Sech-squared Pockels solitons in the microresonator parametric down-conversion.

We present an explicit sech-squared-soliton solution associated with the optical Pockels effect, achieved through the generation of the frequency combs via parametric down-conversion in optical microresonators with quadratic nonlinearity. This soliton contrasts the parametric sech-soliton describing the half-harmonic field in the limit of the large index mismatch, and associated with the cascaded-Kerr effect. We predict differences in the spectral profiles and powers of the Pockels and cascaded-Kerr solitons, and report that the pump power threshold of the former agree with the recent experimental observations.

Soliton blockade in bidirectional microresonators.

We report a method to control, disrupt, and restore a regime of unidirectional soliton generation in a bidirectionally pumped ring microresonator. This control, i.e., the soliton blockade, is achieved by tuning the pump frequency of the counterrotating field. The blockade effect is correlated with the emergence of a dark-bright nonlinear resonance of cw states.

Frequency Comb Generation via Cascaded Second-Order Nonlinearities in Microresonators.

Optical frequency combs are revolutionizing modern time and frequency metrology. In the past years, their range of applications has increased substantially, driven by their miniaturization through microresonator-based solutions. The combs in such devices are typically generated using the third-order χ^{(3)} nonlinearity of the resonator material. An alternative approach is making use of second-order χ^{(2)} nonlinearities. While the idea of generating combs this way has been around for almost two decades, so far only few demonstrations are known, based either on bulky bow-tie cavities or on relatively low-Q waveguide resonators. Here, we present the first such comb that is based on a millimeter-sized microresonator made of lithium niobate, that allows for cascaded second-order nonlinearities. This proof-of-concept device comes already with pump powers as low as 2 mW, generating repetition-rate-locked combs around 1064 and 532 nm. From the nonlinear dynamics point of view, the observed combs correspond to Turing roll patterns.

Soliton and quasi-soliton frequency combs due to second harmonic generation in microresonators.

We report how a doublet of the symmetric oppositely tilted bistable resonance peaks in a microring resonator with quadratic nonlinearity set for generation of the second harmonic can transform into a Kerr-like peak on one side of the linear cavity resonance and into a closed loop structure disconnected from the quasi-linear resonance on the other. Both types of the nonlinear resonances are associated with the formation of the soliton combs for dispersion profiles of a typical LiNbO 3 microring. We report bright quasi-solitons propagating on a weakly modulated low intensity background when the group velocity dispersions have the opposite signs for the fundamental and second harmonic. We also show exponentially localized solitons when the dispersion signsare the same. Finally, we demonstrate that the transition between these two types of soliton states is associated with the closure of the forbidden gap in the spectrum of quasi-linear waves.

Spatiotemporal dissipative solitons and vortices in a multi-transverse-mode fiber laser.

We introduce a model for spatiotemporal modelocking in multimode fiber lasers, which is based on the (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation (cGLE) with conservative and dissipative nonlinearities and a 2-dimensional transverse trapping potential. Systematic numerical analysis reveals a variety of stable nonlinear modes, including stable fundamental solitons and breathers, as well as solitary vortices with winding number n = 1, while vortices with n = 2 are unstable, splitting into persistently rotating bound states of two unitary vortices. A characteristic feature of the system is bistability between the fundamental and vortex spatiotemporal solitons.

Two-Dimensional Topological Polariton Laser.

We provide proof-of-principle illustration of lasing in a two-dimensional polariton topological insulator. Topological edge states may arise in a structured polariton microcavity under the combined action of spin-orbit coupling and Zeeman splitting in the magnetic field. Their properties and lifetime are strongly affected by gain. Thus, gain concentrated along the edge of the insulator can counteract intrinsic losses in such a selective way that the topologically protected edge states become amplified, while bulk modes remain damped. When gain is compensated by nonlinear absorption the metastable nonlinear edge states are formed. Taking a triangular structure instead of an infinite edge we observed persistent topological currents accompanied by the time-periodic oscillations of the polariton density.

One- and two-dimensional modes in the complex Ginzburg-Landau equation with a trapping potential.

We propose a new mechanism for the stabilization of confined modes in lasers and semiconductor microcavities holding exciton-polariton condensates, with spatially uniform linear gain, cubic loss, and cubic self-focusing or defocusing nonlinearity. We demonstrated that the commonly known background instability driven by the linear gain can be suppressed by a combination of a harmonic-oscillator trapping potential and effective diffusion. Systematic numerical analysis of one- and two-dimensional (1D and 2D) versions of the model reveals a variety of stable modes, including stationary ones, breathers, and quasi-regular patterns filling the trapping area in the 1D case. In 2D, the analysis produces stationary modes, breathers, axisymmetric and rotating crescent-shaped vortices, stably rotating complexes built of up to 8 individual vortices, and, in addition, patterns featuring vortex turbulence. Existence boundaries for both 1D and 2D stationary modes are found in an exact analytical form, and an analytical approximation is developed for the full stationary states.

Cavity solitons in a microring dimer with gain and loss.

We address a pair of vertically coupled microring resonators with gain and loss pumped by a single-frequency field. Coupling between microrings results in a twofold splitting of the single microring resonance that increases when gain and losses decrease, giving rise to two cavity soliton (CS) families. We show that the existence regions of CSs are tunable and that both CS families can be stable in the presence of an imbalance between gain and losses in the two microrings. These findings enable experimental realization of frequency combs in configurations with active microrings and contribute toward the realization of compact multisoliton comb sources.

Stationary and oscillatory bound states of dissipative solitons created by third-order dispersion.

We consider the model of fiber-laser cavities near the zero-dispersion point, based on the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity and third-order dispersion (TOD) term. It is known that this model supports stable dissipative solitons. We demonstrate that the same model gives rise to several specific families of robust bound states of solitons. There are both stationary and dynamical bound states, with constant or oscillating separation between the bound solitons. Stationary states are multistable, corresponding to different values of the separation. Following the increase of the TOD coefficient, the stationary bound state with the smallest separation gives rise to the oscillatory one through the Hopf bifurcation. Further growth of TOD leads to a bifurcation transforming the oscillatory bound state into a chaotically oscillating one. Families of multistable three- and four-soliton complexes are found too, the ones with the smallest separation between the solitons again ending by the transition to oscillatory states through the Hopf bifurcation.

Clusters of Cavity Solitons Bounded by Conical Radiation.

We introduce a new class of self-sustained states, which may exist as single solitons or form multisoliton clusters, in driven passive cylindrical microresonators. Remarkably, such states are stabilized by the radiation they emit, which strongly breaks spatial symmetry and leads to the appearance of long polychromatic conical tails. The latter induce long-range soliton interactions that make possible the formation of clusters, which can be stable if their spatial arrangement is noncollinear with the soliton rotation direction in the microcavity. The clusters are intrinsically two dimensional and, also, spatially rich. The mechanism behind the formation of the clusters is explained using soliton clustering theory. Our results bring fundamental understanding of a new class of multidimensional cavity solitons and may lead to the development of monolithic multisoliton sources.

Bistable Topological Insulator with Exciton-Polaritons.

The functionality of many nonlinear and quantum optical devices relies on the effect of optical bistability. Using microcavity exciton-polaritons in a honeycomb arrangement of microcavity pillars, we report the resonance response and bistability of topological edge states. A balance between the pump, loss, and nonlinearity ensures a broad range of dynamical stability and controls the distribution of power between counterpropagating states on the opposite edges of the honeycomb lattice stripe. Tuning energy and polarization of the pump photons, while keeping their momentum constant, we demonstrate control of the propagation direction of the dominant edge state. Our results facilitate the development of practical applications of topological photonics.

Temporal dark polariton solitons.

We predict that strong coupling between waveguide photons and excitons of quantum well embedded into waveguide results in the formation of hybrid-dark and antidark light-matter solitons. Such temporal solitons exist due to interplay between repulsive excitonic nonlinearity and giant group-velocity dispersion arising in the vicinity of excitonic resonance. Such fully conservative states do not require external pumping to counteract losses and form continuous families parameterized by the power-dependent phase shift and velocity of their motion. Dark solitons are stable in the considerable part of their existence domain, while antidark solitons are always unstable. Both families exist outside the forbidden frequency gap of the linear system.

Two-dimensional lattice solitons in polariton condensates with spin-orbit coupling.

We study two-dimensional fundamental and vortex solitons in polariton condensates with spin-orbit coupling and Zeeman splitting evolving in square arrays of microcavity pillars. Due to the repulsive excitonic nonlinearity, such states are encountered in finite gaps in the spectrum of the periodic array. Spin-orbit coupling between two polarization components stemming from the TE-TM energy splitting of the cavity photons acting together with Zeeman splitting lifts the degeneracy between vortex solitons with opposite topological charges and makes their density profiles different for a fixed energy. This results in the formation of four distinct families of vortex solitons with topological charges m=±1, all of which can be stable. At the same time, only two stable families of fundamental gap solitons characterized by the domination of different polarization components are encountered.

Vortex algebra by multiply cascaded four-wave mixing of femtosecond optical beams.

Experiments performed with different vortex pump beams show for the first time the algebra of the vortex topological charge cascade, that evolves in the process of nonlinear wave mixing of optical vortex beams in Kerr media due to competition of four-wave mixing with self-and cross-phase modulation. This leads to the coherent generation of complex singular beams within a spectral bandwidth larger than 200nm. Our experimental results are in good agreement with frequency-domain numerical calculations that describe the newly generated spectral satellites.

Two-colour dissipative solitons and breathers in microresonator second-harmonic generation.

Frequency conversion of dissipative solitons associated with the generation of broadband optical frequency combs having a tooth spacing of hundreds of giga-hertz is a topical challenge holding the key to practical applications in precision spectroscopy and data processing. The work in this direction is underpinned by fundamental problems in nonlinear and quantum optics. Here, we present the dissipative two-colour bright-bright and dark-dark solitons in a quasi-phase-matched microresonator pumped for the second-harmonic generation in the near-infrared spectral range. We also found the breather states associated with the pulse front motion and collisions. The soliton regime is found to be typical in slightly phase-mismatched resonators, while the phase-matched ones reveal broader but incoherent spectra and higher-order harmonic generation. Soliton and breather effects reported here exist for the negative tilt of the resonance line, which is possible only via the dominant contribution of second-order nonlinearity.

Stable spatial plasmon solitons in a dielectric-metal-dielectric geometry with gain and loss.

Using a combination of numerical and analytical techniques we demonstrate that a metal stripe surrounded by the active and passive dielectrics supports propagation of stable spatial surface-plasmon solitons. Our analytical methods include the multiple scale reduction of the Maxwell's equations to the coupled Ginzburg-Landau system, and the soliton perturbation theory developed in the framework of the latter.

Supermode dispersion and waveguide-to-slot mode transition in arrays of silicon-on-insulator waveguides.

In this Letter, we report group index measurements of the supermodes of an array of two strongly coupled silicon-on-insulator waveguides. We observe coupling-induced dispersion that is greater than the material and waveguide dispersion of the individual waveguides. We demonstrate that the system transforms from supporting the two supermodes associated with two coupled waveguides to the single mode of a slot waveguide within the investigated spectral range. During the cutoff of the antisymmetric supermode, an anti-crossing between the symmetric TM and antisymmetric TE supermodes has been observed.

Coupling induced anomalous group velocity dispersion in nonlinear arrays of silicon photonic wires.

We demonstrate that the group velocity dispersion (GVD) of the supermodes in a small array of silicon photonic wires can differ dramatically from the single wire GVD. This enables soliton propagation and modulational instability to be seen at wavelengths where single wires have strongly normal GVD.

Spatiotemporal continuum generation in polariton waveguides.

We demonstrate the generation of a spatiotemporal optical continuum in a highly nonlinear exciton-polariton waveguide using extremely low excitation powers (2-ps, 100-W peak power pulses) and a submillimeter device suitable for integrated optics applications. We observe contributions from several mechanisms over a range of powers and demonstrate that the strong light-matter coupling significantly modifies the physics involved in all of them. The experimental data are well understood in combination with theoretical modeling. The results are applicable to a wide range of systems with linear coupling between nonlinear oscillators and particularly to emerging polariton devices that incorporate materials, such as gallium nitride and transition metal dichalcogenide monolayers that exhibit large light-matter coupling at room temperature. These open the door to low-power experimental studies of spatiotemporal nonlinear optics in submillimeter waveguide devices.

Soliton self-frequency shift, non-solitonic radiation and self-induced transparency in air-core fibers.

We report numerical investigation of several effects accompanying propagation of femtosecond pulses in air-core photonic crystal fibers.We have found that the strong Raman response of air does not always result in the large soliton self-frequency shift, because it can simultaneously stimulate energy losses into non-solitonic radiation. We demonstrate that the pronounced spectral tails seen in many recent experiments on the short wavelength side of the soliton spectra can be associated with emission of Airy waves by the decelerating solitons. For pulse durations close to 10fs all radiation effects due to Raman response of air become negligible for a special choice of the peak power leading to propagation in the self-induced transparency regime.