Thokala Soloman Raju

Modulational instability of copropagating light beams induced by cubic–quintic nonlinearity in nonlinear negative-index material

We study the modulational instability (MI) of the continuous wave propagating through negative-index materials, based on the coupled cubic–quintic nonlinear Schrodinger equations. A comparison is made with the already available results on MI without including the quintic term. We find that this term helps in achieving MI, in otherwise impossible combinations of dispersion and nonlinearity. For example, spatial MI can occur in the focusing regime, and temporal MI becomes possible in the anomalous dispersion for defocusing nonlinearity, while in the case of the normal dispersion regime, it occurs for focusing nonlinearity, and spatiotemporal MI can occur in the focusing nonlinearity and normal dispersion. Moreover, this additional term provides extra freedom to control the amplitude of the MI gain profile.

Compression and propagation of dispersive and rectangular similaritons in asymmetric twin-core fibers

We explore dispersive and rectangular similariton solutions to the generalized nonlinear Schrodinger equation with varying dispersion, nonlinearity, gain, and source. The obtained similariton solutions are approximate but nevertheless highly accurate. As an application, we delineate the nonlinear compression of these similaritons for a dispersion-decreasing management profile. Also, for a periodic distributed amplification system, we demonstrate the formation of bound-state similaritons.

Compression of optical similaritons induced by cubic-quintic nonlinear media in a graded-index waveguide

We employ the similarity reductions in two steps to obtain a family of bright and dark similaritons for the variable coefficient cubic–quintic nonlinear Schrodinger equation. Also, parameter domains are delineated in which kink and double-kink similaritons exist for this model. This methodology introduces a free parameter through cubic nonlinearity coefficient which gives us freedom to tune the amplitude and the propagation distance of similaritons in a tapered graded-index waveguide. Furthermore, we observe rapid beam compression of these similaritons for varying detuning parameter and the coefficient of cubic nonlinearity.

Semirational and symbiotic self-similar rogue waves in a (2+1)-dimensional graded-index waveguide

We have investigated the ()-dimensional variable coefficient-coupled nonlinear Schrödinger equation (vc-CNLSE) in a graded-index waveguide. Similarity transformations are used to convert the vc-CNLSE into constant coefficient CNLSE. Under certain functional constraints we could extract semirational, multi-parametric solution of the associated Manakov system. This family of solutions include known Peregrine soliton, mixture of either bright soliton and rogue wave or dark soliton and rogue wave or breather and rogue wave. Under a distinct set of self-phase modulation and cross-phase modulation coefficients we could establish symbiotic existence of different soliton pairs as solutions. These soliton pairs may constitute of one bright and a dark soliton, two bright solitons or two dark solitons. Finally, when two wave components are directly proportional, we find bright and dark similaritons, self-similar breathers, and rogue waves as different solutions.

Symbiotic multimode spatial similaritons and rogons in inhomogeneously coupled optical fibers

Abstract We study the multimode wave propagation in inhomogeneously coupled nonlinear optical fibers modeled by variable coefficient coupled nonlinear Schrödinger equations (vc-CNLSE). Under specific conditions on the self- and cross-phase coupling terms, we find that this system supports bright–dark, bright, dark similaritons, self-similar breathers, and rogue waves as possible localized configurations. For each of these solutions, one of the propagating modes can be made prominent by lowering the strength of its self-phase modulation in comparison to the other. We further show that this inhomogeneous system supports semi-rational self-similar rogue waves (rogons) for the equal contribution of self- and cross-phase modulation.

Periodic and solitary wave solutions for ultrashort pulses in negative-index materials

Abstract We present a detailed analysis for the existence of dark and bright solitary waves as also fractional-transform solutions in a nonlinear Schrödinger equation model for competing cubic–quintic and higher-order nonlinearities with dispersive permittivity and permeability. Parameter domains are delineated in which these ultrashort optical pulses exist in negative-index materials (NIMs). For example, dark solitons exist for the case of normal second-order dispersion, anomalous third-order dispersion, self-focusing Kerr nonlinearity, and non-Kerr nonlinearities, while the bright solitons exist for the case of anomalous second-order dispersion, normal third-order dispersion, self-focusing Kerr nonlinearity, and non-Kerr nonlinearities. This is contrary to the situation in ordinary materials.

Chirped double-kink and fractional-transform solitons in an optical gain medium with two-photon absorption

We demonstrate that localized gain induces chirped double-kink, fractional-transform, bell and kink-type solitons in a nonlinear optical medium in the presence of two-photon absorption (TPA). We have seen that by modulating the properties of the gain medium one can control the width of double-kink solitons. It is shown that the nonlinear chirp associated with optical solitons is directly proportional to the intensity of the wave. We have further investigated the variation of gain with the TPA coefficient and found that the gain is transversally localized and its amplitude is directly proportional to the value of the TPA coefficient.

Unbreakable PT symmetry of exact solitons in inhomogeneous nonlinear optical media

We demonstrate analytically and numerically the existence of exact solitons in the form of double kink and fractional transform, supported by a symmetric transversally modulated defocusing nonlinearity acting as a pseudopotential combined with an antisymmetric gain–loss profile. We explain here that the PT symmetry is never broken in the dynamical system under study, even in the absence of any symmetric modulation of linear refractive index, and the transversally modulated defocusing nonlinearity comes in the way as a requirement to establish the ensuing PT symmetry.

Super and subluminal propagation in nonlinear Schrödinger equation model with self-steepening and self-frequency shift

We investigate exact traveling wave solutions of higher order nonlinear Schrodinger equation (NLSE) in the absence of third-order dispersion, which exhibit nontrivial self-phase modulation. It is shown that the corresponding dynamical equation, governing the evolution of intensity in the femtosecond regime, is that of NLSE with a source. The exact localized solutions to this system can have both super and subluminal propagation belonging to two distinct classes. A number of these solitons exhibit chirality, thereby showing preferential propagation behavior determined by group velocity dispersion. Both localized bright and dark solitons are found in complementary velocity and experimental parameter domains, which can exist for anomalous and normal dispersion regimes. It is found that dark solitons in this system propagate with nonzero velocity, unlike their counterpart in nanosecond regime. Interestingly, subluminal propagation is observed for solitons having a nontrivial Pade type intensity profile.

Lorentzian-type soliton solutions of ac-driven complex Ginzburg–Landau equation

Abstract Fractional transform solutions of modified complex Ginzburg–Landau equation phase locked to a time-dependent force have been found. The reported solutions are necessarily of the Lorentzian-type containing trigonometric, hyperbolic and pure cnoidal functions. Numerical simulations indicated that the periodic solutions and soliton solutions are quite stable against finite perturbations.