Nonlinear Microresonators Research Articles

Discrete and Parallel Frequency‐Bin Entanglement Generation from Quantum Frequency Comb

AbstractPhotons’ frequency degree of freedom is promising to realize large‐scale quantum information processing. Quantum frequency combs (QFCs) generated in integrated nonlinear microresonators can produce multiple frequency modes with narrow linewidth. Here, polarization‐entangled QFCs are utilized to generate discrete frequency‐bin entangled states. Fourteen pairs of polarization‐entangled photons with different frequencies are simultaneously transformed into frequency‐bin entangled states. The characteristic of frequency‐bin entanglement is demonstrated by Hong‐Ou‐Mandel interference, which can be performed with single or multiple frequency pairs in parallel. This work paves the way for harnessing large‐scale frequency‐bin entanglement and converting between different degrees of freedom in quantum information processing.

Phase evolution and control in a synchronized Duffing-type nonlinear micro-oscillator

Synchronization, as a typical nonlinear phenomenon, has been widely observed and harnessed in various natural and engineered systems. However, the limited synchronization range restricts its potential applications. In this study, conducting comprehensive theoretical analysis and experimental exploration of the phase evolution, we gain valuable insights into the transition process from synchronization to desynchronization, focusing on the perspective of phase. For the first time, we unveil the restriction imposed on the synchronization range by the phase and propose an automatic phase tracking controller that can expand the synchronization range to encompass the entire hysteresis region of the Duffing-type nonlinear micro-resonator. This breakthrough opens up new possibilities for a broader array of applications in diverse fields.

On-chip Kerr parametric oscillation with integrated heating for enhanced frequency tuning and control.

Nonlinear microresonators can convert light from chip-integrated sources into new wavelengths within the visible and near-infrared spectrum. For most applications, such as the interrogation of quantum systems with specific transition wavelengths, tuning the frequency of converted light is critical. Nonetheless, demonstrations of wavelength conversion have mostly overlooked this metric. Here, we apply efficient integrated heaters to tune the idler frequency produced by the Kerr optical parametric oscillation in a silicon nitride microring across a continuous 1.5 terahertz range. Finally, we suppress idler frequency noise between DC and 5 kHz by several orders of magnitude using feedback to the heater drive.

Stable soliton dual-microcomb generation via sideband thermal compensation for spectroscopy

Microcombs—generated by coherently pumping nonlinear microresonators—have emerged as a state-of-the-art scheme at the chip scale. Dual-comb spectroscopy (DCS) technology further takes advantage of the miniature system, and has been demonstrated as a powerful tool for real-time and broadband optical sampling of molecular spectra. Here, a novel soliton dual-microcomb generation method by rapid frequency sweep and sideband thermal compensation is put forward, and dual-microcomb optical spectra range beyond 200-nm has been successfully demonstrated in two microresonators with moderate quality factors. Compared to the dual-microcomb with a weak thermal compensation effect, the demonstrated dual-microcomb shows much lower-noise RF beat notes (<10 kHz) and smaller Allan deviations (1.0 × 10–4 at 1 ms) by increasing sideband power. Moreover, the dual-microcomb has been utilized in the gas absorption detection of H12CN for demonstration with high signal-to-noise ratios (SNRs) and fast acquisition rates. This work also lays a technical foundation for other dual-microcomb applications of ranging and microwave photonics.

Coherent terahertz radiation with 2.8-octave tunability through chip-scale photomixed microresonator optical parametric oscillation

High-spectral-purity frequency-agile room-temperature sources in the terahertz spectrum are foundational elements for imaging, sensing, metrology, and communications. Here we present a chip-scale optical parametric oscillator based on an integrated nonlinear microresonator that provides broadly tunable single-frequency and multi-frequency oscillators in the terahertz regime. Through optical-to-terahertz down-conversion using a plasmonic nanoantenna array, coherent terahertz radiation spanning 2.8-octaves is achieved from 330 GHz to 2.3 THz, with ≈20 GHz cavity-mode-limited frequency tuning step and ≈10 MHz intracavity-mode continuous frequency tuning range at each step. By controlling the microresonator intracavity power and pump-resonance detuning, tunable multi-frequency terahertz oscillators are also realized. Furthermore, by stabilizing the microresonator pump power and wavelength, sub-100 Hz linewidth of the terahertz radiation with 10−15 residual frequency instability is demonstrated. The room-temperature generation of both single-frequency, frequency-agile terahertz radiation and multi-frequency terahertz oscillators in the chip-scale platform offers unique capabilities in metrology, sensing, imaging and communications.

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.

Engineered Raman Lasing in Photonic Integrated Chalcogenide Microresonators

AbstractPhotonic integrated Raman lasers have extended the wavelength range of chip‐scale laser sources and have enabled applications including molecular spectroscopy, environmental analysis, and biological detection. Yet, the performance is strongly determined by the pumping condition and Raman shift value of nonlinear medias, leaving challenges to have a widely and continuously tunable Raman laser (e.g., over 100 nm). Here, photonic engineered Raman lasers based on chip‐integrated chalcogenide microresonators are demonstrated. The home‐developed chalcogenide photonic platform is of high nonlinearity, wide transparency, and low loss. The strong and broadband material Raman response has promised rich dynamics of Raman lasing. Indeed, both single‐mode Raman lasing and a broadband Raman‐Kerr comb, which are found engineered by tuning the dispersion of the chalcogenide microresonator, are demonstrated. The single‐mode Raman laser, together with its cascaded modes, supports a gap‐free tuning range over 140 nm, while the threshold power is as low as 3.25 mW. The results may contribute to the understanding of Raman and Kerr nonlinear interactions in dissipative and nonlinear microresonators, and on application aspect, may pave a way to integrated and efficient laser sources that is desired in spectroscopic applications in the infrared.

Dissipative Kerr solitons in semiconductor ring lasers

Dissipative Kerr solitons are self-organized optical waves arising from the interplay between Kerr effect and dispersion. They can form spontaneously in nonlinear microresonators pumped with an external continuous-wave laser, which provides the parametric gain for the proliferation of an ultrastable frequency comb. These miniaturized and battery driven microcombs have become a disruptive technology for precision metrology, broadband telecommunication and ultrafast optical ranging. In this work, we report on the first experimental observation of dissipative Kerr solitons generated in a ring cavity with a fast semiconductor gain medium. The moderate quality factor of the ring cavity is compensated by the giant resonant Kerr nonlinearity of a quantum cascade laser, which is more than a million times larger than in Si3N4. By engineering the dispersion of the cavity, we observe the formation of bright dissipative Kerr solitons in the mid-infrared range. Soliton formation appears after an abrupt symmetry breaking between the two lasing directions of the ring cavity. The pump field of the soliton is generated by direct electrical driving and closely resembles the soliton Cherenkov radiation observed in passive microcombs. Two independent techniques shed light on the waveform and coherence of the solitons and confirm a pulse width of approximately 3 ps. Our results extend the spectral range of soliton microcombs to mid-infrared wavelengths and will lead to integrated, battery driven and turnkey spectrometers in the molecular fingerprint region.

Suppression of avoided resonance crossing in microresonators.

Kerr frequency comb generation in microresonators is enabled by notable developments in fabrication technology and novel nonlinear material platforms. However, even in a low loss and highly nonlinear microresonator, the avoided resonance crossing may hamper reliable frequency comb generation. We present a method to suppress the avoided resonance crossing induced by polarization mode coupling. Our approach employs a filter waveguide coupled to a microring resonator for selective filtering of the TM00 mode while keeping the operational TE00 mode with low loss. We experimentally demonstrate an avoided-crossing-suppressed microresonator in the AlGaAs-on-insulator platform.

Dynamics of soliton self-injection locking in optical microresonators

Soliton microcombs constitute chip-scale optical frequency combs, and have the potential to impact a myriad of applications from frequency synthesis and telecommunications to astronomy. The demonstration of soliton formation via self-injection locking of the pump laser to the microresonator has significantly relaxed the requirement on the external driving lasers. Yet to date, the nonlinear dynamics of this process has not been fully understood. Here, we develop an original theoretical model of the laser self-injection locking to a nonlinear microresonator, i.e., nonlinear self-injection locking, and construct state-of-the-art hybrid integrated soliton microcombs with electronically detectable repetition rate of 30 GHz and 35 GHz, consisting of a DFB laser butt-coupled to a silicon nitride microresonator chip. We reveal that the microresonator’s Kerr nonlinearity significantly modifies the laser diode behavior and the locking dynamics, forcing laser emission frequency to be red-detuned. A novel technique to study the soliton formation dynamics as well as the repetition rate evolution in real-time uncover non-trivial features of the soliton self-injection locking, including soliton generation at both directions of the diode current sweep. Our findings provide the guidelines to build electrically driven integrated microcomb devices that employ full control of the rich dynamics of laser self-injection locking, key for future deployment of microcombs for system applications.

Single-electron detection utilizing coupled nonlinear microresonators

Since the discovery of the electron, the accurate detection of electrical charges has been a dream of the scientific community. Owing to some remarkable advantages, micro/nanoelectromechanical system-based resonators have been used to design electrometers with excellent sensitivity and resolution. Here, we demonstrate a novel ultrasensitive charge detection method utilizing nonlinear coupling in two micromechanical resonators. We achieve single-electron charge detection with a high resolution up to 0.197 ± 0.056 {mathrm{e}}/sqrt {{mathrm{Hz}}} at room temperature. Our findings provide a simple strategy for measuring electron charges with extreme accuracy.

Laser intensity-dependent nonlinear-optical effects in organic whispering gallery mode cavity microstructures.

Nonlinear microresonators are very desired for a wide variety of applications. Up-conversion processes responsible for the transformation of IR laser radiation into visible are intensity-dependent and thus rather sensitive to all involved effects, which can mask each other. In this work we study the phenomena that are the most important for possible lasing in 4-(dicyanomethylene)-2-methyl-6-(4-dimethylaminostyryl)-4 H-pyran dye spherical microresonators: the two-photon absorption and photobleaching. Based on the suggested model of the threshold-like dependence of the two-photon luminescence (TPL) on pump power, we demonstrate the role of intensity-dependent photobleaching in the appearance of the TPL and find a good agreement with the experiment. This finding is important for the analysis of lasing in nonlinear dye-based resonators.

Chaotic synchronization of two optical cavity modes in optomechanical systems

The synchronization of the motion of microresonators has attracted considerable attention. In previous studies, the microresonators for synchronization were studied mostly in the linear regime. While the important problem of synchronizing nonlinear microresonators was rarely explored. Here we present theoretical methods to synchronize the motions of chaotic optical cavity modes in an optomechanical system, where one of the optical modes is strongly driven into chaotic motion and transfers chaos to other weakly driven optical modes via a common mechanical resonator. This mechanical mode works as a common force acting on each optical mode, which, thus, enables the synchronization of states. We find that complete synchronization can be achieved in two identical chaotic cavity modes. For two arbitrary nonidentical chaotic cavity modes, phase synchronization can also be achieved in the strong-coupling small-detuning regime.

Kerr-Microresonator Soliton Frequency Combs at Cryogenic Temperatures

We present measurements of silicon nitride nonlinear microresonators and frequency comb generation at cryogenic temperatures as low as 7~K. The resulting two orders of magnitude reduction in the thermo-refractive coefficient relative to room-temperature enables direct access to single bright Kerr soliton states through adiabatic frequency tuning of the pump laser while remaining in thermal equilibrium. Our experimental results, supported by theoretical modeling, show that single solitons are easily accessible at temperatures below 60~K for the microresonator device under study. We further demonstrate that the cryogenic temperature primarily impacts the thermo-refractive coefficient. Other parameters critical to the generation of solitons, such as quality factor, dispersion, and effective nonlinearity, are unaltered. Finally, we discuss the potential improvement in thermo-refractive noise resulting from cryogenic operation. The results of this study open up new directions in advancing chip-scale frequency comb optical clocks and metrology at cryogenic temperatures.

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 20dB improvement in extraction at short wavelengths compared to straight waveguide coupling.

Symmetry-breaking-induced dynamics in a nonlinear microresonator.

Optically induced symmetry-breaking plays a key role in nonlinear photonics. Recently, the experiment has successfully observed the Kerr-nonlinearity-induced chiral symmetry breaking in a single ultrahigh-Q whispering-gallery microresonator. Here, we show this symmetry-breaking can generate exotic dynamics between two counter-propagating modes. In particular, we predict two kinds of self-trappings, in which the corresponding relative phase oscillates around π or runs without bound although they have both the nonzero mean energy imbalance. Finally, we also clarify the impacts of the mode loss, finding a dynamical transition from self-trappings to an anharmonic oscillation. The presented scheme offers a new route to understanding the nonlinear dynamics and wave chaos in the microresonator.

PyLLE: A Fast and User Friendly Lugiato-Lefever Equation Solver.

The Lugiato-Lefever Equation (LLE), first developed to provide a description of spatial dissipative structures in optical systems, has recently made a significant impact in the integrated photonics community, where it has been adopted to help understand and predict Kerr-mediated nonlinear optical phenomena such as parametric frequency comb generation inside microresonators. The LLE is essentially an application of the nonlinear Schrodinger equation (NLSE) to a damped, driven Kerr nonlinear resonator, so that a periodic boundary condition is applied. Importantly, a slow-varying time envelope is stipulated, resulting in a mean-field solution in which the field does not vary within a round trip. This constraint, which differentiates the LLE from the more general Ikeda map, significantly simplifies calculations while still providing excellent physical representation for a wide variety of systems. In particular, simulations based on the LLE formalism have enabled modeling that quantitatively agrees with reported experimental results on microcomb generation (e.g., in terms of spectral bandwidth), and have also been central to theoretical studies that have provided better insight into novel nonlinear dynamics that can be supported by Kerr nonlinear microresonators. The great potential of microresonator frequency combs (microcombs) in a wide variety of applications suggests the need for efficient and widely accessible computational tools to more rapidly further their development. Although LLE simulations are commonly performed by research groups working in the field, to our knowledge no free software package for solving this equation in an easy and fast way is currently available. Here, we introduce pyLLE, an open-source LLE solver for microcomb modeling. It combines the user-friendliness of the Python programming language and the computational power of the Julia programming language.

Spectral Purification of Microwave Signals with Disciplined Dissipative Kerr Solitons.

Continuous-wave-driven Kerr nonlinear microresonators give rise to self-organization in terms of dissipative Kerr solitons, which constitute optical frequency combs that can be used to generate low-noise microwave signals. Here, by applying either amplitude or phase modulation to the driving laser we create an intracavity potential trap to discipline the repetition rate of the solitons. We demonstrate that this effect gives rise to a novel spectral purification mechanism of the external microwave signal frequency, leading to reduced phase noise of the output signal. We experimentally observe that the microwave signal generated from disciplined solitons is injection locked by the external drive at long timescales, but exhibits an unexpected suppression of the fast timing jitter. Counterintuitively, this filtering takes place for frequencies that are substantially lower than the cavity decay rate. As a result, while the long timescale stability of the Kerr frequency comb's repetition rate is improved by more than 4 orders of magnitude, the purified microwave signal shows a reduction of the phase noise by 30dB at offset frequencies above 10kHz.

Influence of the microresonator nonlinearity on the self-injection locking effect

The effect of self-injection locking of a laser to a nonlinear microresonator is considered. It is shown that an additional detuning arises in the system, depending on the pump power. This effect can contribute to the generation of optical combs in the pull mode, which will increase the stability of the generated signal.

Kerr-microresonator solitons from a chirped background

Optical frequency combs based on solitons in nonlinear microresonators open up new regimes for optical metrology and signal processing across a range of expanding and emerging applications. In this work, we advance these combs toward applications by demonstrating protected single-soliton formation and operation in a Kerr-nonlinear microresonator using a phase-modulated pump laser. Phase modulation gives rise to spatially/temporally varying effective loss and detuning parameters, leading to an operation regime in which multi-soliton degeneracy is lifted and a single soliton is the only observable behavior. We achieve direct, on-demand excitation of single solitons as indicated by reversal of the characteristic “soliton step.” Phase modulation also enables precise, high bandwidth control of the soliton pulse train’s properties, and we measure dynamics that agree closely with simulations. We show that the technique can be extended to high-repetition-frequency Kerr solitons through subharmonic phase modulation. These results will facilitate straightforward generation and control of Kerr-soliton microcombs for integrated photonics systems.