Integrated microcavity electric field sensors using Pound-Drever-Hall detection.

Discerning weak electric fields has important implications for cosmology, quantum technology, and identifying power system failures. Photonic integration of electric field sensors is highly desired for practical considerations and offers opportunities to improve performance by enhancing microwave and lightwave interactions. Here, we demonstrate a high-Q microcavity electric field sensor (MEFS) by leveraging the silicon chip-based thin film lithium niobate photonic integrated circuits. Using the Pound-Drever-Hall detection scheme, our MEFS achieves a detection sensitivity of 5.2 µV/(m[Formula: see text]), which surpasses previous lithium niobate electro-optical electric field sensors by nearly two orders of magnitude, and is comparable to atom-based quantum sensing approaches. Furthermore, our MEFS has a bandwidth that can be up to three orders of magnitude broader than quantum sensing approaches and measures fast electric field amplitude and phase variations in real-time. The ultra-sensitive MEFSs represent a significant step towards building electric field sensing networks and broaden the application spectrum of integrated microcavities.

Theoretical Analysis of Microcavity Simultons Reinforced by χ

High-Q microcavities with quadratic and cubic nonlinearities add lots of versatility in controlling microcombs. Here, we study microcavity simulton and soliton dynamics reinforced by both χ^{(2)} and χ^{(3)} nonlinearities in a continuously pumped microcavity. Theoretical analysis based on the Lagrangian approach reveals the soliton peak power and gain-loss balance are impacted by the flat part of the intracavity pump, while the dark-pulse part of the pump leads to a nearly constant soliton group velocity change. We also derived a soliton conversion efficiency upper limit that is fully determined by the coupling condition and the quantum-limited soliton timing jitter in the χ^{(2,3)} system. Numerical simulations confirm the analytical results. Our theory is particularly useful for investigating AlN microcombs and sheds light on the interplay between χ^{(2)} and χ^{(3)} nonlinearities within microcavity simultons.

Spatiotemporal mode-locking and dissipative solitons in multimode fiber lasers.

Multimode fiber (MMF) lasers are emerging as a remarkable testbed to study nonlinear spatiotemporal physics with potential applications spanning from high energy pulse generation, precision measurement to nonlinear microscopy. The underlying mechanism for the generation of ultrashort pulses, which can be understood as a spatiotempoal dissipative soliton (STDS), in the nonlinear multimode resonators is the spatiotemporal mode-locking (STML) with simultaneous synchronization of temporal and spatial modes. In this review, we first introduce the general principles of STML, with an emphasize on the STML dynamics with large intermode dispersion. Then, we present the recent progress of STML, including measurement techniques for STML, exotic nonlinear dynamics of STDS, and mode field engineering in MMF lasers. We conclude by outlining some perspectives that may advance STML in the near future.

Fundamental linewidth of an AlN microcavity Raman laser.

Raman lasing can be a promising way to generate highly coherent chip-based lasers, especially in high-quality (high-Q) crystalline microcavities. Here, we measure the fundamental linewidth of a stimulated Raman laser in an aluminum nitride (AlN)-on-sapphire microcavity with a record Q-factor up to 3.7 million. An inverse relationship between fundamental linewidth and emission power is observed. A limit of the fundamental linewidth, independent of Q-factor, due to Raman-pump-induced Kerr parametric oscillation is derived.

Self-starting spatiotemporal mode-locking using Mamyshev regenerators.

Bridging multi-mode fibers and Mamyshev regenerators holds promise for pulse energy scaling in fiber lasers. However, initialization of a multi-mode Mamyshev oscillator remains a practical challenge. Here we report self-starting spatiotemporal mode-locking (STML) in a multi-mode Mamyshev oscillator without active assistance. The first initialized mode-locking is unstable, but stable STML can be attained by increasing the filter separation. Simulations verify the capability of reaching self-starting STML using Mamyshev regenerators and unveil the effect of filter separation on the self-starting ability.

Architecture for microcomb-based GHz-mid-infrared dual-comb spectroscopy.

Dual-comb spectroscopy (DCS) offers high sensitivity and wide spectral coverage without the need for bulky spectrometers or mechanical moving parts. And DCS in the mid-infrared (mid-IR) is of keen interest because of inherently strong molecular spectroscopic signatures in these bands. We report GHz-resolution mid-IR DCS of methane and ethane that is derived from counter-propagating (CP) soliton microcombs in combination with interleaved difference frequency generation. Because all four combs required to generate the two mid-IR combs rely upon stability derived from a single high-Q microcavity, the system architecture is both simplified and does not require external frequency locking. Methane and ethane spectra are measured over intervals as short as 0.5 ms, a time scale that can be further reduced using a different CP soliton arrangement. Also, tuning of spectral resolution on demand is demonstrated. Although at an early phase of development, the results are a step towards mid-IR gas sensors with chip-based architectures for chemical threat detection, breath analysis, combustion studies, and outdoor observation of trace gases.

Self-frequency shift of AlN-on-sapphire Kerr solitons.

We study the self-frequency shift of continuously pumped Kerr solitons in AlN-on-sapphire microcavities with Raman gain bandwidths narrower than the cavity free-spectral range. Solitons are generated in ∼230GHz microcavities via high-order mode dispersion engineering. The dependence of the self-frequency shift on soliton pulse width is measured and differs from amorphous material microcavities. Our measurement and simulation reveal the impact of frequency detuning between the cavity resonances and Raman gain peaks, as well as the importance of all three Raman gain peaks. The interplay between the Raman effect and dispersive wave recoil and a potential quiet point are also observed.

Dispersive-wave induced noise limits in miniature soliton microwave sources.

Compact, low-noise microwave sources are required throughout a wide range of application areas including frequency metrology, wireless-communications and airborne radar systems. And the photonic generation of microwaves using soliton microcombs offers a path towards integrated, low noise microwave signal sources. In these devices, a so called quiet-point of operation has been shown to reduce microwave frequency noise. Such operation decouples pump frequency noise from the soliton's motion by balancing the Raman self-frequency shift with dispersive-wave recoil. Here, we explore the limit of this noise suppression approach and reveal a fundamental noise mechanism associated with fluctuations of the dispersive wave frequency. At the same time, pump noise reduction by as much as 36 dB is demonstrated. This fundamental noise mechanism is expected to impact microwave noise (and pulse timing jitter) whenever solitons radiate into dispersive waves belonging to different spatial mode families.

Greater than one billion Q factor for on-chip microresonators.

High optical quality (Q) factors are critically important in optical microcavities, where performance in applications spanning nonlinear optics to cavity quantum electrodynamics is determined. Here, a record Q factor of over 1.1 billion is demonstrated for on-chip optical resonators. Using silica whispering-gallery resonators on silicon, Q-factor data is measured over wavelengths spanning the C/L bands (100 nm) and for a range of resonator sizes and mode families. A record low sub-milliwatt parametric oscillation threshold is also measured in 9 GHz free-spectral-range devices. The results show the potential for thermal silica on silicon as a resonator material.

Characterizing pump line phase offset of a single-soliton Kerr comb by dual comb interferometry.

We report phase retrieval of a single-soliton Kerr comb using electric field cross-correlation implemented via dual-comb interferometry. The phase profile of the Kerr comb is acquired through the heterodyne beat between the Kerr comb and an electro-optic comb with a pre-characterized phase profile. The soliton Kerr comb has a nearly flat phase profile, and the pump line is observed to show a phase offset which depends on the pumping parameters. The experimental results are in agreement with numerical simulations.

Vernier spectrometer using counterpropagating soliton microcombs.

Determination of laser frequency with high resolution under continuous and abrupt tuning conditions is important for sensing, spectroscopy, and communications. We show that a single microresonator provides rapid and broadband measurement of optical frequencies with a relative frequency precision comparable to that of conventional dual-frequency comb systems. Dual-locked counterpropagating solitons having slightly different repetition rates were used to implement a vernier spectrometer, which enabled characterization of laser tuning rates as high as 10 terahertz per second, broadly step-tuned lasers, multiline laser spectra, and molecular absorption lines. Besides providing a considerable technical simplification through the dual-locked solitons and enhanced capability for measurement of arbitrarily tuned sources, our results reveal possibilities for chip-scale spectrometers that exceed the performance of tabletop grating and interferometer-based devices.

Observation of Breathing Dark Pulses in Normal Dispersion Optical Microresonators.

Breathers are localized waves in nonlinear systems that undergo a periodic variation in time or space. The concept of breathers is useful for describing many nonlinear physical systems including granular lattices, Bose-Einstein condensates, hydrodynamics, plasmas, and optics. In optics, breathers can exist in either the anomalous or the normal dispersion regimes, but they have only been characterized in the former, to our knowledge. Here, externally pumped optical microresonators are used to characterize the breathing dynamics of localized waves in the normal dispersion regime. High-Q optical microresonators featuring normal dispersion can yield mode-locked Kerr combs whose time-domain waveform corresponds to circulating dark pulses in the cavity. We show that with relatively high pump power these Kerr combs can enter a breathing regime, in which the time-domain waveform remains a dark pulse but experiences a periodic modulation on a time scale much slower than the microresonator round trip time. The breathing is observed in the optical frequency domain as a significant difference in the phase and amplitude of the modulation experienced by different spectral lines. In the highly pumped regime, a transition to a chaotic breathing state where the waveform remains dark-pulse-like is also observed, for the first time to our knowledge; such a transition is reversible by reducing the pump power.

Direct soliton generation in microresonators.

We investigate, numerically and experimentally, the effect of thermo-optical (TO) chaos on soliton generation dynamics in microresonators. Numerical simulations that include the thermal dynamics show that the generated solitons can either survive or annihilate when the pump laser is scanned from blue to red and then stop at a fixed wavelength; the outcome is stochastic and is strongly related to the number of solitons generated. The random fluctuations of the cavity resonance occurring under TO chaos are also found to trigger delayed spontaneous soliton generation after the laser scan ends, which could enable soliton excitation with slow laser tuning speed. Stochastic soliton annihilation/survival, as well as delayed spontaneous soliton generation, is observed experimentally in a silicon-nitride microresonator.

Dispersion engineering and frequency comb generation in thin silicon nitride concentric microresonators.

Kerr nonlinearity-based frequency combs and solitons have been generated from on-chip microresonators. The initiation of the combs requires global or local anomalous dispersion which leads to many limitations, such as material choice, film thickness, and spectral ranges where combs can be generated, as well as fabrication challenges. Using a concentric racetrack-shaped resonator, we show that such constraints can be lifted and resonator dispersion can be engineered to be anomalous over moderately broad bandwidth. We demonstrate anomalous dispersion in a 300 nm thick silicon nitride film, suitable for semiconductor manufacturing but previously thought to result in waveguides with high normal dispersion. Together with a mode-selective, tapered coupling scheme, we generate coherent mode-locked frequency combs. Our method can realize anomalous dispersion for resonators at almost any wavelength and simultaneously achieve material and process compatibility with semiconductor manufacturing.Kerr frequency comb generation from microresonators requires anomalous dispersion, imposing restrictions on materials and resonator design. Here, Kim et al. propose a concentric racetrack-resonator design where the dispersion can be engineered to be anomalous via resonant mode coupling.

Soliton repetition rate in a silicon-nitride microresonator.

The repetition rate of a Kerr comb composed of a single soliton in an anomalous group velocity dispersion silicon-nitride microcavity is measured as a function of pump frequency. By comparing operation in the soliton and non-soliton states, the contributions from the Raman soliton self-frequency shift (SSFS) and the thermal effects are evaluated; the SSFS is found to dominate the changes in the repetition rate, similar to silica cavities. The relationship between the changes in the repetition rate and the pump frequency detuning is found to be independent of the nonlinearity coefficient and dispersion of the cavity. Modeling of the repetition rate change by using the generalized Lugiato-Lefever equation is discussed; the Kerr shock is found to have only a minor effect on repetition rate for cavity solitons with duration down to ∼50 fs.

Observation of Fermi-Pasta-Ulam Recurrence Induced by Breather Solitons in an Optical Microresonator.

We present, experimentally and numerically, the observation of Fermi-Pasta-Ulam recurrence induced by breather solitons in a high-Q SiN microresonator. Breather solitons can be excited by increasing the pump power at a relatively small pump phase detuning in microresonators. Out of phase power evolution is observed for groups of comb lines around the center of the spectrum compared to groups of lines in the spectral wings. The evolution of the power spectrum is not symmetric with respect to the spectrum center. Numerical simulations based on the generalized Lugiato-Lefever equation are in good agreement with the experimental results and unveil the role of stimulated Raman scattering in the symmetry breaking of the power spectrum evolution. Our results show that optical microresonators can be exploited as a powerful platform for the exploration of soliton dynamics.

Intracavity characterization of micro-comb generation in the single-soliton regime.

Soliton formation in on-chip micro-comb generation balances cavity dispersion and nonlinearity and allows coherent, low-noise comb operation. We study the intracavity waveform of an on-chip microcavity soliton in a silicon nitride microresonator configured with a drop port. Whereas combs measured at the through port are accompanied by a very strong pump line which accounts for >99% of the output power, our experiments reveal that inside the microcavity, most of the power is in the soliton. Time-domain measurements performed at the drop port provide information that directly reflects the intracavity field. Data confirm a train of bright, close to bandwidth-limited pulses, accompanied by a weak continuous wave (CW) background with a small phase shift relative to the comb.

Generation of wavelength-tunable soliton molecules in a 2-µm ultrafast all-fiber laser based on nonlinear polarization evolution.

We report on the experimental observation of stable single solitons and soliton molecules in a 2-µm thulium-holmium-doped fiber laser mode-locked through the nonlinear polarization evolution technique within an anomalously dispersive cavity. Single 0.65 nJ solitons feature a 7.3 nm spectral FWHM and 540 fs temporal duration, yielding a time-bandwidth product close to the Fourier-transform limitation. Under the same pumping power of 740 mW, stable out-of-phase twin-soliton molecules, featuring a temporal separation of 2.5 ps between the two ∼700 fs pulses, are generated in a deterministic way, while the central wavelength of the soliton molecules can be tuned from 1920 to 1940 nm. Finally, we present strong experimental evidence of vibrating soliton molecules.

Soliton breathing induced by stimulated Raman scattering and self-steepening in octave-spanning Kerr frequency comb generation.

We investigate the impact of stimulated Raman scattering (SRS) and self-steepening (SS) on breather soliton dynamics in octave-spanning Kerr frequency comb generation. SRS and SS can transform chaotic fluctuations in cavity solitons into periodic breathing. Furthermore, with SRS and SS considered, bandwidth of the soliton breathes more than two times stronger. The simultaneous presence of SRS and SS also make the soliton breathe slower and degrades the coherence of the soliton.

Observation of Coexisting Dissipative Solitons in a Mode-Locked Fiber Laser.

We show, experimentally and numerically, that a mode-locked fiber laser can operate in a regime where two dissipative soliton solutions coexist and the laser will periodically switch between the solutions. The two dissipative solitons differ in their pulse energy and spectrum. The switching can be controlled by an external perturbation and triggered even when switching does not occur spontaneously. Numerical simulations unveil the importance of the double-minima loss spectrum and nonlinear gain to the switching dynamics.