Universal nonlinear scattering in ultra-high Q whispering gallery-mode resonators

Subharmonic instabilities in Kerr microcombs

We report experimental observation of subharmonic mode excitation in primary Kerr optical frequency combs generated using crystalline whispering-gallery mode resonators. We show that the subcombs can be controlled and span a single or multiple free spectral ranges around the primary comb modes. In the spatial domain, the resulting multiscale combs correspond to an amplitude modulation of intracavity roll patterns. We perform a theoretical analysis based on eigenvalue decomposition that evidences the mechanism leading to the excitation of these combs.

Impact of stimulated Raman scattering on dark soliton generation in a silica microresonator

Generating a coherent optical frequency comb at an arbitrary wavelength is important for fields such as precision spectroscopy and optical communications. Dark solitons which are coherent states of optical frequency combs in normal dispersion microresonators can extend the operating wavelength range of these combs. While the existence and dynamics of dark solitons has been examined extensively, requirements for the modal interaction for accessing the soliton state in the presence of a strong Raman interaction at near visible wavelengths has been less explored. Here, analysis on the parametric and Raman gain in a silica microresonator is performed, revealing that four-wave mixing parametric gain which can be created by a modal-interaction-aided additional frequency shift is able to exceed the Raman gain. The existence range of the dark soliton is analyzed as a function of pump power and detuning for given modal coupling conditions. We anticipate these results will benefit fields requiring optical frequency combs with high efficiency and selectable wavelength such as biosensing applications using silica microcavities that have a strong Raman gain in the normal dispersion regime.

Deterministic generation of a perfect soliton crystal microcomb with a saturable absorber

We numerically investigate the deterministic generation of a perfect soliton crystal (PSC) in an optical microresonator functionalized with a saturable absorber (SA). The SA allows the direct formation of a PSC from an initial, periodic Turing roll. It prevents passage through a chaotic state, which induces a stochastic nature with regard to the number of generated dissipative Kerr solitons. We show that PSCs form deterministically, and the number is controlled by adjusting the input power and SA parameter. Our work provides a simple approach for obtaining a stable PSC that offers an ultrahigh repetition rate and a high comb output power.

Nonlinear dynamics of miniature optoelectronic oscillators based on whispering-gallery mode electrooptical modulators

We propose a time-domain model to analyze the dynamical behavior of miniature optoelectronic oscillators (OEOs) based on whispering-gallery mode resonators. In these systems, the whispering-gallery mode resonator features a quadratic nonlinearity and operates as an electrooptical modulator, thereby eliminating the need for an integrated Mach-Zehnder modulator. The narrow optical resonances also eliminate the need for both an optical fiber delay line and an electric bandpass filter in the optoelectronic feedback loop. The architecture of miniature OEOs therefore appears as significantly simpler than the one of their traditional counterparts and permits us to achieve competitive metrics in terms of size, weight, and power. Our theoretical approach is based on the closed-loop coupling between the optical intracavity modes and the microwave signal generated via the photodetection of the output electrooptical comb. The resulting nonlinear oscillator model involves the slowly-varying envelopes of the microwave and optical fields, and its stability analysis permits the analytical determination the critical value of the feedback gain needed to trigger self-sustained oscillations. This stability analysis also allows us to understand how key parameters of the system such as cavity detuning or coupling efficiency influence the onset of the radiofrequency oscillation. Our study is complemented by time-domain simulations for the microwave and optical signals, which are in excellent agreement with the analytical predictions.

Fluctuations and correlations in Kerr optical frequency combs with additive Gaussian noise

We investigate the effects of environmental stochastic fluctuations on Kerr optical frequency combs. This spatially extended dynamical system can be accurately studied using the Lugiato-Lefever equation, and we show that when additive noise is accounted for, the correlations of the modal field fluctuations can be determined theoretically. We propose a general theory for the computation of these field fluctuations and correlations, which is successfully compared to numerical simulations.

Cascaded Stokes and anti-Stokes laser based on an optical resonator with a self-assembled organic monolayer

Due to their high circulating intensities, ultra-high quality factor dielectric whispering gallery mode resonators have enabled the development of low threshold Raman microlasers. Subsequently, other Raman-related phenomena, such as cascaded stimulated Raman scattering (CSRS) and stimulated anti-Stokes Raman scattering (SARS), were observed. While low threshold frequency conversion and generation have clear applications, CSRS and SARS have been limited by the low Raman gain. In this work, the surface of a silica resonator is modified with an organic monolayer, increasing the Raman gain. Up to four orders of CSRS are observed with sub-milliwatt (mW) input power, and the SARS efficiency is improved by three orders of magnitude compared to previous studies with hybrid resonators.

Coupler-induced phase matching of resonant hyperparametric scattering

We show that an evanescent field coupler can break the symmetry of a high quality factor monolithic ring microcavity, enabling generation of strongly nondegenerate frequency harmonics involving a few mode families that are orthogonal in an unperturbed microcavity. Using this property, we explain observed experimental generation of frequency combs in magnesium fluoride whispering gallery mode resonators characterized with strong normal group velocity dispersion.

Experimental observation of internally pumped parametric oscillation and quadratic comb generation in a χ(2) whispering-gallery-mode microresonator

We report on the experimental observation of internally pumped parametric oscillation in a high-$\!Q$Q lithium niobate microresonator under conditions of natural phase matching. Specifically, launching near-infrared pump light around 1060 nm into a $ z $z-cut congruent lithium niobate microresonator, we observe the generation of optical sidebands around the input pump under conditions where second-harmonic generation is close to natural phase matching. We find that a wide range of different sideband frequency shifts can be generated by varying the experimental parameters. Under particular conditions, we observe the cascaded generation of several sidebands around the pump-the first steps of optical frequency comb generation via cavity-enhanced second-harmonic generation.

On the transition to secondary Kerr combs in whispering-gallery mode resonators

We demonstrate that extended dissipative structures in Kerr-nonlinear whispering-gallery mode resonators undergo a spatiotemporal instability, as the pumping parameters are varied. We show that the dynamics of the patterns beyond this bifurcation yield specific Kerr comb and sub-comb spectra that can be subjected to a phase of frequency-locking when optimal conditions are met. Our numerical results are found to be in agreement with experimental measurements.

A taxonomy of optical dissipative structures in whispering-gallery mode resonators with Kerr nonlinearity

In this paper, the research related to the formation of optical dissipative structures in Kerr-nonlinear whispering-gallery mode resonators pumped with continuous-wave lasers is reviewed. Pattern formation in these systems can be analysed using the paradigmatic Lugiato-Lefever model, which is a partial differential equation ruling the dynamics of the intra-cavity laser field. Various dissipative structures such as Turing rolls, solitons, breathers and spatio-temporal chaos can emerge in the resonator depending on the laser power and frequency. The bifurcation analysis enables a classification of these patterns, and also permits identification of their basins of attraction.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Dependence of quality factor on surface roughness in crystalline whispering-gallery mode resonators

We present an experimental study of the variation of quality factor (Q-factor) of WGM resonators as a function of surface roughness. We consider mm-size whispering-gallery mode resonators manufactured with fluoride crystals, featuring Q-factors of the order of 1 billion at 1550 nm. The experimental procedure consists of repeated polishing steps, after which the surface roughness is evaluated using profilometry by white-light phase-shifting interferometry, while the Q-factors are determined using the cavity-ring-down method. This protocol permits us to establish an explicit curve linking the Q-factor of the disk-resonator to the surface roughness of the rim. We have performed measurements with four different crystals, namely, magnesium, calcium, strontium, and lithium fluoride. We have thereby found that the variations of Q-factor as a function of surface roughness is universal, in the sense that it is globally independent of the bulk material under consideration. We also discuss our experimental results in the light of theoretical estimates of surface scattering Q-factors already published in the literature.

Raman-Kerr frequency combs in microresonators with normal dispersion

We generalize the coupled mode formalism to study the generation of frequency combs in microresonators with simultaneous Raman and Kerr nonlinearities and investigate an impact of the former on the formation of frequency combs and dynamics of platicons in the regime of the normal group velocity dispersion. We demonstrate that the Raman effect initiates generation of sidebands, which cascade further in four-wave mixing and reshape into the Raman-Kerr frequency combs. We reveal that the Raman scattering induces a strong instability of the platicon pulses associated with the Kerr effect and normal dispersion. This instability results in branching of platicons and complex spatiotemporal dynamics.

Effect of crystalline family and orientation on stimulated Brillouin scattering in whispering-gallery mode resonators

Ultra-high Q whispering-gallery mode resonators pumped by a continuous-wave laser are known to enhance stimulated Brillouin scattering when optimal resonance and phase-matching conditions are met. In crystalline resonators, this process depends critically on the crystal orientation and family, which impose the elastic constants defining the velocity of the acoustic waves. In this article, we investigate the effect of crystalline orientation and family on this velocity which is proportional to the Brillouin frequency down-shift. In particular, the study is based on the development of a model and numerical simulations of acoustic wave velocities that propagate along the periphery of four fluoride crystals, namely calcium, magnesium, lithium and barium fluoride. We find that depending on the crystal and its orientation, the frequency excursion around the Brillouin offset can vary from few tens of kHz to more than a GHz.

Optimization of primary Kerr optical frequency combs for tunable microwave generation

We analyze the condition under which Kerr combs generate the highest microwave output power after photodetection. These optimal comb states correspond to configurations in which the sidemode-to-pump ratio is the highest possible. For the case of primary combs, we show how the interplay between the power and frequency of the pump laser critically influences this ratio, which has a direct influence on the phase noise performance of the generated microwaves. We also experimentally demonstrate primary combs with a sidemode-to-pump ratio as high as -2  dB, thereby leading to efficient energy conversion from the lightwave to the microwave frequency range.

Tunable Raman laser in a hollow bottle-like microresonator

A tunable Raman laser in the hollow bottle-like microresonator is demonstrated. By controlling the pump laser frequency, we have demonstrated continuous Raman laser frequency tuning. We also have studied the interesting transient mode evolution with Raman gain by sweeping the pump and probe laser, and verified the thermal tuning mechanism by theoretical simulations. By mechanically stretching the resonator, we have achieved the large range frequency tuning of the Raman laser, with the tuning range of 132 GHz with the resolution about 85 MHz. The demonstrated tunable Raman laser can be used as a source for future optical applications.

Efficient frequency generation in phoXonic cavities based on hollow whispering gallery mode resonators

We report on nonlinear optical effects on phoxonic cavities based on hollow whispering gallery mode resonators pumped with a continuous wave laser. We observed stimulated scattering effects such as Brillouin and Raman, Kerr effects such as degenerated and non-degenerated four wave mixing, and dispersive wave generation. These effects happened concomitantly. Hollow resonators give rise to a very rich nonlinear scenario due to the coexistence of several family modes.

Phase-locking transition in Raman combs generated with whispering gallery mode resonators

We investigate the mechanisms leading to phase locking in Raman optical frequency combs generated with ultrahigh Q crystalline whispering gallery mode disk resonators. We show that several regimes can be triggered depending on the pumping conditions, such as single-frequency Raman lasing, multimode operation involving more than one family of cavity eigenmodes, and Kerr-assisted Raman frequency comb generation. The phase locking and coherence of the combs are experimentally monitored through the measurement of beat signal spectra. These phase-locked combs, which feature high coherence and wide spectral spans, are obtained with pump powers in the range of a few tens of mW. In particular, Raman frequency combs with multiple free-spectral range spacings are reported, and the measured beat signal in the microwave domain features a 3 dB linewidth smaller than 50 Hz, thereby indicating phase locking.