Wideband multimode optical parametric oscillation in a Kerr microresonator.

Parametric oscillation in Kerr microresonators provides an attractive pathway for the generation of new optical frequencies in a low-power, small-footprint device. The frequency shift of the newly generated parametric sidebands is set by the phasematching of the underlying four-wave-mixing process, with the generation of large frequency shift sidebands typically placing exacting requirements on a resonator's dispersion profile. In practice, this limits the range of viable pump wavelengths, and ultimately the range of output frequencies. In this paper, we consider a multimode four-wave-mixing process in which the pump and sidebands propagate in different mode families of the resonator. We show that this multimode configuration yields a considerable relaxation in the phasematching requirements needed to generate large frequency shift parametric sidebands, allowing their formation even in resonators with strong second-order dispersion. Experimentally we use a magnesium-fluoride micro-disk resonator to demonstrate this multimode phasematching. By accessing different pump and sideband modes, four distinct multimode parametric processes generating frequency shifts between 118 and 216 THz are reported. The resulting separation between the two sidebands is almost three octaves.

Kerr microresonator dual-comb source with adjustable line-spacing.

Optical microresonators offer a highly-attractive new platform for the generation of optical frequency combs. Recently, several groups have been able to demonstrate the generation of dual-frequency combs in a single microresonator driven by two optical pumps. This opens the possibility for microresonator-based dual-comb systems suitable for measurement applications such as spectroscopy, ranging and imaging. Key to the performance of these systems are the parameters of the radio-frequency comb spectrum that arises from the interference of the two optical combs. In this work, we present a simple mechanism to enable the discrete fine-tuning of these parameters by driving the two optical combs with optical pumps with different azimuthal mode numbers. The mechanism consists of tuning the difference in azimuthal mode number between the two pumps by selection of the pumps' frequencies. We are able to implement this technique when the two counter-propagating pumps are set to drive resonances of the same spatial mode family, as well as different mode families. In each case, we experimentally observe ∼1 MHz of discrete tunability in the line-spacing of the radio-frequency comb as the frequency offset between the two pumps is scanned between 0 to 80 free-spectral-ranges.

Temporal characteristics of stationary switching waves in a normal dispersion pulsed-pump fiber cavity.

Kerr cavities driven in the normal dispersion regime are known to host switching waves. These consist of a traveling wavefront that connects separate regions associated with high- and low-intensity steady states of the cavity. In this Letter, we drive a 230-m custom built fiber ring cavity with strong normal dispersion using nanosecond pulses, allowing us to directly resolve the fine structure of individual switching waves, including resonant oscillations occurring over periods of the order of ∼10 ps. We demonstrate the intimate connection between the temporal and spectral features of the dispersive waves associated with switching waves, while also investigating how these dispersive waves evolve with cavity parameters, namely the frequency detuning and pump desynchronization. Furthermore, by applying a localized and temporary perturbation to our driving field in the presence of a phase modulation trapping potential, we are able to generate a stable and persistent dark pulse, allowing us to directly observe and model the interlocking of two stationary switching waves under quasi-CW pumping conditions. These results further verify the accuracy of the dispersive wave formalism used, and show that their temporal modulation frequency and decay rate in a pulsed-pumped cavity are accurately captured from theory previously applied to CW-pumped systems.

Random number generation using spontaneous symmetry breaking in a Kerr resonator.

We demonstrate an all-optical random number generator based on spontaneous symmetry breaking in a coherently driven Kerr resonator. Random bit sequences are generated by repeatedly tuning a control parameter across a symmetry-breaking bifurcation that enacts random selection between two possible steady-states of the system. Experiments are performed in a fiber ring resonator, where the two symmetry-broken steady-states are associated with orthogonal polarization modes. Detrimental biases due to system asymmetries are suppressed by leveraging a recently discovered self-symmetrization phenomenon that ensures the symmetry-breaking dynamics act as an unbiased coin toss, with a genuinely random selection between the two available steady-states. We optically generate bits at a rate of 3 MHz without post-processing and verify their randomness using the National Institute of Standards and Technology and Dieharder statistical test suites.

Impact of early waves of the COVID-19 pandemic on family medicine residency training: Analysis of survey data.

OBJECTIVE: To identify how graduating and incoming family medicine residents (FMR) experienced changes to their education during the early waves of the COVID-19 pandemic. DESIGN: The Family Medicine Longitudinal Survey was modified with questions related to the impact of COVID-19 on FMR and their training. Short-answer responses underwent thematic analysis. Responses to Likert scale and multiple-choice questions were reported as summary statistics. SETTING: Department of Family and Community Medicine at the University of Toronto in Ontario. PARTICIPANTS: Graduating FMR in spring 2020 and incoming FMR in fall 2020. MAIN OUTCOME MEASURES: Residents' perceptions of the impact of COVID-19 on clinical skills acquisition and preparedness for practice. RESULTS: Surveys response rates were 124 of 167 (74%) and 142 of 162 (88%) for graduating and incoming residents, respectively. Important themes for both cohorts included reduced access to clinical environments, reduced patient volumes, and lack of exposure to procedural skills. While the graduating cohort indicated they felt confident to begin practising family medicine, they described being impacted by the loss of a tailored learning environment, including canceled or altered electives. In contrast, incoming residents reported the loss of core skills, such as physical examination competency, as well as the loss of face-to-face communication, rapport, and relationship-building opportunities. However, both cohorts endorsed gaining new skills during the pandemic, including conducting telemedicine appointments, pandemic planning, and interfacing with public health. CONCLUSION: Based on these results, residency programs can specifically tailor solutions and modifications to address common themes across cohorts to facilitate optimal learning environments in pandemic times.

Breathing dynamics of symmetry-broken temporal cavity solitons in Kerr ring resonators.

We investigate theoretically and experimentally the instabilities of symmetry-broken, vectorial, bright cavity solitons (CSs) of two-mode nonlinear passive Kerr resonators. Through comprehensive theoretical analyses of coupled Lugiato-Lefever equations, we identify two different breathing regimes where the two components of the vectorial CSs breathe respectively in-phase and out-of-phase. Moreover, we find that deep out-of-phase breathing can lead to intermittent self-switching of the two components, spontaneously transforming a soliton into its mirror-symmetric state. In this process, solitons are also sometimes observed to decay. All our theoretical predictions are confirmed in experiments performed in an optical fiber ring resonator, where CS symmetry breaking occurs across the polarization modes of the resonator. To the best of our knowledge, our study constitutes the first experimental report of breathing instabilities of multi-component optical solitons of driven nonlinear resonators.

Inter-mode soliton linear-wave scattering in a Kerr microresonator.

Soliton microresonator frequency combs (microcombs) have recently emerged as an attractive new type of optical comb source with a wide range applications proposed and demonstrated. To extend the optical bandwidth of these microresonator sources, several previous studies have proposed and studied the injection of an additional optical probe wave into the resonator. In this case, nonlinear scattering between the injected probe and the original soliton enables the formation of new comb frequencies through a phase-matched cascade of four-wave mixing processes. In this work, we expand the relevant analyses to consider soliton-linear wave interactions when the soliton and the probe fields propagate in different mode families. We obtain an expression for the phase-matched idler locations as a function of the dispersion of the resonator and the phase detuning of the injected probe. We confirm our theoretical predictions in experiments performed in a silica waveguide ring microresonator.

Dual-microcomb generation in a synchronously driven waveguide ring resonator.

Microcombs-optical frequency combs generated in coherently driven nonlinear microresonators-have attracted significant attention over the last decade. The ability to generate two such combs in a single resonator device has, in particular, enabled a host of applications from spectroscopy to imaging. Concurrently, novel comb generation techniques such as synchronous pulsed driving have been developed to enhance the efficiency and flexibility of microcomb generation. Here, we report on the first, to the best of our knowledge, experimental demonstration of dual-microcomb generation via synchronous pulsed pumping of a single microresonator. Specifically, we use two electro-optically generated pulse trains derived from a common continuous wave laser to simultaneously drive two orthogonal polarization modes of an integrated silica ring resonator, observing the generation of coherent dissipative Kerr cavity soliton combs on both polarization axes. Thanks to the resonator birefringence, the two soliton combs are associated with different repetition rates, thus realizing a dual-microcomb source. To illustrate the source's application potential, we demonstrate proof-of-concept spectroscopic measurements.

Frequency comb generation in a pulse-pumped normal dispersion Kerr mini-resonator.

Kerr microresonators driven in the normal dispersion regime typically require the presence of localized dispersion perturbations, such as those induced by avoided mode crossings, to initiate the formation of optical frequency combs. In this work, we experimentally demonstrate that this requirement can be lifted by driving the resonator with a pulsed pump source. We also show that controlling the desynchronization between the pump repetition rate and the cavity free-spectral range (FSR) provides a simple mechanism to tune the center frequency of the output comb. Using a fiber mini-resonator with a radius of only 6 cm, we experimentally present spectrally flat combs with a bandwidth of 3 THz whose center frequency can be tuned by more than 2 THz. By driving the cavity at harmonics of its 0.54 GHz FSR, we are able to generate combs with line spacings selectable between 0.54 and 10.8 GHz. The ability to tune both the center frequency and frequency spacing of the output comb highlights the flexibility of this platform. Additionally, we demonstrate that under conditions of large pump-cavity desynchronization, the same cavity also supports a new, to the best of our knowledge, form of Raman-assisted anomalous dispersion cavity soliton.

Dissipative Polarization Domain Walls in a Passive Coherently Driven Kerr Resonator.

Using a passive, coherently driven nonlinear optical fiber ring resonator, we report the experimental realization of dissipative polarization domain walls. The domain walls arise through a symmetry breaking bifurcation and consist of temporally localized structures where the amplitudes of the two polarization modes of the resonator interchange, segregating domains of orthogonal polarization states. We show that dissipative polarization domain walls can persist in the resonator without changing shape. We also demonstrate on-demand excitation, as well as pinning of domain walls at specific positions for arbitrary long times. Our results could prove useful for the analog simulation of ubiquitous domain-wall related phenomena, and pave the way to an all-optical buffer adapted to the transmission of topological bits.

Nonlinear Localization of Dissipative Modulation Instability.

Modulation instability (MI) in the presence of noise typically leads to an irreversible and complete disintegration of a plane wave background. Here we report on experiments performed in a coherently driven nonlinear optical resonator that demonstrate nonlinear localization of dissipative MI: formation of persisting domains of MI-driven spatiotemporal chaos surrounded by a stable quasi-plane-wave background. The persisting localization ensues from a combination of bistability and complex spatiotemporal nonlinear dynamics that together permit a locally induced domain of MI to be pinned by a shallow modulation on the plane wave background. We further show that the localized domains of spatiotemporal chaos can be individually addressed-turned on and off at will-and we explore their transport behavior as the strength of the pinning is controlled. Our results reveal new fundamental dynamics at the interface of front dynamics and MI, and offer a route for tailored patterns of noiselike bursts of light.

Does spaced education improve clinical knowledge among Family Medicine residents? A cluster randomized controlled trial.

Spaced education is a learning strategy to improve knowledge acquisition and retention. To date, no robust evidence exists to support the utility of spaced education in the Family Medicine residency. We aimed to test whether alerts to encourage spaced education can improve clinical knowledge as measured by scores on the Canadian Family Medicine certification examination. METHOD: We conducted a cluster randomized controlled trial to empirically and pragmatically test spaced education using two versions of the Family Medicine Study Guide mobile app. 12 residency training programs in Canada agreed to participate. At six intervention sites, we consented 335 of the 654 (51%) eligible residents. Residents in the intervention group were sent alerts through the app to encourage the answering of questions linked to clinical cases. At six control sites, 299 of 586 (51%) residents consented. Residents in the control group received the same app but with no alerts. Incidence rates of case completion between trial arms were compared using repeated measures analysis. We linked residents in both trial arms to their knowledge scores on the certification examination of the College of Family Physicians of Canada. RESULTS: Over 67 weeks, there was no statistically significant difference in the completion of clinical cases by participants. The difference in mean exam scores and the associated confidence interval did not exceed the pre-defined limit of 4 percentage points. CONCLUSION: Further research is recommended before deploying spaced educational interventions in the Family Medicine residency to improve knowledge.

Polarization modulation instability in a nonlinear fiber Kerr resonator.

We report on the experimental and numerical observation of polarization modulation instability (PMI) in a nonlinear fiber Kerr resonator. This phenomenon is phased-matched through the relative phase detuning between the intracavity fields associated with the two principal polarization modes of the cavity. Our experimental investigation is based on a 12 m long fiber ring resonator in which a polarization controller is inserted to finely control the level of intracavity birefringence. Depending on the amount of birefringence, the temporal patterns generated via PMI are found to be either stationary or to exhibit a period-doubled dynamics. The experimental results are in good agreement with numerical simulations based on an Ikeda map for the two orthogonally polarized modes. This Letter provides new insights into the control of modulation instability in multimode Kerr resonators.

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.

Real-time spectral analysis of ultrafast pulses using a free-space angular chirp-enhanced delay.

Frequency-to-time mapping is a powerful technique for observing ultrafast phenomena and nonrepetitive events in optics. However, many optical sources operate in wavelength regions, or at power levels, that are not compatible with standard frequency-to-time mapping implementations. The recently developed free-space angular chirp-enhanced delay (FACED) removes many of these limitations and offers a linear frequency-to-time mapping in any wavelength region where high-reflectivity mirrors and diffractive optics are available. In this work, we present a detailed formulation of the optical transfer function of a FACED device. Experimentally, we verify the properties of this transfer function and then present simple guidelines to guarantee the correct operation of a FACED frequency-to-time measurement. We also experimentally demonstrate the real-time spectral analysis of femtosecond and picosecond pulses using this system.

Coexistence and Interactions between Nonlinear States with Different Polarizations in a Monochromatically Driven Passive Kerr Resonator.

We report on experimental observations of coexistence and interactions between nonlinear states with different polarizations in a passive Kerr resonator driven at a single carrier frequency. Using a fiber ring resonator with adjustable birefringence, we partially overlap nonlinear resonances of two orthogonal polarization modes, achieving coexistence between different nonlinear states by locking the driving laser frequency at various points within the overlap region. In particular, we observe coexistence between temporal cavity solitons and modulation instability patterns, as well as coexistence between two nonidentical cavity solitons with different polarizations. We also observe interactions between the distinctly polarized cavity solitons, as well as spontaneous excitation and annihilation of solitons by a near-orthogonally polarized unstable modulation instability pattern. By demonstrating that a single frequency driving field can support coexistence between differentially polarized solitons and complex modulation instability patterns, our work sheds light on the rich dissipative dynamics of multimode Kerr resonators. Our findings could also be of relevance to the generation of multiplexed microresonator frequency combs.

Experimental observations of breathing Kerr temporal cavity solitons at large detunings.

It was recently predicted that, due to stimulated Raman scattering, temporal Kerr cavity solitons may exhibit oscillatory instabilities at large cavity detunings [Phys. Rev. Lett.120, 053902 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.053902]. Here, we report experimental observations of this behavior. To access the appropriate oscillatory regime, we construct a macroscopic fiber ring resonator with a high finesse of F≈240. By synchronously driving the resonator with flat-top nanosecond pulses, we can reach very large intracavity power levels, where Raman-induced soliton oscillations can be observed. We also surprisingly find that, in the limit of large cavity driving strengths, new soliton instability regimes that are not accounted for in the known bifurcation structure of driven Kerr resonators can emerge even in the absence of Raman effects. Our experimental results are in good agreement with numerical simulations.

Addressing temporal Kerr cavity solitons with a single pulse of intensity modulation.

We experimentally and numerically study the use of intensity modulation for the controlled addressing of temporal Kerr cavity solitons (CSs). Using a coherently driven fiber ring resonator, we demonstrate that a single temporally broad intensity modulation pulse applied on the cavity driving field permits systematic and efficient writing and erasing of ultrashort cavity solitons. We use numerical simulations based on the mean-field Lugiato-Lefever model to investigate the addressing dynamics, and present a simple physical description of the underlying physics.

Origins of clustered frequency combs in Kerr microresonators.

Recent experiments have demonstrated the generation of widely spaced parametric sidebands that can evolve into "clustered" optical frequency combs in Kerr microresonators. Here we describe the physics that underpins the formation of such clustered comb states. In particular, we show that the phase matching required for the initial sideband generation is such that (at least) one of the sidebands experiences anomalous dispersion, enabling the sideband to drive frequency comb formation via degenerate and non-degenerate four-wave mixing. We validate our proposal through a combination of experimental observations made in a magnesium-fluoride microresonator and corresponding numerical simulations. We also investigate the coherence properties of the resulting clustered frequency combs. Our findings provide valuable insights on the generation and dynamics of widely spaced parametric sidebands and clustered frequency combs in Kerr microresonators.

Stimulated Raman Scattering Imposes Fundamental Limits to the Duration and Bandwidth of Temporal Cavity Solitons.

Temporal cavity solitons (CS) are optical pulses that can persist in passive resonators, and they play a key role in the generation of coherent microresonator frequency combs. In resonators made of amorphous materials, such as fused silica, they can exhibit a spectral redshift due to stimulated Raman scattering. Here we show that this Raman-induced self-frequency-shift imposes a fundamental limit on the duration and bandwidth of temporal CSs. Specifically, we theoretically predict that stimulated Raman scattering introduces a previously unidentified Hopf bifurcation that leads to destabilization of CSs at large pump-cavity detunings, limiting the range of detunings over which they can exist. We have confirmed our theoretical predictions by performing extensive experiments in synchronously driven fiber ring resonators, obtaining results in excellent agreement with numerical simulations. Our results could have significant implications for the future design of Kerr frequency comb systems based on amorphous microresonators.