All-optical frequency division on-chip using a single laser.

The generation of spectrally pure microwave signals is a critical functionality in fundamental and applied sciences, including metrology and communications. Optical frequency combs enable the powerful technique of optical frequency division (OFD) to produce microwave oscillations of the highest quality1,2. Current implementations of OFD require multiple lasers, with space- and energy-consuming optical stabilization and electronic feedback components, resulting in device footprints incompatible with integration into a compact and robust photonic platform3-5. Here we demonstrate all-optical OFD on a photonic chip by synchronizing two distinct dynamical states of Kerr microresonators pumped by a single continuous-wave laser. The inherent stability of the terahertz beat frequency between the signal and idler fields of an optical parametric oscillator is transferred to a microwave frequency of a Kerr soliton comb, and synchronization is achieved via a coupling waveguide without the need for electronic locking. OFD factors of N = 34 and 468 are achieved for 227 GHz and 16 GHz soliton combs, respectively. In particular, OFD enables a 46 dB phase-noise reduction for the 16 GHz soliton comb, resulting in the lowest microwave noise observed in an integrated photonics platform. Our work represents a simple, effective approach for performing OFD and provides a pathway towards chip-scale devices that can generate microwave frequencies comparable to the purest tones produced in metrological laboratories.

Integrated femtosecond pulse generator on thin-film lithium niobate.

Integrated femtosecond pulse and frequency comb sources are critical components for a wide range of applications, including optical atomic clocks1, microwave photonics2, spectroscopy3, optical wave synthesis4, frequency conversion5, communications6, lidar7, optical computing8 and astronomy9. The leading approaches for on-chip pulse generation rely on mode-locking inside microresonators with either third-order nonlinearity10 or with semiconductor gain11,12. These approaches, however, are limited in noise performance, wavelength and repetition rate tunability 10,13. Alternatively, subpicosecond pulses can be synthesized without mode-locking, by modulating a continuous-wave single-frequency laser using electro-optic modulators1,14-17. Here we demonstrate a chip-scale femtosecond pulse source implemented on an integrated lithium niobate photonic platform18, using cascaded low-loss electro-optic amplitude and phase modulators and chirped Bragg grating, forming a time-lens system19. The device is driven by a continuous-wave distributed feedback laser chip and controlled by a single continuous-wave microwave source without the need for any stabilization or locking. We measure femtosecond pulse trains (520-femtosecond duration) with a 30-gigahertz repetition rate, flat-top optical spectra with a 10-decibel optical bandwidth of 12.6 nanometres, individual comb-line powers above 0.1 milliwatts, and pulse energies of 0.54 picojoules. Our results represent a tunable, robust and low-cost integrated pulsed light source with continuous-wave-to-pulse conversion efficiencies an order of magnitude higher than those achieved with previous integrated sources. Our pulse generator may find applications in fields such as ultrafast optical measurement19,20 or networks of distributed quantum computers21,22.

Quantum state tomography in a third-order integrated optical parametric oscillator.

We measured the covariance matrix of the fields generated in an integrated third-order optical parametric oscillator operating above threshold. We observed up to (2.3 ± 0.3) dB of squeezing in amplitude difference and inferred (4.9 ± 0.7) dB of on-chip squeezing, while an excess of noise for the sum of conjugated quadratures hinders the entanglement. The degradation of amplitude correlations and state purity for increasing the pump power is consistent with the observed growth of the phase noise of the fields, showing the necessity of strategies for phase noise control aiming at entanglement generation in these systems.

Battery-operated integrated frequency comb generator.

Optical frequency combs are broadband sources that offer mutually coherent, equidistant spectral lines with unprecedented precision in frequency and timing for an array of applications1. Frequency combs generated in microresonators through the Kerr nonlinearity require a single-frequency pump laser and have the potential to provide highly compact, scalable and power-efficient devices2,3. Here we demonstrate a device-a laser-integrated Kerr frequency comb generator-that fulfils this potential through use of extremely low-loss silicon nitride waveguides that form both the microresonator and an integrated laser cavity. Our device generates low-noise soliton-mode-locked combs with a repetition rate of 194 gigahertz at wavelengths near 1,550 nanometres using only 98 milliwatts of electrical pump power. The dual-cavity configuration that we use combines the laser and microresonator, demonstrating the flexibility afforded by close integration of these components, and together with the ultra low power consumption should enable production of highly portable and robust frequency and timing references, sensors and signal sources. This chip-based integration of microresonators and lasers should also provide tools with which to investigate the dynamics of comb and soliton generation.

Active tuning of dispersive waves in Kerr soliton combs.

Kerr soliton combs operate in the anomalous group-velocity dispersion regime through the excitation of dissipative solitons. The generated bandwidth is largely dependent on the cavity dispersion, with higher-order dispersion contributing to dispersive-wave (DW) generation that allows for power enhancement of the comb lines at the wings of the spectrum. However, the spectral position of the DW is highly sensitive to the overall cavity dispersion, and the inevitable dimension variations that occur during the fabrication process result in deviations in the DW emission wavelength. Here, we demonstrate active tuning of the DW wavelength, enabling post-fabrication spectral shaping of the soliton spectrum. We control the DW position by introducing a wavelength-controllable avoided mode crossing through actively tuning the resonances of a silicon nitride coupled microresonator via integrated heaters. We demonstrate DW tuning over 113 nm with a spectral power that can exceed the peak soliton spectral power. In addition, our modeling reveals buildup and enhancement of the DW in the auxiliary resonator, indicating that the mode hybridization arising from the strong coupling between the two resonators is critical for DW formation.

Theory of χ(2)-microresonator-based frequency conversion.

Microresonator-based platforms with ${\chi ^{(2)}}$ nonlinearities have the potential to perform frequency conversion at high efficiencies and ultralow powers with small footprints. The standard doctrine for achieving high conversion efficiency in cavity-based devices requires "perfect matching," that is, zero phase mismatch while all relevant frequencies are precisely at a cavity resonance, which is difficult to achieve in integrated platforms due to fabrication errors and limited tunabilities. In this Letter, we show that the violation of perfect matching does not necessitate a reduction in conversion efficiency. On the contrary, in many cases, mismatches should be intentionally introduced to improve the efficiency or tunability of conversion. We identify the universal conditions for maximizing the efficiency of cavity-based frequency conversion and show a straightforward approach to fully compensate for parasitic processes such as thermorefractive and photorefractive effects that, typically, can limit the conversion efficiency. We also show the design criteria that make these high-efficiency states stable against nonlinearity-induced instabilities.

Conversion efficiency of soliton Kerr combs.

We investigate the conversion efficiency (CE) of soliton modelocked Kerr frequency combs. Our analysis reveals three distinct scaling regimes of CE with the cavity free spectral range (FSR), which depends on the relative contributions of the coupling and propagation loss to the total cavity loss. Our measurements, for the case of critical coupling, verify our theoretical prediction over a range of FSRs and pump powers. Our numerical simulations also indicate that mode crossings have an adverse effect on the achievable CE. Our results indicate that microresonator combs operating with spacings in the electronically detectable regime are highly inefficient, which could have implications for integrated Kerr comb devices.

Nonlinear refractive index of solids in mid-infrared.

We measure the third-order nonlinear optical response of various dielectrics and semiconductors using the spectrally resolved two-beam coupling method at 2.3 µm, 3.5 µm, 4.5 µm, and 8.3 µm. These materials include fused silica, sapphire, calcium fluoride, magnesium fluoride, zinc sulphide, and zinc selenide. We compare our results with previous literature results and theoretically expected values using two-band model theory. The dispersion of the nonlinear refractive index n2 over this wavelength range is found to be negligible.

Soliton-effect compression of picosecond pulses on a photonic chip.

We report soliton-effect pulse compression of low energy (∼25pJ), picosecond pulses on a photonic chip. An ultra-low-loss, dispersion-engineered 40-cm-long waveguide is used to compress 1.2-ps pulses by a factor of 18, which represents, to our knowledge, the largest compression factor yet experimentally demonstrated on-chip. Our scheme allows for interfacing with an on-chip picosecond source and offers a path towards a fully integrated stabilized frequency comb source.

Performance scaling of a 10-GHz solid-state laser enabling self-referenced CEO frequency detection without amplification.

A simple and compact straight-cavity laser oscillator incorporating a cascaded quadratic nonlinear crystal and a semiconductor saturable absorber mirror (SESAM) can deliver stable femtosecond modelocking at high pulse repetition rates >10 GHz. In this paper, we experimentally investigate the influence of intracavity dispersion, pump brightness, and cavity design on modelocking with high repetition rates, and use the resulting insights to demonstrate a 10.4-GHz straight-cavity SESAM-modelocked Yb:CALGO laser delivering 108-fs pulses with 812 mW of average output power. This result represents a record-level performance for diode-pumped femtosecond oscillators with repetition rates above 10 GHz. Using the oscillator output without any optical amplification, we demonstrate coherent octave-spanning supercontinuum generation (SCG) in a silicon nitride waveguide. Subsequent f-to-2f interferometry with a periodically poled lithium niobate waveguide enables the detection of a strong carrier-envelope offset (CEO) beat note with a 33-dB signal-to-noise ratio.

Near-Degenerate Quadrature-Squeezed Vacuum Generation on a Silicon-Nitride Chip.

Squeezed states are a primary resource for continuous-variable (CV) quantum information processing. To implement CV protocols in a scalable and robust way, it is desirable to generate and manipulate squeezed states using an integrated photonics platform. In this Letter, we demonstrate the generation of quadrature-phase squeezed states in the radio-frequency carrier sideband using a small-footprint silicon-nitride microresonator with a dual-pumped four-wave-mixing process. We record a squeezed noise level of 1.34 dB (±0.16 dB) below the photocurrent shot noise, which corresponds to 3.09 dB (±0.49 dB) of quadrature squeezing on chip. We also show that it is critical to account for the nonlinear behavior of the pump fields to properly predict the squeezing that can be generated in this system. This technology represents a significant step toward creating and manipulating large-scale CV cluster states that can be used for quantum information applications, including universal quantum computing.

Frequency-Domain Quantum Interference with Correlated Photons from an Integrated Microresonator.

Frequency encoding of quantum information together with fiber and integrated photonic technologies can significantly reduce the complexity and resource requirements for realizing all-photonic quantum networks. The key challenge for such frequency domain processing of single photons is to realize coherent and selective interactions between quantum optical fields of different frequencies over a range of bandwidths. Here, we report frequency-domain Hong-Ou-Mandel interference with spectrally distinct photons generated from a chip-based microresonator. We use four-wave mixing to implement an active "frequency beam splitter" and achieve interference visibilities of 0.95±0.02. Our work establishes four-wave mixing as a tool for selective high-fidelity two-photon operations in the frequency domain which, combined with integrated single-photon sources, provides a building block for frequency-multiplexed photonic quantum networks.

Chip-based frequency comb sources for optical coherence tomography.

Optical coherence tomography (OCT) is a powerful interferometric imaging technique widely used in medical fields such as ophthalmology, cardiology and dermatology. Superluminescent diodes (SLDs) are widely used as light sources in OCT. Recently integrated chip-based frequency combs have been demonstrated in numerous platforms and the possibility of using these broadband chip-scale combs for OCT has been raised extensively over the past few years. However, the use of these chip-based frequency combs as light sources for OCT requires bandwidth and power compatibility with current OCT systems and have not been shown to date. Here we generate frequency combs based on chip-scale lithographically-defined microresonators and demonstrate its capability as a novel light source for OCT. The combs are designed with a small spectral line spacing of 0.21 nm which ensure imaging range comparable to commercial system and operated at non-phase locked regime which provide conversion efficiency of 30%. The comb source is shown to be compatible with a standard commercial spectral domain (SD) OCT system and enables imaging of human tissue with image quality comparable to the one achieved with tabletop commercial sources. The comb source also provides a path towards fully integrated OCT systems.

Ionization-assisted refocusing of femtosecond Gaussian beams.

Ionization occurs ubiquitously in intense laser-matter interaction and often leads to rapid decrease in laser intensity via plasma defocusing, shortening the effective interaction length of desired high-field processes. Refocusing of pulses may compensate for this adverse effect. However, it typically relies on Kerr-induced self-focusing and requires sufficiently high power. Here, we present simulations showing the refocusing of intense pulses with an initial Gaussian beam profile in atmospheric pressure gases at relatively low power. We attribute this refocusing to the formation of ring-structure plasmas. We find that tighter focusing leads to stronger refocusing, and the initial chirp of the pulse greatly affects its dynamics due to spatiotemporal coupling of focused broadband pulses. Our results highlight a novel aspect of complex pulse dynamics and can be relevant to applications involving tightly focused ultrafast Gaussian beams.

Coherent two-octave-spanning supercontinuum generation in lithium-niobate waveguides.

We demonstrate coherent supercontinuum generation (SCG) in a monolithically integrated lithium-niobate waveguide, under the presence of second- and third-order nonlinear effects. We achieve more than two octaves of optical bandwidth in a 0.5-cm-long waveguide with 100-picojoule-level pulses. Dispersion engineering of the waveguide allows for spectral overlap between the SCG and the second harmonic, which enables direct detection of the carrier-envelope offset frequency fCEO using a single waveguide. We measure the fCEO of our femtosecond pump source with a 30-dB signal-to-noise ratio.

Microfluidic mid-infrared spectroscopy via microresonator-based dual-comb source.

Over the past decade, microresonator-based soliton combs based on photonic integration have broadened the scope of applications in sensing, ranging, and imaging. The large comb line spacing on the order of hundreds of gigahertz allows for rapid acquisition of absorption spectra in the condensed matter phase without aliasing via a dual-comb interferometer. We present a proof-of-principle demonstration of high-throughput label-free microresonator-based dual-comb spectroscopy in a microfluidic chip that dynamically probes the linear absorption of liquid acetone in the mid-infrared wavelength regime. We measure the flow dynamics of an acetone droplet with a spectral acquisition rate of 25 kHz (40 µs per spectrum) covering a spectral range from 2900 to 2990 nm. Combining microfluidics and silicon-photonic technology would potentially enable a compact time-resolved spectroscopy system for a wide range of applications such as chemical synthesis, biological cell-sorting, and lab-on-a-chip.

Turn-key, high-efficiency Kerr comb source.

We demonstrate an approach for automated Kerr comb generation in the normal group-velocity dispersion (GVD) regime. Using a coupled-ring geometry in silicon nitride, we precisely control the wavelength location and splitting strength of avoided mode crossings to generate low-noise frequency combs with pump-to-comb conversion efficiencies of up to 41%, which is the highest reported to date for normal-GVD Kerr combs. Our technique enables on-demand generation of a high-power comb source for applications such as wavelength-division multiplexing in optical communications.

Supercontinuum generation in angle-etched diamond waveguides.

We experimentally demonstrate on-chip supercontinuum generation in the visible region in angle-etched diamond waveguides. We measure an output spectrum spanning 670-920 nm in a 5-mm-long waveguide using 100-fs pulses with 187 pJ of incident pulse energy. Our fabrication technique, combined with diamond's broad transparency window, offers a potential route toward broadband supercontinuum generation in the UV domain.

Observation of Arnold Tongues in Coupled Soliton Kerr Frequency Combs.

We demonstrate various regimes of synchronization in systems of two coupled cavity soliton-based Kerr frequency combs. We show subharmonic, harmonic, and harmonic-ratio synchronization of coupled microresonators, and reveal their dynamics in the form of Arnold tongues, structures that are ubiquitous in nonlinear dynamical systems. Our experimental results are well corroborated by numerical simulations based on coupled Lugiato-Lefever equations. This Letter illustrates the newfound degree of flexibility in synchronizing Kerr combs across a wide range of comb spacings and could find applications in time and frequency metrology, spectroscopy, microwave photonics, optical communications, and astronomy.

Strong Nonlinear Coupling in a Si_{3}N_{4} Ring Resonator.

We demonstrate that nondegenerate four-wave mixing in a Si_{3}N_{4} microring resonator can result in a nonlinear coupling rate between two optical fields exceeding their energy dissipation rate in the resonator, corresponding to strong nonlinear coupling. We demonstrate that this leads to a Rabi-like splitting, for which we provide a theoretical description in agreement with our experimental results. This yields new insight into the dynamics of nonlinear optical interactions in microresonators and access to novel phenomena.