We study the amplitude dynamics of two-dimensional (2D) solitons in a fast collision described by the coupled nonlinear Schrödinger equations with a saturable nonlinearity and weak nonlinear loss. We extend the perturbative technique for calculating the collision-induced dynamics of two one-dimensional (1D) solitons to derive the theoretical expression for the collision-induced amplitude dynamics in a fast collision of two 2D solitons. Our perturbative approach is based on two major steps. The first step is the standard adiabatic perturbation for the calculations on the energy balance of perturbed solitons and the second step, which is the crucial one, is for the analysis of the collision-induced change in the envelope of the perturbed 2D soliton. Furthermore, we also present the dependence of the collision-induced amplitude shift on the angle of the two 2D colliding-solitons. In addition, we show that the current perturbative technique can be simply applied to study the collision-induced amplitude shift in a fast collision of two perturbed 1D solitons. Our analytic calculations are confirmed by numerical simulations with the corresponding coupled nonlinear Schrödinger equations in the presence of the cubic loss and in the presence of the quintic loss.
We study systematically the scattering of solitons on localized impurities in the discrete nonlinear Schrödinger (DNLS) equation with a saturable nonlinearity. We show that, apart from the generic scenario of the outcome of the scattering process, namely the emergence of a reflected and a transmitted soliton, other effects can occur. In particular, it is found that, in the case of an attractive impurity, a soliton trapped at the impurity can coexist with the reflected and transmitted ones. This effect, which resembles the behaviour of a quantum particle interacting with a narrow impurity, has …
We investigate the spatiotemporal dynamics of cavity solitons in a broad area vertical-cavity surface-emitting laser with saturable absorption subjected to time-delayed optical feedback. Using a combination of analytical, numerical and path continuation methods we analyze the bifurcation structure of stationary and moving cavity solitons and identify two different types of traveling localized solutions, corresponding to slow and fast motion. We show that the delay impacts both stationary and moving solutions either causing drifting and wiggling dynamics of initially stationary cavity solitons …
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 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 investigate the switching dynamics in a $\mathcal{PT}$-symmetric fiber coupler composed of a saturable nonlinear material as the core. In such a saturable nonlinear medium, bistable solitons may evolve due to the balance between dispersion and saturable nonlinearity, which we extend in the context of the $\mathcal{PT}$-symmetric coupler. Our investigations of power-controlled and phase-sensitive switching show richer soliton switching dynamics than the currently existing conventional counterparts, which may lead to ultrafast and efficient all-optical switching dynamics at very low power owi…
We theoretically study the properties of one-dimensional nonlinear saturable photonic lattices exhibiting multiple mobility windows for stationary solutions. The effective energy barrier decreases to a minimum in those power regions where a new intermediate stationary solution appears. As an application, we investigate the dynamics of high-power gaussian-like beams finding several regions where the light transport is enhanced.
We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of the saturable nonlinearity in such PT -symmetric waveguides. The dependence of the propagation constant on the soliton's power is presented for different strengths of the nonlinearity saturation, S. …
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…
In last 50 years, a significant progress was noticed in medicine, communications and entertainment. Such advanced development of these fields was directly related to ability of controlling light. Photonics is exactly about this ability. At the present time, photonics is walking together with a fundamental physical concept, optical soliton. Optical solitons are shape-preserving laser beams. They are found potentially useful in data transmission, which is very significant nowadays. Hence, research in the field of optical solitons is still a vital issue. When optical soliton is perturbed in a spe…
We have introduced a class of spiraling elliptic breathers in saturable nonlinear media with linear anisotropy. Two kinds of evolution behaviors of the breathers, rotating and pendulum-like librating, are both predicted by the variational approach, and confirmed by the numerical simulation.The spiraling elliptic breathers can rotate even though they have no initial orbital angular momentum (OAM). Due to the linear anisotropy of the media, the OAM is no longer conserved. Therefore, the angular velocity is found to be not a constant but a periodic function of the propagation distance. When the l…
We investigate numerically interactions between two in-phase or out-of-phase Airy beams and nonlinear accelerating beams in Kerr and saturable nonlinear media in one transverse dimension. We discuss different cases in which the beams with different intensities are launched into the medium, but accelerate in opposite directions. Since both the Airy beams and nonlinear accelerating beams possess infinite oscillating tails, we discuss interactions between truncated beams, with finite energies. During interactions we see solitons and soliton pairs generated that are not accelerating. In general, t…
We theoretically present a design of self-starting operation of microcombs based on laser-cavity solitons in a system composed of a micro-resonator nested in and coupled to an amplifying laser cavity. We demonstrate that it is possible to engineer the modulational-instability gain of the system's zero state to allow the start-up with a well-defined number of robust solitons. The approach can be implemented by using the system parameters, such as the cavity length mismatch and the gain shape, to control the number and repetition rate of the generated solitons. Because the setting does not requi…
In the present work, we consider the dynamics of dark solitons as one mode of a defocusing photorefractive lattice coupled with bright solitons as a second mode of the lattice. Our investigation is motivated by an experiment which illustrates that such coupled states can exist with both components in the first gap of the linear band spectrum. This finding is further extended by the examination of different possibilities from a theoretical perspective, such as symbiotic ones where the bright component is supported by states of the dark component in the first or second gap, or non-symbiotic ones…
We report a novel spontaneous symmetry breaking phenomenon and ghost states existed in the framework of the fractional nonlinear Schrödinger (FNLS) equation with focusing saturable nonlinearity and PT-symmetric potential. The continuous asymmetric soliton branch bifurcates from the fundamental symmetric one as the power exceeds some critical value. Intriguingly, the symmetry of fundamental solitons is broken into two branches of asymmetry solitons (alias ghost states) with complex conjugate propagation constants, which is solely in fractional media. Besides, the dipole (antisymmetry) and tripo…
In the present work, we examine "binary" waveguide arrays, where the coupling between adjacent sites alternates between two distinct values $C_1$ and $C_2$ and a saturable nonlinearity is present on each site. Motivated by experimental investigations of this type of system in fabricated LiNbO$_3$ arrays, we proceed to analyze the nonlinear wave excitations arising in the self-defocusing nonlinear regime, examining, in particular, dark solitons and bubbles. We find that such solutions may, in fact, possess a reasonably wide, experimentally relevant parametric interval of stability, while they m…
We address the problem of directional mobility of discrete solitons in two-dimensional rectangular lattices, in the framework of a discrete nonlinear Schrödinger model with saturable on-site nonlinearity. A numerical constrained Newton-Raphson method is used to calculate two-dimensional Peierls-Nabarro energy surfaces, which describe a pseudopotential landscape for the slow mobility of coherent localized excitations, corresponding to continuous phase-space trajectories passing close to stationary modes. Investigating the two-parameter space of the model through independent variations of the no…
For a number of nonlocal nonlinear equations such as nonlocal, nonlinear Schrödinger equation (NLSE), nonlocal Ablowitz-Ladik (AL), nonlocal, saturable discrete NLSE (DNLSE), coupled nonlocal NLSE, coupled nonlocal AL and coupled nonlocal, saturable DNLSE, we obtain periodic solutions in terms of Jacobi elliptic functions as well as the corresponding hyperbolic soliton solutions. Remarkably, in all the six cases, we find that unlike the corresponding local cases, all the nonlocal models simultaneously admit both the bright and the dark soliton solutions. Further, in all the six cases, not only…
Due to its unique electronic property and the Pauli Blocking Principle, atomic layer graphene possesses wavelength-independent ultrafast saturable absorption, which can be exploited for the ultrafast photonics application. Through chemical functionalization, a graphene-polymer nanocomposite membrane was fabricated and firstly used to mode lock a fiber laser. Stable mode locked solitons with 3 nJ pulse energy, 700 fs pulse width at the 1590 nm wavelength have been directly generated from the laser. We show that graphene-polymer nanocomposites could be an attractive saturable absorber for high p…
We introduce a system of two component two-dimensional (2D) complex Ginzburg-Landau equations (CGLEs) with spin-orbit-coupling (SOC) describing a wide-aperture microcavity laser with saturable gain and absorption. We report families of two-component self-trapped dissipative laser solitons in this system. The SOC terms are represented by the second-order differential operators, which sets the difference, $|ΔS|=2$, between the vorticities of the two components. We have found stable solitons of two types: vortex-antivortex (VAV) and semi-vortex (SV) bound states, featuring vorticities $\left( -1,…
We formulate and study dynamics from a complex Ginzburg-Landau system with saturable nonlinearity, including asymmetric cross-phase modulation (XPM) parameters. Such equations can model phenomena described by complex Ginzburg-Landau systems under the added assumption of saturable media. When the saturation parameter is set to zero, we recover a general complex cubic Ginzburg-Landau system with XPM. We first derive conditions for the existence of bounded dynamics, approximating the absorbing set for solutions. We use this to then determine conditions for amplitude death of a single wavefunction…
We use the cubic complex Ginzburg-Landau equation coupled to a dissipative linear equation as a model of lasers with an external frequency-selective feedback. It is known that the feedback can stabilize the one-dimensional (1D) self-localized mode. We aim to extend the analysis to 2D stripe-shaped and vortex solitons. The radius of the vortices increases linearly with their topological charge, $m$, therefore the flat-stripe soliton may be interpreted as the vortex with $m=\infty$, while vortex solitons can be realized as stripes bent into rings. The results for the vortex solitons are applicab…
Saturable nonlinear Schrödinger equation with space- and time-dependent variable coefficients
Instituto de Física, Universidade Federal de Goiás（戈亚斯联邦大学物理研究所）；Instituto de Ciências Tecnológicas e Exatas, Universidade Federal do Triângulo Mineiro（米纳斯吉拉斯三角联邦大学科技与理学院）；Instituto Federal do Maranhão（马拉尼昂联邦学院）
Travelling solitary waves in the one-dimensional discrete nonlinear Schrödinger equation (DNLSE) with saturable onsite nonlinearity are studied. A variational approximation (VA) for the solitary waves is derived in an analytical form. The stability is also studied by means of the VA, demonstrating that the solitons are stable, which is consistent with previously published results. Then, the VA is applied to predict parameters of travelling solitons with non-oscillatory tails (\textit{embedded solitons}, ESs). Two-soliton bound states are considered too. The separation distance between the soli…
We have introduced a class of spiraling elliptic solitons in generic nonlocal nonlinear media. The spiraling elliptic solitons carry the orbital angular momentum. This class solitons are stable for any degree of nonlocality except for the local case when the response function of the material is Gaussian function.
The dynamics of light beams in the nonlinear optical media with periodically modulated in the longitudinal direction parity-time distribution of the complex refractive index is investigated. The possibility of dynamical stabilization of PT-symmetric solitons is demonstrated.
Nonlocality is a key feature of many physical systems since it prevents a catastrophic collapse and a symmetry-breaking azimuthal instability of intense wave beams in a bulk self-focusing nonlinear media. This opens up an intriguing perspective for stabilization of complex topological structures such as higher-order solitons, vortex rings and vortex ring-on-line complexes. Using direct numerical simulations, we find a class of cylindrically-symmetric $n$-th order spatial solitons having the intensity distribution with a central bright spot surrounded by $n$ bright rings of varying size. We inv…
We study the stability of multipole-mode solitons in one-dimensional thermal nonlinear media. We show how the sample geometry impacts the stability of mutlipole-mode solitons and reveal that the tripole and quadrupole can be made stable in their whole domain of existence, provided that the sample width exceeds a critical value. In spite of such geometry-dependent soliton stability, we find that the maximal number of peaks in stable multipole-mode solitons in thermal media is the same as that in nonlinear materials with finite-range nonlocality.
