Solitons In Optical Media Research Articles

Generic quartic solitons in optical media

Our analysis suggests strongly that stationary pulses exist in nonlinear media with second-, third-, and fourth-order dispersion. A theory, based on the variational approach, is developed for finding approximate parameters of such solitons. It is obtained that the soliton velocity in the retarded reference frame can be different from the inverse of the group velocity of linear waves. It is shown that the interaction of the pulse spectrum with that of linear waves can affect the existence of stationary solitons. These theoretical results are supported by numerical simulations. Transformations between solitons of different systems are derived. A generalization for solitons in media with the highest even-order dispersion is suggested. Published by the American Physical Society 2024

Tubular topological bright-dark and dark laser solitons

We investigate, analytically and numerically, tubular topological laser solitons, which serve as intermediate link between 2D- and 3D-dissipative optical solitons in media with nonlinear amplification and absorption of light or in large-size laser with such a medium. Features of both 3D-dark solitons (with nonvanishing intensity at periphery for all spatial dimensions) and bright-dark solitons (vanishing in two of three dimensions) are studied, including their stability.

Tail-free self-accelerating solitons and vortices

Self-accelerating waves in conservative systems, which usually feature slowly decaying tails, such as Airy waves, have drawn great interest in studies of quantum and classical wave dynamics. They typically appear in linear media, while nonlinearities tend to deform and eventually destroy them. We demonstrate, by means of analytical and numerical methods, the existence of robust one- and two-dimensional (1D and 2D) self-accelerating tailless solitons and solitary vortices in a model of two-component Bose-Einstein condensates, dressed by a microwave (MW) field, whose magnetic component mediates long-range interaction between the matter-wave constituents, with the feedback of the matter waves on the MW field taken into account. In particular, self-accelerating 2D solitons may move along a curved trajectory in the coordinate plane. The system may also include the spin-orbit coupling between the components, leading to similar results for the self-acceleration. The effect persists if the contact cubic nonlinearity is included. A similar mechanism may generate 1D and 2D self-accelerating solitons in optical media with thermal nonlinearity.

Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential.

We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time ([Formula: see text])-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 [Formula: see text]-symmetric waveguides. The dependence of the propagation constant on the soliton's power is presented for different strengths of the nonlinearity saturation, S The stability of fundamental, dipole, tripole and quadrupole solitons is investigated by means of the linear-stability analysis and direct numerical simulations of the corresponding (1+1)-dimensional nonlinear Schrödinger-type equation. The results show that the instability of the stationary solutions can be mitigated or completely suppressed, increasing the value of SThis article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Beta-derivative and sub-equation method applied to the optical solitons in medium with parabolic law nonlinearity and higher order dispersion

By using the sub-equation method, we construct the analytical solutions of the space-time generalized nonlinear Schrödinger equation involving the beta-derivative. This equation describing the propagation of ultra-short optical solitons through parabolic law medium. Nonlinear perturbations of higher-order and self-steepening terms are taken into account. As a result, some new exact solutions are constructed under constraint conditions.

Optical solitons in media with time-modulated nonlinearities and spatiotemporal dispersion

This work studies the optical solitons with time-modulated nonlinearities and spatiotemporal dispersion. Four types of nonlinearity—Kerr law nonlinearity, parabolic law nonlinearity, power law nonlinearity, and dual-power law nonlinearity—are considered. The non-auto-Backlund transformation is obtained. Analytical soliton solutions are constructed. The presented results can be applied in the area of dispersion- and nonlinearity-managed solitons.

Dissipative quadratic solitons supported by a localized gain

We propose two models for the creation of stable dissipative solitons in optical media with the $\chi^{(2)}$ (quadratic) nonlinearity. To compensate spatially uniform loss in both the fundamental-frequency (FF) and second-harmonic (SH) components of the system, a strongly localized "hot spot", carrying the linear gain, is added, acting either on the FF component, or on the SH one. In both systems, we use numerical methods to find families of dissipative $\chi^{(2)}$ solitons pinned to the "hot spot". The shape of the existence and stability domains may be rather complex. An existence boundary for the solitons, which corresponds to the guided mode in the linearized version of the systems, is obtained in an analytical form. The solitons demonstrate noteworthy features, such as spontaneous symmetry breaking (of spatially symmetric solitons) and bistability.

Optical solitons in medium with parabolic law nonlinearity and higher order dispersion

The nonlinear Schrödinger equation, describing the propagation of ultra-short optical solitons through parabolic law medium, has been studied analytically. The perturbations that are third-order dispersion, fourth-order dispersion, and self-steepening are taken into account. The Ricatti equation expansion approach and Ansatz method are applied. Finally, Bright, dark as well as singular solitons are constructed under some constraint conditions.

Pseudospectral Renormalization Method for Solitons in Quasicrystal Lattice with the Cubic-Quintic Nonlinearity

We modified the spectral renormalization method as the pseudospectral renormalization method in order to find the localized solutions. The pseudospectral renormalization method can be applied to a large class of problems including different homogeneities. Using this computational method, we demonstrate the existence of two different solitons in optical media described by the self-focusing cubic and the self-defocusing quintic nonlinear Schrödinger equation with quasicrystal lattice. It is shown that there are two different lattice solitons corresponding to the first and the second renormalization factors for the self-focusing cubic and the self-defocusing quintic model. However, the self-focusing quintic nonlinearity without optical lattice does not support two different solitons. We showed that the lattice solitons corresponding to the first and the second renormalization factors have the same powers and amplitudes. We also demonstrate that quintic nonlinearity supports bistable solitons by adding the optical lattice such as a quasicrystal lattice. The linear and nonlinear stabilities of these solitons are investigated using direct simulation of the nonlinear Schrödinger equation with the cubic-quintic nonlinearity and its linearized equation.

Rotary dissipative spatial solitons in cylindrical lattices

We study both the stability and rotational dynamics of dissipative spatial solitons in optical media described by the cubic-quintic complex Ginzburg–Landau equation in the presence of periodic cylindrical lattices. We consider three kinds of cylindrical lattices, which are generated by (a) the refractive index modulation, (b) the linear-loss modulation, and (c) the combined modulation of both refractive index and linear-loss coefficient. The solitons can be trapped inside each concentric lattice ring (circular “trough”) and can be set into rotary motion by imposing onto the input field distribution a phase slope (or angle), which is proportional to the initial momentum imparted to the soliton in the tangential direction. The rotary motion can be effectively controlled by tuning the amplitude of the modulation profile. For either refractive index or linear-loss modulated cylindrical lattices, the spatial soliton can exhibit stably persistent rotation along the circular lattice orbit only if its initial momentum does not exceed a certain allowable maximum value. But for cylindrical lattices generated by combined refractive index modulation and linear-loss modulation, soliton rotary motion only appears in the initial propagation stage and then stops at certain spatial position. When the initial momentum imparted to the soliton is absent we find that for cylindrical lattices with only linear-loss modulation profile, by varying the modulation depth, the dissipative spatial soliton can display a transverse drift, can spread out into a stable multi-ring-shaped mode, or can decay.

Analytical study of optical solitons in media with Kerr and parabolic-law nonlinearities

The nonlinear optical transmission equation was investigated in the presence of detuning, inter-modal dispersion, time- and space-modulated external potentials, and dissipation. Optical solitons, triangular periodic solutions, and Jacobian elliptic periodic solutions are constructed with the aid of the self-similarity transformation and Jacobian elliptic equation expansion methods. The conditions for analytical solutions to exist are obtained. Both Kerr-law as well as parabolic-law nonlinear media are considered.

Lattice solitons in optical media described by the complex Ginzburg-Landau model withPT-symmetric periodic potentials

We report the existence, stability, and rich dynamics of dissipative lattice solitons in optical media described by the cubic-quintic complex Ginzburg-Landau model with parity-time ($\mathcal{PT}$) symmetric potentials. We focus on studying the generic spatial soliton propagation scenarios by changing (a) the linear loss coefficient in the complex Ginzburg-Landau model, (b) the amplitudes, and (c) the periods of real and imaginary parts of the complex-valued $\mathcal{PT}$-symmetric optical lattice potential. Generically, it is found that if the period of the real part of the $\mathcal{PT}$-symmetric optical lattice potential is close to $\ensuremath{\pi},$ the spatial solitons are tightly bound and they can propagate straightly along the lattice, while if the period of the real part of the $\mathcal{PT}$-symmetric optical lattice potential is larger than $\ensuremath{\pi},$ the launched solitons are loosely bound and they can exhibit either a transverse (lateral) drift or a persistent swing around the input launching point due to gradient force arising from the spatially inhomogeneous loss. These latter features are intimately related to the dissipative nature of the system under consideration because they do not arise in the conservative counterpart of the dynamical model. These generic propagation scenarios can be effectively managed by properly changing the profile of the spatially inhomogeneous loss.

Derivation of a generalized double-sine-Gordon equation describing ultrashort-soliton propagation in optical media composed of multilevel atoms

We consider the propagation of ultrashort optical solitons in media described by a general Hamiltonian of multilevel atoms. Assuming that all transition frequencies of the medium are well below the typical wave frequency, i.e., only the contribution of infrared transitions is taken into account, we use a short-wave approximation and a rigorous application of the reductive perturbation formalism to derive a cumbersome coupled system of nonlinear partial differential equations describing ultrashort soliton evolution in such systems. The rather complicated set of coupled equations can be simplified to a generic double-sine-Gordon equation for a special case of identical three-level atoms, whereas for a special case of identical four-level atoms the system of coupled equations can be reduced to a generalized double-sine-Gordon equation. Numerical simulations showing the formation of robust breather-type solutions of both the standard double-sine-Gordon and of the generalized double-sine-Gordon equations from sinusoidal inputs with Gaussian envelopes are also presented.

Soliton dynamics induced by periodic spatially inhomogeneous losses in optical media described by the complex Ginzburg–Landau model

We study the rich dynamics of dissipative spatial solitons in optical media described by the complex Ginzburg–Landau equation in the presence of periodic, sinusoidal-type spatially inhomogeneous losses. It is revealed that in the case when the soliton is launched at the point where the periodic spatial modulation loss profile has its zero value, the gradient force of the inhomogeneous loss easily induces three generic propagation scenarios: (a) soliton transverse drift, (b) persistent swing around the soliton input launching position, and (c) damped oscillations near or even far from the input position. The soliton exhibiting damped oscillations eventually evolves into a stable one, whose output position can be controlled by the amplitude of the inhomogeneous loss profile. Conversely, when the launching point coincides with an extremum (a maximum or a minimum) of the sinusoidal-type loss landscape, both soliton transverse drift and soliton damped oscillations occur due to transverse modulation instability. Moreover, in this case, depending on the balance between the amplitude of the inhomogeneous loss modulation profile and the homogeneous linear loss coefficient, either the launched soliton can maintain its stable propagation at the input position or a stable plump dissipative soliton can be formed while preserving the launching point.

Self-Similar Vortex Solitons for the Distributed-Coefficient Nonlinear Schrödinger Equation

Via the similarity transformation method, we obtain an approximate vortex solution to the generalized (2+1)-dimensional nonlinear Schrödinger equation with space-dependent diffraction, nonlinearity and gain/loss coefficients. Under certain parametric conditions, we investigate the propagation dynamics of self-similar vortex solitons in optical media.

Boundary effects on the dynamics of higher-order optical spatial solitons in nonlocal thermal media

We study theoretically the propagation of higher-order two-dimensional spatial solitons in optical media with nonlocal thermal nonlinear response. We show that these localized states experience complex dynamics including transformations between solitons of different symmetries which depend strongly on the geometry of a nonlinear sample. Boundaries exert repulsive forces on a soliton and, depending on its initial position relative to the boundaries, we observe transverse motion of a beam as a whole across the sample, effectively facilitating transformations.

Stabilization of vortex solitons in nonlocal nonlinear media

We study the evolution of vortex solitons in optical media with a nonlocal nonlinear response. We employ a modulation theory for the vortex parameters based on an averaged Lagrangian, and analyze the azimuthal evolution of both the vortex width and diffractive radiation. We describe analytically the physical mechanism for vortex stabilization due to the long-range nonlocal nonlinear response, the effect observed earlier in numerical simulations only.

On conservative and dissipative solitons in media with a periodic spatial modulation

A comparative theoretical analysis of properties of conservative and dissipative optical solitons in media with a periodic spatial modulation of optical characteristics is performed. It is shown that, in the case of modulation in the longitudinal (with respect to the axis of predominant propagation) direction, the mechanism of decay of conservative solitons because of the delocalization of their Fourier harmonics takes place, whereas, for dissipative solitons, this mechanism is absent. In the case of modulation in the transverse direction, the presence of discrete dissipative solitons in a set of optical fibers with nonlinear (saturable) amplification and absorption is shown, which, to a considerable extent, are similar to conservative discrete solitons.

Criteria for the experimental observation of multidimensional optical solitons in saturable media

Criteria for experimental observation of multidimensional optical solitons in media with saturable refractive nonlinearities are developed. The criteria are applied to actual material parameters (characterizing the cubic self-focusing and quintic self-defocusing nonlinearities, two-photon loss, and optical-damage threshold) for various glasses. This way, we identify operation windows for soliton formation in these glasses. It is found that two-photon absorption sets stringent limits on the windows. We conclude that, while a well-defined window of parameters exists for two-dimensional solitons (spatial or spatiotemporal), for their three-dimensional spatiotemporal counterparts such a window does not exist, due to the nonlinear loss in glasses.

HIGHLY NONLOCAL OPTICAL SOLITONS AND THEIR OBSERVATION IN NEMATIC LIQUID CRYSTALS

We investigate 2-dimensional spatial optical solitons in media exhibiting a large nonlocal response coupled with a self-focusing nonlinearity. To this extent, with reference to a specific system in undoped nematic liquid crystals, we develop a general theory of spatial solitons in media with an arbitrary degree of nonlocality and carry out experimental observations to validate the model. The remarkable agreement between predictions and data yields evidence of narrow-waist solitons, revealing an important connection between nonparaxiality and nonlocality and emphasizing the role of nonlocality.