Kerr-induced synchronization of a cavity soliton to an optical reference.

The phase-coherent frequency division of a stabilized optical reference laser to the microwave domain is made possible by optical-frequency combs (OFCs)1,2. OFC-based clockworks3-6 lock one comb tooth to a reference laser, which probes a stable atomic transition, usually through an active servo that increases the complexity of the OFC photonic and electronic integration for fieldable clock applications. Here, we demonstrate that the Kerr nonlinearity enables passive, electronics-free synchronization of a microresonator-based dissipative Kerr soliton (DKS) OFC7 to an externally injected reference laser. We present a theoretical model explaining this Kerr-induced synchronization (KIS), which closely matches experimental results based on a chip-integrated, silicon nitride, micro-ring resonator. Once synchronized, the reference laser captures an OFC tooth, so that tuning its frequency provides direct external control of the OFC repetition rate. We also show that the stability of the repetition rate is linked to that of the reference laser through the expected frequency division factor. Finally, KIS of an octave-spanning DKS exhibits enhancement of the opposite dispersive wave, consistent with the theoretical model, and enables improved self-referencing and access to the OFC carrier-envelope offset frequency. The KIS-mediated enhancements we demonstrate can be directly implemented in integrated optical clocks and chip-scale low-noise microwave generators.

High-performance Kerr microresonator optical parametric oscillator on a silicon chip.

Optical parametric oscillation (OPO) is distinguished by its wavelength access, that is, the ability to flexibly generate coherent light at wavelengths that are dramatically different from the pump laser, and in principle bounded solely by energy conservation between the input pump field and the output signal/idler fields. As society adopts advanced tools in quantum information science, metrology, and sensing, microchip OPO may provide an important path for accessing relevant wavelengths. However, a practical source of coherent light should additionally have high conversion efficiency and high output power. Here, we demonstrate a silicon photonics OPO device with unprecedented performance. Our OPO device, based on the third-order (χ(3)) nonlinearity in a silicon nitride microresonator, produces output signal and idler fields widely separated from each other in frequency ( > 150 THz), and exhibits a pump-to-idler conversion efficiency up to 29 % with a corresponding output idler power of > 18 mW on-chip. This performance is achieved by suppressing competitive processes and by strongly overcoupling the output light. This methodology can be readily applied to existing silicon photonics platforms with heterogeneously-integrated pump lasers, enabling flexible coherent light generation across a broad range of wavelengths with high output power and efficiency.

Fourier Synthesis Dispersion Engineering of Photonic Crystal Microrings for Broadband Frequency Combs.

Dispersion engineering of microring resonators is crucial for optical frequency comb applications, to achieve targeted bandwidths and powers of individual comb teeth. However, conventional microrings only present two geometric degrees of freedom - width and thickness - which limits the degree to which dispersion can be controlled. We present a technique where we tune individual resonance frequencies for arbitrary dispersion tailoring. Using a photonic crystal microring resonator that induces coupling to both directions of propagation within the ring, we investigate an intuitive design based on Fourier synthesis. Here, the desired photonic crystal spatial profile is obtained through a Fourier relationship with the targeted modal frequency shifts, where each modal shift is determined based on the corresponding effective index modulation of the ring. Experimentally, we demonstrate several distinct dispersion profiles over dozens of modes in transverse magnetic polarization. In contrast, we find that the transverse electric polarization requires a more advanced model that accounts for the discontinuity of the field at the modulated interface. Finally, we present simulations showing arbitrary frequency comb spectral envelope tailoring using our Frequency synthesis approach.

Conversion Efficiency in Kerr-Microresonator Optical Parametric Oscillators: From Three Modes to Many Modes.

Optical parametric oscillation in a Kerr nonlinear microresonator can generate coherent laser light with frequencies that are widely separated from the pump frequency, allowing, for example, visible light to be generated using a near-infrared pump. To be practically useful, the pump-to-signal conversion efficiency must be far higher than what has been demonstrated in microresonator-based oscillators with widely-separated output frequencies. To address this challenge, here we theoretically and numerically study parametric oscillations in Kerr nonlinear microresonators, revealing an intricate solution space that arises from an interplay of nonlinear processes. As a start, we use a three-mode approximation to derive an efficiency-maximizing relation between pump power and frequency mismatch. However, realistic devices, such as integrated microring resonators, support far more than three modes. Hence, a more accurate model that includes the entire modal landscape is necessary to determine potential inefficiencies arising from unwanted competing nonlinear processes. To this end, we numerically simulate the Lugiato-Lefever Equation that accounts for the full spectrum of nonlinearly-coupled resonator modes. We observe and characterize two nonlinear phenomena linked to parametric oscillations in multi-mode resonators: Mode competition and cross phase modulation-induced modulation instability. Both processes may impact conversion efficiency. Finally, we show how to increase the conversion efficiency to ≈ 25 % by tuning the microresonator loss rates. Our analysis will guide microresonator designs that aim for high conversion efficiency and output power.

Efficient chip-based optical parametric oscillators from 590 nm to 1150 nm.

Optical parametric oscillators are widely used to generate coherent light at frequencies not accessible by conventional laser gain. However, chip-based parametric oscillators operating in the visible spectrum have suffered from pump-to-signal conversion efficiencies typically less than 0.1 %. Here, we demonstrate efficient optical parametric oscillators based on silicon nitride photonics that address frequencies between 260 THz (1150 nm) and 510 THz (590 nm). Pumping silicon nitride microrings near 385 THz (780 nm) yields monochromatic signal and idler waves with unprecedented output powers in this wavelength range. We estimate on-chip output powers (separately for the signal and idler) between 1 mW and 5 mW and conversion efficiencies reaching ≈15 %. Underlying this improved performance is our development of pulley waveguides for broadband near-critical coupling, which exploits a fundamental connection between the waveguide-resonator coupling rate and conversion efficiency. Finally, we find that mode competition reduces conversion efficiency at high pump powers, thereby constraining the maximum realizable output power. Our work proves that optical parametric oscillators built with integrated photonics can produce useful amounts of visible laser light with high efficiency.

Ultra-broadband Kerr microcomb through soliton spectral translation.

Broadband and low-noise microresonator frequency combs (microcombs) are critical for deployable optical frequency measurements. Here we expand the bandwidth of a microcomb far beyond its anomalous dispersion region on both sides of its spectrum through spectral translation mediated by mixing of a dissipative Kerr soliton and a secondary pump. We introduce the concept of synthetic dispersion to qualitatively capture the system's key physical behavior, in which the second pump enables spectral translation through four-wave mixing Bragg scattering. Experimentally, we pump a silicon nitride microring at 1063 nm and 1557 nm to enable soliton spectral translation, resulting in a total bandwidth of 1.6 octaves (137-407 THz). We examine the comb's low-noise characteristics, through heterodyne beat note measurements across its spectrum, measurements of the comb tooth spacing in its primary and spectrally translated portions, and their relative noise. These ultra-broadband microcombs provide new opportunities for optical frequency synthesis, optical atomic clocks, and reaching previously unattainable wavelengths.

Impact of the precursor gas ratio on dispersion engineering of broadband silicon nitride microresonator frequency combs.

Microresonator frequency combs, or microcombs, have gained wide appeal for their rich nonlinear physics and wide range of applications. Stoichiometric silicon nitride films grown via low-pressure chemical vapor deposition (LPCVD), in particular, are widely used in chip-integrated Kerr microcombs. Critical to such devices is the ability to control the microresonator dispersion, which has contributions from both material refractive index dispersion and geometric confinement. Here, we show that modifications to the ratio of the gaseous precursors in LPCVD growth have a significant impact on material dispersion and hence the overall microresonator dispersion. In contrast to the many efforts focused on comparisons between Si-rich films and stoichiometric (Si3N4) films, here, we focus on films whose precursor gas ratios should nominally place them in the stoichiometric regime. We further show that microresonator geometric dispersion can be tuned to compensate for changes in the material dispersion.

Towards integrated photonic interposers for processing octave-spanning microresonator frequency combs.

Microcombs-optical frequency combs generated in microresonators-have advanced tremendously in the past decade, and are advantageous for applications in frequency metrology, navigation, spectroscopy, telecommunications, and microwave photonics. Crucially, microcombs promise fully integrated miniaturized optical systems with unprecedented reductions in cost, size, weight, and power. However, the use of bulk free-space and fiber-optic components to process microcombs has restricted form factors to the table-top. Taking microcomb-based optical frequency synthesis around 1550 nm as our target application, here, we address this challenge by proposing an integrated photonics interposer architecture to replace discrete components by collecting, routing, and interfacing octave-wide microcomb-based optical signals between photonic chiplets and heterogeneously integrated devices. Experimentally, we confirm the requisite performance of the individual passive elements of the proposed interposer-octave-wide dichroics, multimode interferometers, and tunable ring filters, and implement the octave-spanning spectral filtering of a microcomb, central to the interposer, using silicon nitride photonics. Moreover, we show that the thick silicon nitride needed for bright dissipative Kerr soliton generation can be integrated with the comparatively thin silicon nitride interposer layer through octave-bandwidth adiabatic evanescent coupling, indicating a path towards future system-level consolidation. Finally, we numerically confirm the feasibility of operating the proposed interposer synthesizer as a fully assembled system. Our interposer architecture addresses the immediate need for on-chip microcomb processing to successfully miniaturize microcomb systems and can be readily adapted to other metrology-grade applications based on optical atomic clocks and high-precision navigation and spectroscopy.

Proposal for noise-free visible-telecom quantum frequency conversion through third-order sum and difference frequency generation.

Quantum frequency conversion (QFC) between the visible and telecom is a key to connect quantum memories in fiber-based quantum networks. Current methods for linking such widely separated frequencies, such as sum/difference frequency generation and four-wave mixing Bragg scattering, are prone to broadband noise generated by the pump laser(s). To address this issue, we propose to use third-order sum/difference frequency generation (TSFG/TDFG) for an upconversion/downconversion QFC interface. In this process, two long wavelength pump photons combine their energy and momentum to mediate frequency conversion across the large spectral gap between the visible and telecom bands, which is particularly beneficial from the noise perspective. We show that waveguide-coupled silicon nitride microring resonators can be designed for efficient QFC between 606 and 1550 nm via a 1990 nm pump through TSFG/TDFG. We simulate the device dispersion and coupling, and from the simulated parameters, estimate that the frequency conversion can be efficient (${\gt}80 \%$) at 50 mW pump power. Our results suggest that microresonator TSFG/TDFG is promising for compact, scalable, and low-power QFC across large spectral gaps.

Tailoring Broadband Kerr Soliton Microcombs via Post-Fabrication Tuning of the Geometric Dispersion.

Geometric dispersion in integrated microresonators plays a major role in nonlinear optics applications, especially at short wavelengths, to compensate the natural material normal dispersion. Tailoring of geometric confinement allows for anomalous dispersion, which in particular enables the formation of microcombs which can be tuned into the dissipative Kerr soliton (DKS) regime. Due to processes like soliton-induced dispersive wave generation, broadband DKS combs are particularly sensitive to higher-order dispersion, which in turn is sensitive to the ring dimensions at the nanometer-level. For microrings exhibiting a rectangular cross section, the ring width and thickness are the two main control parameters to achieve the targeted dispersion. The former can be easily varied through parameter variation within the lithography mask, yet the latter is defined by the film thickness during growth of the starting material stack, and can show a significant variation (few percent of the total thickness) over a single wafer. In this letter, we demonstrate that controlled dry-etching allows for fine tuning of the device layer (silicon nitride) thickness at the wafer level, allowing multi-project wafers targeting different wavelength bands, and post-fabrication trimming in air-clad ring devices. We demonstrate that such dry etching does not significantly affect either the silicon nitride surface roughness or the optical quality of the devices, thereby enabling fine tuning of the dispersion and the spectral shape of the resulting DKS states.

Efficient photo-induced second harmonic generation in silicon nitride photonics.

Silicon photonics lacks a second-order nonlinear optical (χ(2)) response in general because the typical constituent materials are centro-symmetric and lack inversion symmetry, which prohibits χ(2) nonlinear processes such as second harmonic generation (SHG). Here, we realize record-high SHG efficiency in silicon photonics by combining a photo-induced effective χ(2) nonlinearity with resonant enhancement and perfect-phase matching. We show a conversion efficiency of (2,500 ± 100) %/W, which is 2 to 4 orders of magnitude larger than previous field-induced SHG works. In particular, our devices realize milliwatt-level SHG output powers with up to (22 ± 1) % power conversion efficiency. This demonstration is a major breakthrough in realizing efficient χ(2) processes in silicon photonics, and paves the way for further integration of self-referenced frequency combs and optical frequency references.

Automated on-axis direct laser writing of coupling elements for photonic chips.

Direct laser writing (DLW) has recently been used to create versatile micro-optic structures that facilitate photonic-chip coupling, like free-form lenses, free-form mirrors, and photonic wirebonds. However, at the edges of photonic chips, the top-down/off-axis printing orientation typically used limits the size and complexity of structures and the range of materials compatible with the DLW process. To avoid these issues, we develop a DLW method in which the photonic chip's optical input/output (IO) ports are co-linear with the axis of the lithography beam (on-axis printing). Alignment automation and port identification are enabled by a 1-dimensional barcode-like pattern that is fabricated within the chip's device layer and surrounds the IO waveguides to increase their visibility. We demonstrate passive alignment to these markers using standard machine vision techniques, and print single-element elliptical lenses along an array of 42 ports with a 100 % fabrication yield. These lenses improve fiber-to-chip misalignment tolerance relative to other fiber-based coupling techniques. The 1 dB excess loss diameter increases from ≈ 2.3 µm when using a lensed fiber to ≈ 9.9 µm when using the DLW printed micro-optic and a cleaved fiber. The insertion loss penalty introduced by moving to this misalignment-tolerant coupling approach is limited, with an additional loss (in comparison to the lensed fiber) as small as ≈1 dB and ≈2 dB on average. Going forward, on-axis printing can accommodate a variety of multi-element free-space and guided wave coupling elements, without requiring calibration of printing dose specific to the geometry of the 3D printed structure or to the materials comprising the photonic chip. It also enables novel methods for interconnection between chips. To that end, we fabricate a proof-of-concept 3D photonic wire bond between two vertically stacked photonic chips.

Broadband resonator-waveguide coupling for efficient extraction of octave-spanning microcombs: publisher's note.

This publisher's note contains corrections to Opt. Lett.44, 4737 (2019) OPLEDP0146-959210.1364/OL.44.004737.

Ultra-efficient frequency comb generation in AlGaAs-on-insulator microresonators.

Recent advances in nonlinear optics have revolutionized integrated photonics, providing on-chip solutions to a wide range of new applications. Currently, state of the art integrated nonlinear photonic devices are mainly based on dielectric material platforms, such as Si3N4 and SiO2. While semiconductor materials feature much higher nonlinear coefficients and convenience in active integration, they have suffered from high waveguide losses that prevent the realization of efficient nonlinear processes on-chip. Here, we challenge this status quo and demonstrate a low loss AlGaAs-on-insulator platform with anomalous dispersion and quality (Q) factors beyond 1.5 × 106. Such a high quality factor, combined with high nonlinear coefficient and small mode volume, enabled us to demonstrate a Kerr frequency comb threshold of only ∼36 µW in a resonator with a 1 THz free spectral range, ∼100 times lower compared to that in previous semiconductor platforms. Moreover, combs with broad spans (>250 nm) have been generated with a pump power of ∼300 µW, which is lower than the threshold power of state-of the-art dielectric micro combs. A soliton-step transition has also been observed for the first time in an AlGaAs resonator.

A universal frequency engineering tool for microcavity nonlinear optics: multiple selective mode splitting of whispering-gallery resonances.

Whispering-gallery microcavities have been used to realize a variety of efficient parametric nonlinear optical processes through the enhanced light-matter interaction brought about by supporting multiple high quality factor and small modal volume resonances. Critical to such studies is the ability to control the relative frequencies of the cavity modes, so that frequency matching is achieved to satisfy energy conservation. Typically this is done by tailoring the resonator cross-section. Doing so modifies the frequencies of all of the cavity modes, that is, the global dispersion profile, which may be undesired, for example, in introducing competing nonlinear processes. Here, we demonstrate a frequency engineering tool, termed multiple selective mode splitting (MSMS), that is independent of the global dispersion and instead allows targeted and independent control of the frequencies of multiple cavity modes. In particular, we show controllable frequency shifts up to 0.8 nm, independent control of the splitting of up to five cavity modes with optical quality factors ≳ 105, and strongly suppressed frequency shifts for untargeted modes. The MSMS technique can be broadly applied to a wide variety of nonlinear optical processes across different material platforms, and can be used to both selectively enhance processes of interest and suppress competing unwanted processes.

Improved coupled-mode theory for high-index-contrast photonic platforms.

Coupled-mode theory (CMT) has been widely used in optics and photonics design. Despite its popularity, several different formulations of CMT exist in the literature, and their applicable range is not entirely clear, in particular when it comes to high-index-contrast photonics platforms. Here we propose an improved formulation of CMT and demonstrate its superior performance through numerical simulations that compare CMT-derived quantities with supermode calculations and full wave propagation simulations. In particular, application of the improved CMT to asymmetric waveguides reveals a necessary correction in the conventional phase matching condition for high-index-contrast systems, which could lead to more accurate photonic circuit designs involving asymmetric elements.

On-chip optical parametric oscillation into the visible: generating red, orange, yellow, and green from a near-infrared pump.

The on-chip generation of coherent, single-frequency laser light that can be tuned across the visible spectrum would help enable a variety of applications in spectroscopy, metrology, and quantum science. Recently, third-order optical parametric oscillation (OPO) in a microresonator has shown great promise as an efficient and scalable approach towards this end. However, considering visible light generation, so far only red light at < 420 THz (near the edge of the visible band) has been reported. In this work, we overcome strong material dispersion at visible wavelengths and demonstrate on-chip OPO in a Si3N4 microresonator covering >130 THz of the visible spectrum, including red, orange, yellow, and green wavelengths. In particular, using an input pump laser that is scanned 5 THz in the near-infrared from 386 THz to 391 THz, the OPO output signal is tuned from the near-infrared at 395 THz to the visible at 528 THz, while the OPO output idler is tuned from the near-infrared at 378 THz to the infrared at 254 THz. The widest signal-idler separation of 274 THz is more than an octave in span and is the widest demonstrated for a nanophotonic OPO to date. More generally, our work shows how nonlinear nanophotonics can transform light from readily accessible compact near-infrared lasers to targeted visible wavelengths of interest.

Broadband resonator-waveguide coupling for efficient extraction of octave-spanning microcombs.

Octave-spanning frequency combs have been successfully demonstrated in Kerr nonlinear microresonators. These microcombs rely on both engineered dispersion, to enable generation of frequency components across the octave, and on engineered coupling, to efficiently extract the generated light into an access waveguide while maintaining a close to critically coupled pump. The latter is challenging, as the spatial overlap between the access waveguide and the ring modes decays with frequency. This leads to strong coupling variation across the octave, with poor extraction at short wavelengths. Here, we investigate how a waveguide wrapped around a portion of the resonator, in a pulley scheme, can improve the extraction of octave-spanning microcombs, in particular at short wavelengths. We use the coupled-mode theory to predict the performance of the pulley couplers and demonstrate good agreement with experimental measurements. Using an optimal pulley coupling design, we demonstrate a 20 dB improvement in extraction at short wavelengths compared to straight waveguide coupling.

Chip-integrated visible-telecom photon pair sources for quantum communication.

Photon pair sources are fundamental building blocks for quantum entanglement and quantum communication. Recent studies in silicon photonics have documented promising characteristics for photon pair sources within the telecommunications band, including sub-milliwatt optical pump power, high spectral brightness, and high photon purity. However, most quantum systems suitable for local operations, such as storage and computation, support optical transitions in the visible or short near-infrared bands. In comparison to telecommunications wavelengths, the significantly higher optical attenuation in silica at such wavelengths limits the length scale over which optical-fiber-based quantum communication between such local nodes can take place. One approach to connect such systems over fiber is through a photon pair source that can bridge the visible and telecom bands, but an appropriate source, which should produce narrow-band photon pairs with a high signal-to-noise ratio, has not yet been developed. Here, we demonstrate an on-chip visible-telecom photon pair source for the first time, using high quality factor silicon nitride microresonators to generate bright photon pairs with an unprecedented coincidence-to-accidental ratio (CAR) up to (3.8 ± 0.2) × 103. We further demonstrate dispersion engineering of the microresonators to enable the connection of different species of trapped atoms/ions, defect centers, and quantum dots to the telecommunications bands for future quantum communication systems.