Mid-infrared frequency combs and staggered spectral patterns in χ(2) microresonators.

The potential of frequency comb spectroscopy has aroused great interest in generating mid-infrared frequency combs in the integrated photonic setting. However, despite remarkable progress in microresonators and quantum cascade lasers, the availability of suitable mid-IR comb sources remains scarce. Here, we generate mid-IR microcombs relying on cascaded three-wave-mixing for the first time. By pumping a CdSiP2 microresonator at 1.55 µm wavelength with a low power continuous wave laser, we generate χ(2) frequency combs at 3.1 µm wavelength, with a span of about 30 nm. We observe ordinary combs states with a line spacing of the free spectral range of the resonator, and combs where the sideband numbers around the pump and half-harmonic alternate, forming staggered patterns of spectral lines. Our scheme for mid-IR microcomb generation is compatible with integrated telecom lasers. Therefore, it has the potential to be used as a simple and fully integrated mid-IR comb source, relying on only one single material.

Frequency combs with multiple offsets in THz-rate microresonators.

Octave-wide frequency combs in microresonators are essential for self-referencing. However, it is difficult for the small-size and high-repetition-rate microresonators to achieve perfect soliton modelocking over the broad frequency range due to the detrimental impact of dispersion. Here we examine the stability of the soliton states consisting of one hundred modes in silicon-nitride microresonators with the one-THz free spectral range. We report the coexistence of fast and slow solitons in a narrow detuning range, which is surrounded on either side by the breather states. We decompose the breather combs into a sequence of sub-combs with different carrier-envelope offset frequencies. The large detuning breathers have a high frequency of oscillations associated with the perturbation extending across the whole microresonator. The small detuning breathers create oscillations localised on the soliton core and can undergo the period-doubling bifurcation, which triggers a sequence of intense sub-combs.

Topological solitons in arrays of modelocked lasers.

We report spatiotemporal topological solitons in an array of modelocked lasers. In its conservative limit, our model reduces to the famous Su-Schrieffer-Heeger system possessing topological states inside the gap of its linear spectrum. We report one-dimensional spatial and two-dimensional spatiotemporal topological solitons, i.e., bullets, with the operational frequencies locked to the values inside the topological gap.

Frequency combs in a microring optical parametric oscillator.

We report the soliton frequency comb generation in microring optical parametric oscillators operating in the downconversion regime and with the simultaneous presence of the χ(2) and Kerr nonlinearities. The combs are studied considering a typical geometry of a bulk LiNbO3 toroidal resonator with the normal group velocity dispersion spanning an interval between the pump and the downconverted signal. We have identified critical power signaling a transition between the relatively low pump power predominantly χ(2) combs and the high pump power ones shaped by the competition between the χ(2) and Kerr nonlinearities.

Frequency comb generation in a resonantly pumped exciton-polariton microring resonator.

We develop a scheme for generation of a regular sequence of narrow spectral lines (optical frequency comb) in semiconductor micro-ring resonators operating in the strong-coupling regime. A strong optical nonlinearity of exciton-polaritons, forming as mixed states between the microcavity photons and quantum-well excitons, allows for a low-threshold operation. This work demonstrates visibility of using the exciton-polaritons for the purposes of generation of GHz combs and trains of picoseconds pulses for future all-polariton information processing schemes.

Collision between a dark soliton and a linear wave in an optical fiber.

We report an experimental observation of the collision between a linear wave propagating in the anomalous dispersion region of an optical fiber and a dark soliton located in the normal dispersion region. This interaction results in the emission of a new frequency component whose wavelength can be predicted using phase-matching arguments. The measured efficiency of this process shows a strong dependency with the soliton grayness and the linear wave wavelength, and is in a good agreement with theory and numerical simulations.

Two-dimensional nonlinear modes and frequency combs in bottle microresonators.

We theoretically investigate frequency comb generation in a bottle microresonator accounting for the azimuthal and axial degrees of freedom. We first identify a discrete set of the axial nonlinear modes of a bottle microresonator that appear as tilted resonances bifurcating from the spectrum of linear axial modes. We then study azimuthal modulational instability of these modes and show that families of two-dimensional (2D) soliton states localized both azimuthally and axially bifurcate from them at critical pump frequencies. Depending on detuning, 2D solitons can be stable, form persistent breathers or chaotic spatio-temporal patterns, or exhibit collapse-like evolution.

Grayness-dependent emission of dispersive waves from dark solitons in optical fibers.

We report the experimental observation of dispersive wave emission from gray solitons propagating in the normal dispersion region of an optical fiber. Besides observing for the first time, to the best of our knowledge, the emission of a dispersive wave from an isolated dark soliton, we show that the dispersive wave frequency and amplitude strongly depend on soliton grayness. This process can be explained by the higher-order dispersion contribution into the phase-matching condition and the grayness of the soliton. Numerical simulations and theoretical predictions are in good agreement with the experiments.

Transition from Propagating Polariton Solitons to a Standing Wave Condensate Induced by Interactions.

We explore phase transitions of polariton wave packets, first, to a soliton and then to a standing wave polariton condensate in a multimode microwire system, mediated by nonlinear polariton interactions. At low excitation density, we observe ballistic propagation of the multimode polariton wave packets arising from the interference between different transverse modes. With increasing excitation density, the wave packets transform into single-mode bright solitons due to effects of both intermodal and intramodal polariton-polariton scattering. Further increase of the excitation density increases thermalization speed, leading to relaxation of the polariton density from a solitonic spectrum distribution in momentum space down to low momenta, with the resultant formation of a nonequilibrium condensate manifested by a standing wave pattern across the whole sample.

Multiple nonlinear resonances and frequency combs in bottle microresonators.

We introduce the generalized Lugiato-Lefever equation describing nonlinear effects in the bottle microresonators. We demonstrate that the nonlinear modes of these resonators can form multiple coexisting and overlapping nonlinear resonances and that their instabilities lead to the generation of the low repetition rate frequency combs.

Self-locking of the frequency comb repetition rate in microring resonators with higher order dispersions.

We predict that the free spectral range (FSR) of the soliton combs in microring resonators can self-lock through the back-action of the Cherenkov dispersive radiation on its parent soliton under the conditions typical for recent experiments on the generation of the octave wide combs. The comb FSR in the self-locked state remains quasi-constant over sufficiently broad intervals of the pump frequencies, implying that this effect can be potentially used as the comb self-stabilisation technique. The intervals of self-locking form a sequence of the discrete plateaus reminiscent to other staircase-like structures known in the oscillator synchronisation research. We derive a version of the Adler equation for the self-locking regime and confirm that it is favoured by the strong overlap between the soliton and the dispersive radiation parts of the comb signal.

Spectral wings of the fiber supercontinuum and the dark-bright soliton interaction.

We present experimental and numerical data on the supercontinuum generation in an optical fiber pumped in the normal dispersion range where the seeded dark and the spontaneously generated bright solitons contribute to the spectral broadening. We report the dispersive radiation arising from the interaction of the bright and dark solitons. This radiation consists of the two weak dispersing pulses that continuously shift their frequencies and shape the short and long wavelength wings of the supercontinuum spectrum.

Multistability and coexisting soliton combs in ring resonators: the Lugiato-Lefever approach.

We are reporting that the Lugiato-Lefever equation describing the frequency comb generation in ring resonators with the localized pump and loss terms also describes the simultaneous nonlinear resonances leading to the multistability of nonlinear modes and coexisting solitons that are associated with the spectrally distinct frequency combs.

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.

Dark Solitons in High Velocity Waveguide Polariton Fluids.

We study exciton-polariton nonlinear optical fluids in the high momentum waveguide regime for the first time. We demonstrate the formation of dark solitons with the expected dependence of width on fluid density for both main classes of soliton-forming fluid defects. The results are well described by numerical modeling of the fluid propagation. We deduce a continuous wave nonlinearity more than ten times that on picosecond time scales, arising due to interaction with the exciton reservoir.

Emission of dispersive waves from a train of dark solitons in optical fibers.

We report the experimental observation of multiple dispersive waves (DWs) emitted in the anomalous dispersion region of an optical fiber from a train of dark solitons. Each DW can be associated to one dark soliton of the train, using phase-matching arguments involving higher-order dispersion and soliton velocity. For a large number of dark solitons (>10), we observe the formation of a continuum associated with the efficient emission of DWs.

Multi-stability and polariton solitons in microcavity wires.

Nonlinear polaritons in microcavity wires are demonstrated to exhibit multi-stable behavior and rich dynamics, including filamentation and soliton formation. We find that the multi-stability originates from co-existence of different transverse cavity modes. Modulational stability and conditions for multi-mode polariton solitons are studied. Soliton propagation in tilted, relative to the pump momentum, microcavity wires is demonstrated, and a critical tilt angle for the soliton propagation is found.

Spatial Patterns of Dissipative Polariton Solitons in Semiconductor Microcavities.

We report propagating bound microcavity polariton soliton arrays consisting of multipeak structures either along (x) or perpendicular (y) to the direction of propagation. Soliton arrays of up to five solitons are observed, with the number of solitons controlled by the size and power of the triggering laser pulse. The breakup along the x direction occurs when the effective area of the trigger pulse exceeds the characteristic soliton size determined by polariton-polariton interactions. Narrowing of soliton emission in energy-momentum space indicates phase locking between adjacent solitons, consistent with numerical modeling which predicts stable multihump soliton solutions. In the y direction, the breakup originates from inhomogeneity across the wave front in the transverse direction which develops into a stable array only in the solitonic regime via phase-dependent interactions of propagating fronts.

Soliton families and resonant radiation in a micro-ring resonator near zero group-velocity dispersion.

We report theoretical and numerical study of the dynamical and spectral properties of the conservative and dissipative solitons in micro-ring resonators pumped in a proximity of the zero of the group velocity dispersion. We discuss frequency and velocity locking of the conservative solitons, when dissipation is accounted for. We present theory of the dispersive radiation emitted by such solitons, report their Hopf instability and radiation enhancement by multiple solitons.

Tuning resonant interaction of orthogonally polarized solitons and dispersive waves with the soliton power.

We demonstrate that the relatively small power induced changes in the soliton wavenumber comparable with splitting of the effective indexes of the orthogonally polarized waveguide modes result in significant changes of the efficiency of the interaction between solitons and dispersive waves and can be used to control energy transfer between the soliton and newly generated waves and to delay or accelerate solitons.