fit, the corresponding temporal pulse duration is estimated to be ˜23, 22 and 19fs (from top to bottom), respectively.

Since the SHG from the auxiliary laser (1940-2000 nm) available in the laboratory is beyond the soliton spectral coverage shown inFIG.8, the resonator dimensions were further adjusted for extending microcomb spectra below 1 μm. As plotted inFIG.9section A, the phase-matching condition (Dint=0) for high-frequency DW radiations below 1 μm is fulfilled by elevating the resonator radius to 60 μm while maintaining its width around 2.3 μm. In the meantime, low-frequency DWs could also be expected and their spectral separation is adjustable by controlling the resonator width. Guided by the tailored Dintcurves, the AlN resonators were fabricated and recorded octave soliton spectra at a frepof ˜360 GHz (seeFIG.9section B). Lithographic control of DW radiations (indicated by vertical arrows) is also verified by solely adjusting the resonator width, allowing the spectral extension below 1 μm (width of 2.3 or 2.4 μm). The low- and high-frequency DWs are found to exhibit distinct frequency shifting rates, consistent with the Dintprediction. The observable soliton spectra (from top to bottom ofFIG.9section B) cover 1.5, 1.3, and 1.2 optical octaves by normalizing the total span (Δf) to its beginning frequency (f1), that is Δf/f1. Such a definition permits a fair comparison among soliton microcomb generation in distinct pump regimes across different material platforms, suggesting high competitiveness of the AlN microcomb span comparing to state-of-the-art values reported in Si3N4microresonators.

The co-integration of SHG was then explored based on the X2susceptibility of AlN for matching the DW peak below 1 μm (middle panel ofFIG.9section B). To fulfill the demanding requirement of spectral overlaps with the microcomb, a straight waveguide configuration was adopted, which allows a broader phase-matching condition albeit at the cost of reduced conversion efficiencies comparing to its counterpart using dual-resonant microresonators. Through modeling, an optimal waveguide width of ˜1.38 μm was predicted for fulfilling the modal-phase-matching condition, while the actual waveguide width was lithographically stepped from 1.32 to 1.46 μm (spacing of 5 nm) accounting for possible deviations during the manufacturing process.

FIG.10andFIG.11show example experimental second-harmonic generators of device100and associated data.FIG.10is a colored scanning electron microscope images of fabricated AlN nanophotonic chips composed of octave microcomb generators (microring resonators) and SHG waveguides (total length of 6 cm, not fully shown).FIG.11shows SHG spectra collected from a modal phase-matched waveguide (width of 1.395 μm) at an on-chip 1f power of 355 mW, and the insets show modal profiles of the pump (TM00) and SHG (TM20) waves as well as the wavelength-dependent SHG power (pink dots), where a sinc2-function fit (blue curve) is applied. The error bars reflect the SHG power variation from continuous three measurements.

FIG.10shows a section of 6 cm-long SHG waveguides co-fabricated with the microcomb generator. At a fixed fundamental wavelength (1970 nm), the phase-matching waveguide was located at the width of 1.395 μm, close to the predicted width. The corresponding SHG spectra are plotted inFIG.11, where a high off-chip SHG power over 50 μW was achieved by boosting the fundamental pump power from a thulium-doped fiber amplifier to compensate the SHG efficiency. In the meantime, the wavelength-dependent SHG power shown in the inset indicates a large 3-dB phase-matching bandwidth of ˜0.8 nm, which, together with an external heater for thermal fine-tuning, is sufficient to cover the target comb lines for subsequent heterodyne beating.

FIG.12andFIG.13show an example experimental f−2f heterodyne measurement.FIG.12is a schematic diagram for assessing the fceo. The symbol “×2” indicates a RF frequency doubler.FIG.13shows free-running f−2f beatnotes after the down-conversion process, suggesting a signal-to-noise ratio of 10 dB at a resolution bandwidth of 1 MHz. The local oscillator frequencies fLO1and fLO2are chosen to be 11.8 and 9.1 GHz, respectively, and the inset shows the equivalent curve of=2fLO1+fLO2−Δf2.

By combining outgoing light from optimal AlN soliton and SHG generators on the calibrated OSAs, the f−2f beatnote frequency was estimated to be approximately 32 GHz limited by the resolution of the OSAs. The scheme shown inFIG.12was employed to electronically access the fceosignal in real time. The recorded soliton spectrum after suppressing pump light by a fiber Bragg grating (FBG) indicates a high off-chip power close to −40 dBm for the high-frequency DW. Meanwhile, a wavelength-division multiplexer (WMD) is utilized to separate the f and 2f frequency components before sent into the photodetectors (PDs). Two tunable radio frequency (RF) synthesizers are introduced as the local oscillators (LO1 and LO2) to down convert the photodetector signals for effective capture of f−2f beat signal at a convenient low-frequency band with an electronic spectrum analyzer (ESA, range of 20 Hz-26.5 GHz). As highlighted inFIG.13, two down-converted beatnotes of Δf1and Δf2were recorded with a signal-to-noise ratio of 10 dB at a resolution bandwidth of 1 MHz. Much higher signal-to-noise ratios are anticipated by applying a finer detection bandwidth upon locking the telecom pump laser as well as the fceofrequency. The corresponding f−2f beatnote is=2fLO1+fLO2−Δf2(see inset ofFIG.13) since the local oscillator frequencies fLO1and fLO2are chosen to be larger than beatnotes of δ1and δ2. The actual fceoin the current device equals to FSR−which is unveiled by tuning the relative positions of auxiliary laser and comb teeth frequencies, indicating the involvement of fnand f2n+1comb lines in the heterodyne beating. On the other hand, the fLO1and fLO2frequencies are freely adjustable up to 40 and 20 GHz in the scheme, which could further expand the accessible range of fceofrequency based on the down-conversion process presented here. Meanwhile, the RF synthesizers are synchronized to a common external frequency reference, suggesting that the captured down-converted f−2f signals are available for further locking the comb teeth in a feedback loop.

Nanophotonic implementation of f−2f interferometry was demonstrated by leveraging X(3)octave solitons and X(2)SHG co-fabricated from a non-centrosymmetric AlN photonic platform. Thanks to agile GVD engineering offered by epitaxial AlN thin films, the octave soliton microcombs can reliably produce dual DWs and sub-THz repetition rates (220-433 GHz) that are accessible with unitravelling-carrier photodiodes. The overall soliton spectral span is adjustable up to 1.5 octave, on a par with state-of-the-art values (1.4 octave) reported in Si3N4microresonators. The fceomeasurement was performed with the aid of an auxiliary laser for enabling SHG in phase matched AlN waveguides, thus allowing for spectral overlap with the desired octave soliton.

The spectral restriction of octave solitons for matching with the auxiliary laser wavelength can be relaxed by exploiting high-efficiency SHG in dual-resonant microresonators, which allows direct doubling of a selected comb line in the low frequency DW band. Meanwhile, the octave comb's repetition rate can be further reduced by leveraging on-chip Pockels electro-optical frequency division. By shifting the phase matching condition for SHG, octave solitons can be extended into the near-visible band, giving access to self-locked near-visible microcombs for precision metrology. Additional noncentrosymmetric photonic media can be used, such as LN, GaAs and gallium phosphide. For instance, by exploiting periodically poled LN thin films, phase matched X(2)and octave X(3)interactions can be simultaneously achieved in a single microring resonator, thus simplifying the photonic architectures.

The surface roughness and crystal quality of the AlN thin films were respectively characterized by an atomic force microscope and an X-ray diffraction scan, indicating a root-mean-square roughness of 0.2 nm in 1×1 μm2region and an FWHM linewidth of ˜46 and 1000 arcsec along (002) and (102) crystal orientations, respectively. The film thickness was mapped by a spectroscopic ellipsometer (J. A. Woollam M-2000), providing a quick and preliminary selection of the desired AlN piece for octave soliton generation with dual DWs. In spite of varied film thicknesses across a 2-inch AlN wafer, the desired region for reproducible octave device fabrication can be reliably located.

To further reduce the propagation loss, the AlN photonic chips were annealed at 1000° C. for 2 hours. The resonator Q-factors were probed by sweeping a tunable laser (Santec TSL-710) across the cavity resonances and then fitted by a Lorentzian function. In the 100 μm-radius AlN resonators (width of 3.5 μm), a recorded Qintof 3.0 million was achieved, while the 50 μm-radius resonators (width of 2.3 μm) exhibit a decreased Qintof 1.6 million, indicating the dominant sidewall scattering loss of the current fabrication technology.

The Dintof the AlN resonators is investigated using a finite element method (FEM) by simultaneously accounting for the material and geometric chromatic dispersion. The overall Dintvalue is approximated with a fifth-order polynomial fit applied to the simulated modal angular frequencies: ωμ=ω0+μD1+Dint, where D1/(2π) is the resonator's FSR at the pump mode μ=0.

The spectral dynamics of octave soliton microcombs is numerically explored based on nonlinear coupled mode equations by incorporating the Raman effect:

∂∂taμ=-(κR2+i⁢Δμa)⁢aμ+i⁢gK⁢∑k,l,nak*⁢al⁢an⁢δ⁡(l+n-k-μ)-i⁢gR⁢∑k,lal[Rk⁢δ⁡(l+k-μ)+Rk*⁢δ⁡(l-k-μ)]+ξP(3)∂∂tRμ=-(γR2+i⁢ΔμR)⁢Rμ-i⁢gR⁢∑k,lak*⁢al⁢δ⁡(l-k-μ)(4)
Here a and R are the mode amplitudes of cavity photons and Raman phonons with subscripts k,l,n being the mode indices, while gKand gRrepresent the nonlinear coupling strength of Kerr and Raman processes, respectively. The driving signal strength is ξP=

κe,0⁢Pi⁢nℏ⁢ωP
at an on-chip pump power Pin, Kμ(Ke,μ) denotes the total (external) cavity decay rate of the μthphoton mode, and γRis the Raman phonon decay rate. The detuning from a D1-spaced frequency grid is indicated by Δμa=ωμ−ωP−μD1and ΔμR=ωR−μD1with ωPand ωRbeing pump and Raman shift angular frequencies, respectively.

In the simulation, the time derivative of Raman items in Equation 4 was set to zero to speed up the computation since the decay rate of phonons is much larger than that of photons. Frequency is considered independent kμ(2π)≈120 MHz and ke,μ/(2π)≈75 MHz based on measured Q-factors of 50 μm-radius AlN resonators inFIG.8. Because incident light is TM-polarized, the involved ATO1Raman phonon in AlN exhibits an ωR(2π)≈18.3 THz with an FWHM of γR(2π)≈138 GHz. The gK2π is calculated to be 0.73 Hz for a given nonlinear refractive index n2=2.3×10−19m2/W, while an optimal gR2π=0.29 MHz is adopted, resulting in a soliton spectrum matching well with the measured one inFIG.8. The simulated high frequency DW also exhibits an evident blue shift comparing with the case of gR2π=0 MHz.

FIG.14shows example experimental nanophotonic device fabrication details.FIG.14section A shows wafer-scale thickness mapping of a 2-inch AlN wafer using a spectroscopic ellipsometer. The right color bar indicates the corresponding thickness variation.FIG.14section B shows surface roughness characterization of the AlN film using an atomic force microscope.FIG.14section C shows transmittance of a 50 μm-radius AlN resonator (width=2.3 μm) for octave soliton generation. A zoom-in view of the resonance (indicated by dashed lines) around 1542 nm is shown in the right side, revealing a Qintof ˜1.6 million.FIG.14section D shows resonance from an 100 μm-radius AlN resonator (width=3.5 μm), highlighting a reduced resonant linewidth and an improved Qintof ˜3.0 million.

All devices are patterned from 2-inch crystalline AlN-on-sapphire wafers with 1000 nm-thick AlN epilayers. To ensure robust dispersion engineering for reproducible octave-soliton generation, the uniformity of film thickness was first characterized across the wafer. As shown inFIG.14section A, the film thickness of the wafer is very close to target growth thickness apart from the edge of the wafer (colored by purple). By intentionally choosing the desired thickness region, octave-soliton generation can be reliably realized using the current nanofabrication technology. For low-loss nanophotonic applications, the crystal quality of the AlN thin film is also a factor, whose root-mean-square surface roughness was characterized to be as low as 0.2 nm in a 1×1 μm2region. The result is presented inFIG.14section B.

An example of the resonator transmittance is shown inFIG.14section C, where the fundamental transverse magnetic (TM00) mode is effectively excited while higher-order modes are suppressed by adopting a pulley waveguide coupling configuration (wrapped angle of 6°). The intrinsic quality-factors (Qint) are then extracted from a Lorentz fit of the resonance curve at under-coupled conditions. The AlN resonators engineered for octave-soliton generation exhibits a dimension-dependent Qintof 1.6 million and 3.0 million for the devices with radii of 50 μm (width=2.3 μm, right ofFIG.14section C) and 100 μm (width=3.5 μm,FIG.14section D), suggesting the dominant sidewall scattering loss. Further improvement of the Q-factors can be envisioned by leveraging the racetrack resonators, where the straight portions exhibit a much smoother sidewall.

FIG.15shows example experimental data for dispersion engineering for octave soliton generation.FIG.15section A shows height-dependent integrated dispersion (Dint) of 50 μm-radius AlN resonators at a fixed width of 2.3 μm. The top panel ofFIG.15section B shows width-dependent Dintcurves (radius of 50 μm, height of 1.00 μm) and the bottom panel shows numerically simulated soliton comb spectra without (orange) or with (blue) the influence of Raman effects for the Dintcurve at a resonator width of 2.3 μm (height of 1.0 μm).FIG.15section C shows experimentally recorded chaotic comb spectra at a varied resonator width of 2.3, 2.4 and 2.5 μm. The vertical arrows indicate the emergence of dispersive wave-like envelopes, and the corresponding Dintcurves are shown in the top panel of section B.

The AlN resonator's integrated dispersion (Dint) is highly susceptible to the film thickness variation, which affects octave soliton generation with phase-matched dual dispersive waves (DWs). As plotted inFIG.15section A, when the resonator height deviates from an optimal value of 1.00 μm (blue curve), such as increasing to 1.05 μm or decreasing to 0.95 μm, a larger dispersion barrier or a narrower dispersion window will occur on both sides of the Dintcurve, preventing from octave spectral extension via DW radiations. As a result, the AlN piece can be located with the desired thickness around 1000 nm (seeFIG.14) for the octave-soliton device fabrication.

At an optimal height of 1.0 μm, the Dintcurve can be further engineered by tailoring the resonator width. The result is shown in the top panel ofFIG.15section B, where the phase-matching condition (Dint=0) for DW radiations is readily adjusted beyond one octave span when reducing the resonator width from 2.5 to 2.3 μm. The octave soliton spectrum is numerically investigated for the Dintcurve at a width of 2.3 μm. As shown in the bottom panel ofFIG.15section B, the high-frequency DW exhibits an evident blue shift from the Dint=0 position when accounting for the Raman effect, which matches wells with the experimental result inFIG.8. The underlying mechanism for this spectral shift is attributed to the Raman-induced soliton red shift in the spectral center, which in turn blue shifts the high-frequency DW.FIG.15section C plots the noise-state comb spectra recorded from the dispersion engineered AlN resonators (radius of 50 μm, width of 2.3-2.5 μm). It is found that the DW-like envelops at both ends of the spectra exhibit an evident shift when varying the resonator width, in good agreement with the Dintcurve prediction (top panel ofFIG.15section B). In the experiment, the corresponding soliton spectrum can be captured at a resonator width of 2.3 μm (seeFIG.8), while it is inaccessible at the width of 2.4 and 2.5 μm due to the occurrence of Raman lines in the intermediate state, thus hampering soliton mode-locking.

FIG.16shows example experimental data for dispersion engineering for repetition rate-detectable octave solitons. The top panel ofFIG.16section A shows Dintcurves of engineered AlN resonators at a radius of 100 μm and varied widths of 3.3 and 3.5 μm, and the bottom panel shows captured noise-state comb spectra with a reduced repetition rate of ˜220 GHz. The vertical arrows indicate the emergence of DW-like peaks. The top panel ofFIG.16section B shows Dintcurve of AlN resonators at an increasing radius of 200 μm and an optimal width of 50 μm, and the bottom panel shows simulated soliton spectrum at an on-chip pump power of 100 mW, highlighting a reduced repetition rate of 109 GHz.

By further engineering the resonator dimensions, octave solitons are achieved with repetition rates reduced by two times. As shown in the top panel ofFIG.16section A, at an elevated resonator radius of 100 μm, the phase-matching conditions for separated dual DWs by one optical octave are accessible from engineered Dintcurves at optimal resonator widths of 3.3 and 3.5 μm. This prediction is verified by the recorded comb spectra with repetition rates (frep) of ˜220 GHz (see bottom panel ofFIG.16section A), where dual DW-like envelopes indicated by vertical arrows match well with the Dint=0 condition in each case. The abnormal spectral peaks observed in the low-frequency region might arise from the avoided mode-crossing due to imperfections in the device fabrication, which is not included in the dispersion modeling. The soliton comb spectrum was captured at a resonator width of 3.5 μm (seeFIG.8), while the occurrence of intermediate Raman lines prevents from soliton mode-locking for the case of a resonator width=3.3 μm.

The agile dispersion engineering in the material system also offers the capability to achieve octave solitons with electronically detectable repetition rates by commercial high-speed photodetectors (bandwidth>100 GHz). As shown inFIG.16section B, upon increasing the resonator radius to 200 μm, it is possible to achieve a low free spectrum range (FSR) of 109 GHz and an optimal Dintcurve (top panel) for octave soliton generation at a resonator width of 5.0 μm. The corresponding soliton spectrum was numerically investigated and presented in the bottom panel. A Qintof 10 million was chosen at critical coupled conditions for enabling octave soliton generation at a low on-chip pump power of 100 mW. Since the resonator's FSR is already smaller than the ATO1phonon linewidth (˜138 GHz) of crystal AlN films, the Raman effect must be suppressed for soliton mode-locking. For the numerical investigation shown here, the influence of Raman effects is disregarded, while it should be considered in practical devices.

FIG.17shows an example experimental setup and data for octave-soliton characterization.FIG.17section A shows a sketch of the experimental configuration. The SC-SSBM produces a blue-shifted sideband (λp) relative to incident light (λc) from a continuous-wave (CW) laser. The sideband is then boosted by an erbium-doped fiber amplifier (EDFA) and aligned to the vertical polarization before entering the AlN chip via an aspherical lens pair.FIG.17section B shows comb power trace recorded in the OSC, indicating elongated soliton duration time beyond 2 s, and the inset shows initial soliton lifetime of ˜20 ns.FIG.17section C shows free-running soliton power trace as a function of the time.FIG.17section D shows radio-frequency (RF) beating properties of chaotic (red) and soliton microcombs (blue) comparing with the PD background (black).

The experimental setup for the octave soliton generation is sketched inFIG.17section A. The transition from chaotic to soliton states typically accompanies a notable intracavity power drop, which in turn renders thermo cooling of the resonator with blue-shifted resonances, hindering stable soliton formation. This obstacle was addressed by using rapid frequency scan schemes based on a suppressed-carrier single sideband modulator (SC-SSBM). The SC-SSBM is driven by a voltage controller oscillator (VCO) connected to an arbitrary function generator (AFG), allowing rapid frequency shifting (up to 500 MHz/ns) across the resonance at a timescale far beyond the thermal-optic response (microseconds).

For characterization, light existing the chip is collected by a bare fiber (mode diameter of 4 μm) before sent into two grating-based optical spectrum analyzers (OSAs, the other one is not shown) and two photodetectors (PDs) following by an oscilloscope (OSC) and an electronic spectrum analyzer (ESA). A fiber-Bragg grating is also employed to suppress strong pump light.FIG.17section B plots a typical comb power trace when entering the soliton state. Despite the initial soliton lifetime of ˜20 ns, it can be elongated beyond 2 s using the rapid frequency scan scheme. The corresponding octave-soliton spectrum is shown inFIG.8. Upon entering the soliton state, the octave comb maintains a high stability during the full experiment span until the fiber-to-chip coupling becomes misaligned as indicated in inFIG.17section C. The coherence of the spectrum was also evaluated by sending a portion of comb lines (after suppressing pump light) into a PD. As shown inFIG.17section D, there is no evidence of low-frequency radio-frequency (RF) noise within a span of 2 GHz for the octave soliton comparing with the chaotic state, suggesting a high degree of coherence.

FIG.18shows example experimental data for characterization of the device100.FIG.18section A is a plot showing the stability of the free-running soliton duration.FIG.18section B and section C are plots showing the RF power of a pump and comb, respectively, for heterodyne beatnotes (RBW: 100 kHz).

FIG.19shows example experimental data on SHG conversion efficiency.FIG.19section A shows on-chip SHG power versus the pump power as well as the applied second-order polynomial fit (orange solid line), and the inset shows calculated effective indices (neff) of TM00(wavelength of 1970 nm) and second-order TM20(wavelength of 985 nm) modes versus the waveguide width.FIG.19section B shows calculated SHG efficiency (indicated by right color bar) as a function of the TM20mode propagation loss and the waveguide length. The “red star” symbol corresponds to the experimentally estimated SHG efficiency.

To access the carrier-envelop offset frequency (fceo) of octave soliton combs, a set of AlN waveguides were co-fabricated for efficient second-harmonic generation (SHG) as described inFIG.10. The modal-phase-matching case for the pump (TM00) and SHG (TM20) modes were considered, for which an optimal waveguide width can be obtained around 1.38 μm to fulfill the phase-matching condition (see inset ofFIG.19section A). By lithographically scanning the waveguide width at a spacing of 5 nm, the phase-matching waveguide for producing SHG spectra is located as shown inFIG.11. The insertion loss of the TM00mode at 1970 nm was measured to be ˜7 dB/facet, while the insertion loss of the TM20mode at 985 nm is estimated to be around 15 dB/facet because of the small modal overlap between the high-order TM20mode with the fiber mode. The calibrated on-chip SHG power (PSHG) versus the pump power (Pp) is plotted inFIG.19section A, where an on-chip SHG conversion efficiency ηSHG=PSHG/Pp2is derived to be 0.012 W−1.

The SHG efficiency with the coupled wave equation was analytically investigated at a slowly varying amplitude approximation. Since the SHG mode (TM20) is more susceptible to the waveguide sidewall roughness, its propagation loss (a) is also included into the model shown below:

Here a and b are the slowly varying field amplitude of TM00and TM20waves along the waveguide direction z, while kq=nbωq/c is the propagation constant with n, ω, and c being the effective index, angular frequency, and light speed in vacuum, respectively. The subscript q denotes the parameters of the mode a or b. Meanwhile, X(2)is the quadratic optical nonlinearity, Δk equals to 2ka−kb, and Γ describes the modal overlap of a and b modes given by:

By solving Equation 5 for deriving the SHG power

ηS⁢H⁢G=(ωa⁢χ(2)⁢Γ⁢L)22⁢na2⁢nb⁢ε0⁢c3⁢sinh2(α⁢L/4)+sin2(Δ⁢kL/2)(α⁢L/4)2+(Δ⁢kL/2)2(7)
Here ε0is the permittivity in vacuum and L is the overall waveguide length. Based on Equation 7, ηSHG was calculated at phase-matching condition (i.e., Δk=0) as shown inFIG.19section B. It is evident that the mode propagation loss makes a significant impact on the SHG efficiency in such a long waveguide. In the experiment, a waveguide length of 6 cm was adopted and the calculated ηSHG is found to agree with the experimental value when the TM20loss is around 6 dB/cm. The result is in reasonable agreement with the experimentally extracted TM20loss (˜2 dB/cm at 780 nm) when accounting for possible deviation from perfect phase-matching conditions in practical devices.

FIG.20shows example experimental data for implementation of f−2f interferometry.FIG.20section A shows the octave soliton spectrum after suppressing the pump by a FBG (see full spectrum inFIG.11).FIG.20section B shows a sketch of the involved frequencies (monitored by the OSAs) around the f and 2f bands for the fceomeasurement.FIG.20section C shows an illustration of the experimental setup for electronically accessing the fceobased on a down-conversion frequency process. PD1: 830-2150 nm, 0-12.5 GHz; PD2: 800-1700 nm, 0-26 GHz; LNA1: 6-18 GHz, gain≈27 dB; LNA2: 10-800 MHz, gain≈60 dB; Mixer1: L/R port (7.5-20 GHz), I port (0-7.5 GHz); BPF1: 20-1000 MHz; RF doubler: 10-1000 MHz; BPF2: 1.5-2 GHz; Mixer2: L/R port (1-2700 MHz), I port (1-2000 MHz).

Based on the optimized octave soliton comb and SHG generator, a f−2f interferometer was established for accessing the fceofrequency. To enable efficient optical-to-electrical conversion in the PDs, the residual pump light is suppressed by a broadband FBG and the recorded octave comb spectrum is presented inFIG.20section A. By adjusting the auxiliary laser frequency (faux) to overlap with one of the comb line, a strong 2fauxtone was produced in the proximity of f2ncomb line. In the case shown, 2fauxis closer to the f2n+1comb line, which is then selected for implementing the f−2f interferometry. These optical frequencies are monitored by two OSAs (350-1750 nm and 1500-3400 nm) at a resolution of 0.05 and 0.1 nm, respectively. The positions of relevant laser lines are sketched inFIG.20section B, where a positive fceofrequency is ensured at the assigned comb line indices. By setting δ1=faux-fnand δ=f2n+1-2faux, it follows that fceo=2fn-f2n=FSR−(δ2+2δ1).

In order to expand the electronic accessing range of the fceobeatnote, a down-conversion process was leveraged as sketched inFIG.20section C, where the incident lights in the f and 2f paths respectively beat at high-speed photodetectors (PD1 and PD2), and the generated beatnotes are boosted by cascaded low-noise amplifiers (LNA1) before sent into the RF Mixers (Mixer1) for producing down-converted frequency signals below 1 GHz. After bandpass filtering (BPF1, 20-1000 MHz), the down-converted beatnotes are boosted by high-gain LNA2s for driving a RF doubler and a Mixer2 in the f and 2f paths, respectively. The frequency-doubled signal is selected by another bandpass filter (BPF2) and the mixing frequency signals in the Mixer2 are monitored by an ESA (20 Hz-26.5 GHz).

The Mixers are driven by two tuned local oscillators (LO1 and LO2) covering a frequency span of 0-40 GHz (fLO1) and 0-20 GHz (fLO2), respectively. In the experiment, fLO1and fLO2were chosen to be larger than δ1and δ2. As a result, the output frequencies from the Mixer2 read:
Δf1=2fLO1−fLO2−(2δ1−δ2(8)
Δf2=2fLO1+fLO2−(2δ1+δ2)  (9)
It is notable that this scheme allows for an accessible f−2f beatnote (that is 2δ1+δ2) up to 2fLO1+fLO2, which is 100 GHz in the apparatus.

FIG.21shows a sketch of an additional example experimental setup similar to the example experimental setup shown inFIG.17section A. The SC-SSBM produces a blue-shifted sideband (λp) relative to incident light (λc) from a continuous-wave (CW) laser. The sideband is then boosted by an erbium-doped fiber amplifier (EDFA) and aligned to the vertical polarization before entering the AlN chip via an aspherical lens pair. In this experimental setup, a second CW laser is added for use in the production of the ESA output.

FIG.22shows a plot of example experimental data. The top panel ofFIG.22shows data for a soliton comb, and the bottom panel shows data for a noise comb. As shown, the soliton comb has a 1.3 octave span, with 1.1 octave between dispersive peaks.

FIG.23shows example experimental data for example comb structures.FIG.23section A is a plot showing comb power versus scan time showing three solitons (I, II, III) and blue and red detuned regions.FIG.23section B is a plot showing soliton power versus pump detuning for a single soliton (I) and a trigger threshold.FIG.23section C is a plot showing soliton power versus pump detuning for two solitons (I, II)) and a trigger threshold.FIG.23section D is a plot showing optical power versus frequency at phase angles of 360 and 2650 for R equal to 50 μm.FIG.23section E is a plot showing optical power versus frequency at phase angles of 640 and 270° for R equal to 60 μm.

FIG.24is a chart comparing properties of AlN to SiN for use in device100. As shown in the figure, AlN provides for second-harmonic doubling, electro-optic modulation, a larger spectral span, multiple repetition rates, and easily reproducible results.

Further details can be found in “III-Nitride nanophotonics for beyond-octave soliton generation and self-referencing” by X. Liu et al., incorporated herein by reference in its entirety.