Zhiyong Xu, Yuri S. Kivshar
We study the properties of surface solitons generated at the edge of a semi-infinite photonic lattice in nonlinear quadratic media, namely two-color surface lattice solitons. We analyze the impact of phase mismatch on existence and stability of surface modes, and find novel classes of two-color twisted surface solitons which are stable in a large domain of their existence.
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For waveguides with two separate regions of anomalous dispersion, it is possible to create a quasi-stable two-color solitary wave. In this paper we consider how those waves interact with dispersive radiation, both generation of Cherenkov radiation and scattering of incident dispersive waves. We derive the analytic resonance conditions and verify them through numeric experiments. We also report incident radiation driving the internal oscillations of the soliton during the scattering process in case of an intense incident radiation. We generalize the resonance conditions for the case of an oscil…
Soliton microcombs are helping to advance the miniaturization of a range of comb systems. These combs mode lock through the formation of short temporal pulses in anomalous dispersion resonators. Here, a new microcomb is demonstrated that mode locks through the formation of pulse pairs in normal-dispersion coupled-ring resonators. Unlike conventional microcombs, pulses in this system cannot exist alone, and instead must phase lock in pairs to form a bright soliton comb. Also, the pulses can form at recurring spectral windows and the pulses in each pair feature different optical spectra. This pa…
The conditions under which stable evolution of two nonlinear interacting waves are derived within the context of nematic crystals. Two cases are considered: plane waves and solitons. In the first case, the modulation instability analysis reveals that while the nonlocal term suppresses the growth rates, substantially, the coupled system exhibits significantly higher growth rates than its scalar counterpart. In the soliton case, the necessary conditions are derived that lead the solitons to exhibit stable, undistorted evolution, suppressing any breathing behavior and radiation, leading to solito…
We discuss soliton control in reconfigurable optically-induced photonic lattices created by three interfering beams. We reveal novel dynamical regimes for strongly localized solitons, including binary switching and soliton revivals through resonant wave mixing.
We studied numerically the generation of the two-color flat-top solitonic pulses, platicons, in the microresonator based doubly resonant optical parametric oscillator. We revealed that if the signs of the group velocity dispersion (GVD) coefficients at interacting harmonics are opposite, platicon excitation is possible via pump amplitude modulation or controllable mode interaction approach. Upon pump frequency scan generation of platicons was observed at positive pump frequency detunings for the normal GVD at pump frequency and at negative detunings in the opposite case. Interestingly, we foun…
We address the properties of surface solitons supported by optical lattices imprinted in photorefractive media with asymmetric diffusion nonlinearity. Such solitons exist only in finite gaps of lattice spectrum. In contrast to latticeless geometries, where surface waves exist only when nonlinearity deflects light towards the material surface, the surface lattice solitons exist in settings where diffusion would cause beam bending against the surface.
We address soliton transmission and reflection in nonlinear photonic lattices embedded into uniform Kerr nonlinear media. We show that by introducing disorder into the guiding lattice channels, one may achieve soliton transmission even under conditions where regular lattices reflect the input beam completely. In contrast, in the parameter range where the lattice is almost transparent for incoming solitons, disorder may induce a significant reflection.
We introduce multipole soliton complexes in optical lattices induced by nondiffracting parabolic beams. Despite the symmetry-breaking dictated by the curvature of the lattice channels, we find that complex, asymmetric higher-order states can be stable. The unique topology of parabolic lattices affords new types of soliton motion: single solitons launched into the lattice with nonzero transverse momentum perform periodic oscillations along parabolic paths.
We predict new phenomena, such as soliton steering and soliton fission, in optical lattices that fade away exponentially along the propagation direction. Such lattices, featuring tunable decay rates, arise in photorefractive crystals in the wavelength range 360-400 nm. We show that the predicted phenomena offer different opportunities for soliton control.
We study optical solitons in chirped periodic optical lattices whose amplitude or frequency changes in the transverse direction. We discover that soliton propagation in such lattices can be accompanied by the progressive self-bending of the soliton trajectory, and we show that the soliton bending rate and output position can be controlled by varying the lattice depth, as well as the chirp amplitude and frequency modulation rate. This effect has potential applications for controllable soliton steering and routing.
We address light propagation in Vogel optical lattices and show that such lattices support a variety of stable soliton solutions in both self-focusing and self-defocusing media, whose propagation constants belong to domains resembling gaps in the spectrum of a truly periodic lattice. The azimuthally-rich structure of Vogel lattices allows generation of spiraling soliton motion.
We address soliton formation at the edge of chirped optical lattices imprinted in Kerr-type nonlinear media. We find families of power thresholdless surface waves that do not exist at other types of lattice interfaces. Such solitons form due to combined action of internal reflection at the interface, distributed Bragg-type reflection, and focusing nonlinearity. Remarkably, we discover that surfaces of chirped lattices are soliton attractors: Below an energy threshold, solitons launched well within the lattice self-bend toward the interface, and then stick to it.
We demonstrate theoretically and experimentally that the transverse instability of coherent soliton stripes can be greatly suppressed or totally eliminated when the soliton stripes propagate in a one-dimensional photonic lattice under self-defocusing nonlinearity.
We consider soliton dynamics and stability in a nonlinear lattice formed by alternating domains with focusing cubic and saturable nonlinearities. We find that in such lattices solitons centered on cubic domains may be stabilized even in two-dimensional geometries, in spite of their intrinsic catastrophic instability in the absence of the lattice. Solitons centered on saturable domains are always unstable.
We consider parametric amplification of two-dimensional spatial soliton swinging in longitudinally modulated harmonic and Bessel lattices in Kerr-type saturable medium. We show that soliton center oscillations along different axes in two-dimensional lattices are coupled, which give rise to a number of interesting propagation scenarios including periodic damping and excitation of soliton oscillations along perpendicular axes, selective amplification of soliton swinging along one of transverse axes and enhancement of soliton spiraling.
We demonstrate second-band bright vortex-array solitons in photonic lattices. This constitutes the first experimental observation of higher-band solitons in any 2D periodic system. These solitons possess complex intensity and phase structures, yet they can be excited by a simple highly-localized vortex-ring beam. Finally, we show that the linear diffraction of such beams exhibits preferential transport along the lattice axes.
We address surface solitons supported by the interface of optical lattices imprinted in saturable media with surface-localized gain. The nonlinearity saturation puts restrictions on the maximal energy flow carried by surface solitons. As a consequence, the presence of thin amplifying layer near the surface results in the controllable emission of solitons towards the lattice at angles depending on the amplification rate and on lattice depth.
We introduce soliton percolation phenomena in the nonlinear transport of light packets in suitable optical lattices with random properties. Specifically, we address lattices with a gradient of the refractive index in the transverse plane, featuring stochastic phase or amplitude fluctuations, and we discover the existence of a disorder-induced transition between soliton-insu-lator and soliton-conductor regimes. The soliton current is found to reach its maximal value at intermediate disorder levels and to drastically decrease in both, almost regular and strongly disordered lattices.
We address basic properties and stability of two-dimensional solitons in photonic lattices induced by the nondiffracting Mathieu beams. Such lattices allow for smooth topological transformation of radially symmetric Bessel lattices into quasi-one-dimensional periodic ones. The transformation of lattice topology drastically affects properties of ground-state and dipole-mode solitons, including their shape, stability and transverse mobility.
We study basic properties of quiescent and rotating multipole-mode solitons supported by axially symmetric Bessel lattices in a medium with defocusing cubic nonlinearity. The solitons can be found in different rings of the lattice and are stable when the propagation constant exceeds the critical value, provided that the lattice is deep enough. In a high-power limit the multipole-mode solitons feature a multi-ring structure.
Stability of solitons in parity-time (PT)-symmetric periodic potentials (optical lattices) is analyzed in both one- and two-dimensional systems. First we show analytically that when the strength of the gain-loss component in the PT lattice rises above a certain threshold (phase-transition point), an infinite number of linear Bloch bands turn complex simultaneously. Second, we show that while stable families of solitons can exist in PT lattices, increasing the gain-loss component has an overall destabilizing effect on soliton propagation. Specifically, when the gain-loss component increases, th…
Fundamental and vortex solitons in a two-dimensional optically induced waveguide array are reported. In the strong localization regime, the fundamental soliton is largely confined to one lattice site, while the vortex state comprises of four fundamental modes superimposed in a square configuration with a phase structure that is topologically equivalent to the conventional vortex. However, in the weak localization regime, both the fundamental and vortex solitons spread over many lattice sites. We further show that fundamental and vortex solitons are stable against small perturbations in the str…
We report on the phenomenon of controllable soliton dragging by dynamical optical lattices induced by three imbalanced interfering plane waves. Because of such an imbalance, the transverse momentum of the lattice does not vanish, and thus the dynamical lattice can cause soliton dragging. The dragging rate is shown to depend on the amplitude and on the angle of incidence of the third plane wave making the optical lattice.
We address the existence and stability of two-dimensional solitons in optical or matter-wave media, which are supported by purely nonlinear lattices in the form of a periodic array of cylinders with self-focusing nonlinearity, embedded into a linear material. We show that such lattices can stabilize two-dimensional solitons against collapse. We also found that stable multipoles and vortex solitons are also supported by the nonlinear lattices, provided that the nonlinearity exhibits saturation.
We reveal that lattice interfaces imprinted in nonlocal nonlinear media support surface solitons that do not exist in other similar settings, including interfaces of local and nonlocal uniform materials. We show the impact of nonlocality on the domains of existence and stability of the surface solitons, focusing on new types of dipole solitons residing partially inside the optical lattice. We find that such solitons feature strongly asymmetric shapes and that they are stable in large parts of their existence domain.
We address the properties and dynamical stability of one-dimensional vector lattice solitons in Kerr-type cubic medium with harmonic transverse modulation of refractive index. We discovered that unstable families of scalar lattice solitons can be stabilized via the cross-phase modulation (XPM) in the vector case. It was found that multi-humped vector solitons that are unstable in uniform media where XPM strength is higher than that of self-phase modulation, can also be stabilized by the lattice.
We studied numerically the generation of the coherent frequency combs at second harmonic generation in $χ^{(2)}$ microresonators via conventional frequency scan method. It was demonstrated for the first time that under particular conditions it is possible to generate two-color flat-top solitonic pulses, platicons, using pump amplitude modulation or controllable mode interaction approach, if the signs of the group velocity coefficients at pump frequency and its second harmonic are opposite but absolute values of these coefficients are rather close. It was revealed that platicons may be observed…
We report the existence of transversely stable soliton trains in optics. These stable soliton trains are found in two-dimensional square photonic lattices when they bifurcate from X-symmetry points with saddle-shaped diffraction inside the first Bloch band and their amplitudes are above a certain threshold. We also show that soliton trains with low amplitudes or bifurcated from edges of the first Bloch band (Gamma and M points) still suffer transverse instability. These results are obtained in the continuous lattice model and further corroborated by the discrete model.
We address the formation and propagation of vector solitons in optical lattices in the presence of anisotropy-induced walk-off between ordinary and extraordinary polarized field components. Stable vector solitons trapped by the lattice form above a threshold power, while decreasing the lattice depth below a critical value results in the abrupt release of the caged solitons, that then move across the lattice and may get trapped in a desired lattice channel.
We consider the propagation of solitons in media with an imprinted transverse periodic or parabolic refractive index modulation when the modulation depth slightly fluctuates along the propagation direction. We find that, under suitable spectral resonance conditions, small transverse soliton oscillations may get parametrically amplified.
We put forward new properties of lattice solitons in materials and geometries where both, the linear refractive index and the nonlinearity are spatially modulated. We show that the interplay between linear and out-of-phase nonlinear refractive index modulations results in new soliton properties, including modifications of the soliton stability and transverse mobility, as well as shape transformations that may be controlled, e.g., by varying the light intensity.
We have investigated mixed-gap vector solitons involving incoherently coupled fundamental and dipole components in a parity-time (PT) symmetric lattice with saturable nonlinearity. For the focusing case, vector solitons emerge from the semi-infinite and the first finite gaps, while for the defocusing case, vector solitons emerge from the first finite and the second finite gaps. For both cases, we find that stronger saturable nonlinearity is relative to sharper increase/decrease of soliton power with propagation constant and to narrower existence domain of vector solitons. This finding is helpf…
We predict multiband vector Plasmonic Lattice Solitons (PLSs) in metal-dielectric waveguide arrays, in both focusing and defocusing nonlinearities. Such vector solitons consist of two components originating from different transmission bands. By simulating the full nonlinear Maxwell equations (MEs), we demonstrate the diffractionless propagation of vector PLSs and their discrete diffraction when only one component is present. Their subwavelength size characteristics and the influences of metallic losses are also studied.
We present a theoretical study of plasmonic lattice solitons (PLSs) formed in two-dimensional (2D) arrays of metallic nanowires embedded into a nonlinear medium with Kerr nonlinearity. We analyze two classes of 2D PLSs families, namely, fundamental and vortical PLSs in both focusing and defocusing media. Their existence, stability, and subwavelength spatial confinement are studied in detail.
We demonstrate numerically that partially incoherent light can be trapped in the spectral band gaps of a photonic lattice, creating partially incoherent multi-component spatial optical solitons in a self-defocusing nonlinear periodic medium. We find numerically such incoherent multi-gap optical solitons and discuss how to generate them in experiment by interfering incoherent light beams at the input of a nonlinear periodic medium.
The existence and stability of defect solitons in parity-time (PT) symmetric optical lattices with nonlocal nonlinearity are reported. It is found that nonlocality can expand the stability region of defect solitons. For positive or zero defects, fundamental and dipole solitons can exist stably in the semi-infinite gap and the first gap, respectively. For negative defects, fundamental solitons can be stable in both the semi-infinite gap and the first gap, whereas dipole solitons are unstable in the first gap. There exist a maximum degree of nonlocal nonlinearity, above which the fundamental sol…
We report on the experimental observation of two-dimensional solitons at the interface between square and hexagonal waveguide arrays. In addition to the different symmetry of the lattices, the influence of a varying refractive index modulation depth is investigated. Such variation strongly affects the properties of surface solitons residing at different sides of the interface.
We address spectral tunneling of walking spatial solitons in photorefractive media with nonlocal diffusion of the nonlinear response and an imprinted shallow optical lattice. In contrast to materials with local nonlinearities, where solitons travelling across the lattice close to the Bragg angle suffer large radiative losses, in photorefractive media with diffusion nonlinearity resulting in self-bending solitons survive when their propagation angle approaches and even exceeds the Bragg angle. In the spatial frequency domain this effect can be considered as tunneling through the band of spatial…
We experimentally demonstrate the formation and stable propagation of various types of discrete temporal solitons in an optical fiber system. Pulses interacting with a time-periodic potential and defocusing nonlinearity are shown to form gap solitons and nonlinear truncated Bloch waves. Multi-pulse solitons with defects, as well as novel structures composed of a strong soliton riding on a weaker truncated nonlinear Bloch wave are shown to propagate over up to eleven coupling lengths. The nonlinear dynamics of all pulse structures is monitored over the full propagation distance which provides d…
Stability of off-site vortex solitons in a photorefractive optical lattice is analyzed. It is shown that such solitons are linearly unstable in both the high and low intensity limits. In the high-intensity limit, the vortex looks like a familiar ring vortex, and it suffers oscillatory instabilities. In the low-intensity limit, the vortex suffers both oscillatory and Vakhitov-Kolokolov instabilities. However, in the moderate-intensity regime, the vortex becomes stable if the lattice intensity or the applied voltage is above a certain threshold value. Stability regions of vortices are also deter…
We address vortex solitons supported by optical lattices featuring modulation of both the linear and nonlinear refractive indices. We find that when the modulation is out-of-phase the competition between both effects results in remarkable shape transformations of the solitons which profoundly affect their properties and stability. Nonlinear refractive index modulation is found to impose restrictions on the maximal power of off-site solitons, which are shown to be stable only below a maximum nonlinearity modulation depth.
We consider two-component solitons in a medium with a periodic modulation of the nonlinear coefficient. The modulation enables the existence of complex multihump vector states. In particular, vector solitons composed of dipole and fundamental, or dipole and even double-hump components exist and may be stable. Families of unstable scalar solitons can be stabilized in the vectorial form, due to the coupling to a stable second component.
The stabilization of one-dimensional solitons by a nonlinear lattice against the critical collapse in the focusing quintic medium is a challenging issue. We demonstrate that this purpose can be achieved by combining a nonlinearlatticeandsaturationofthequinticnonlinearity. Thesystemsupportsthreespeciesofsolitons, namely, fundamental (even-parity) ones and dipole (odd-parity) modes of on- and off-site-centered types. Very narrow fundamental solitons are found in an approximate analytical form, and systematic results for very broad unstable and moderately broad partly stable solitons, including t…
We study linear transmission and nonlinear soliton transport through quasi-periodic structures, which profiles are described by multiple modulation frequencies. We show that resonant scattering at mixed-frequency resonances limits transmission efficiency of localized wave packets, leading to radiation and possible trapping of solitons. We obtain an explicit analytical expression for optimal quasi-periodic lattice profiles, where additional aperiodic modulations suppress mixed-frequency resonances, resulting in dramatic enhancement of soliton mobility. Our results can be applied to the design o…
We suggest a novel concept in the soliton switching based on the Bloch-wave filtering in periodic photonic structures. Taking a binary waveguide array as an example, we demonstrate that spatial solitons that belong to different spectral band gaps can be selectively reflected from or transmitted through an engineered defect, which acts as a low or high-pass filter for Bloch waves.
Vortex solitons in topological disclination lattices
本文报道了在实现高阶拓扑绝缘体的向错晶格核心处存在无阈值涡旋孤子，揭示了非线性与高阶拓扑的相互作用，该孤子具有强场局域化和增强稳定性，为孤子应用开辟了新前景。
We address the properties of fully three-dimensional solitons in complex parity-time (PT)-symmetric periodic lattices with focusing Kerr nonlinearity, and uncover that such lattices can stabilize both, fundamental and vortex-carrying soliton states. The imaginary part of the lattice induces internal currents in the solitons that strongly affect their domains of existence and stability. The domain of stability for fundamental solitons can extend nearly up to the PT-symmetry breaking point, where the linear lattice spectrum becomes complex. Vortex solitons feature spatially asymmetric profiles i…
I study vector solitons involving two incoherently-coupled field components in periodic PT-symmetric optical lattices. The specific symmetry of the lattice imposes the restrictions on the symmetry of available vector soliton states. While all configurations with asymmetric intensity distributions are prohibited, such lattices support multi-hump solitons with equal number of "in-phase" or "out-of-phase" spots in two components, residing on neighboring lattice channels. In the focusing medium only the solitons containing out-of-phase spots in at least one component can be stable, while in the de…
We propose and theoretically investigate a dispersion-engineered Si3N4 microring resonator, based on a cross-section containing a partially-etched trench, that supports phase-locked, two-color soliton microcomb states. These soliton states consist of a single circulating intracavity pulse with a modulated envelope that sits on a continuous wave background. Such temporal waveforms produce a frequency comb whose spectrum is spread over two widely-spaced spectral windows, each exhibiting a squared hyperbolic secant envelope, with the two windows phase-locked to each other via Cherenkov radiation.…
Dissipative Kerr solitons (DKSs) in optical microresonators have been intensely studied from the perspective of both fundamental nonlinear physics and portable and low power technological applications in communications, sensing, and metrology. In parallel, synthetic dimensions offer the promise of studying physical phenomena with a dimensionality beyond that imposed by geometry, and have been implemented in optics. The interplay of DKS physics with synthetic dimensions promises to unveil numerous new physical and technological insights, yet many fundamental challenges remain. In particular, DK…
We reveal the existence of asymmetric vortex solitons in ideally symmetric periodic lattices, and show how such nonlinear localized structures describing elementary circular flows can be analyzed systematically using the energy-balance relations. We present the examples of rhomboid, rectangular, and triangular vortex solitons on a square lattice, and also describe novel coherent states where the populations of clockwise and anti-clockwise vortex modes change periodically due to a nonlinearity-induced momentum exchange through the lattice. Asymmetric vortex solitons are expected to exist in dif…
We address the impact of asymmetric nonlocal diffusion nonlinearity on the properties of gap solitons supported by photorefractive crystal with an imprinted optical lattice. We reveal how the asymmetric nonlocal response alters the domains of existence and the stability of solitons originating from different gaps. We find that in such media gap solitons cease to exist above a threshold of the nonlocality degree. We discuss how the interplay between nonlocality and lattice strength modifies the gap soliton mobility.
We introduce solitons supported by Bessel photonic lattices in cubic nonlinear media. We show that the cylindrical geometry of the lattice, with several concentric rings, affords unique soliton properties and dynamics. In particular, besides the lowest-order solitons trapped in the center of the lattice, we find soliton families trapped at different lattice rings. Such solitons can be set into controlled rotation inside each ring, thus featuring novel types of in-ring and inter-ring soliton interactions.
We address the transverse mobility of spatial solitons in competing parity-time-symmetric linear and nonlinear lattices. The competition between out-of-phase linear and nonlinear lattices results in a drastic mobility enhancement within a range of soliton energies. We show that within such range, the addition of even a small imaginary part in the linear potential makes soliton mobility strongly asymmetric. The minimal phase tilt required for setting solitons into radiationless motion across the lattice in the direction opposite to that of the internal current drops to nearly zero, while the mi…
We introduce novel optical solitons that consist of a periodic and a spatially localized components coupled nonlinearly via cross-phase modulation. The spatially localized optical field can be treated as a gap soliton supported by the optically-induced nonlinear grating. We find different types of these band-gap composite solitons and demonstrate their dynamical stability.
Dark solitons in nonlinear Su-Schrieffer-Heeger lattices
研究非线性苏-施里弗-海格尔晶格中的暗溶iton特性，探讨其在不同参数下的稳定性及拓扑晶格中的应用潜力。
We report on phenomenon of Anderson-type localization of walking solitons in optical lattices with random frequency modulation, manifested as dramatic enhancement of soliton trapping probability on lattice inhomogeneities with growth of the frequency fluctuation level. The localization process is strongly sensitive to the lattice depth since in shallow lattices walking solitons experience random refraction and/or multiple scattering in contrast to relatively deep lattices, where solitons are typically immobilized in the vicinity of local minimums on modulation frequency.
We report on the frst experimental observation of discrete vortex solitons in two-dimensional optically-induced photonic lattices. We demonstrate strong stabilization of an optical vortex by the lattice in a self-focusing nonlinear medium and study the generation of the discrete vortices from a broad class of singular beams.
We study the soliton mobility in nonlocal nonlinear media with an imprinted fading optical lattice. The results show that the transverse mobility of solitons varies with the lattice decay rate and the nonlocality degree, which provides an opportunity for all-optical control of light.
We address soliton spiraling in optical lattices induced by multiple coherent Bessel beams and show that the dynamical nature of such lattices make them able to drag different soliton structures, setting them into rotation. The rotation rate can be controlled by varying the topological charges of lattice-inducing Bessel beams.
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