Generation of bright and dark solitons in photonic nanowire
26 Jul 2012-pp 1-3
TL;DR: In this article, the authors generate bright and dark soliton type ultrashort laser pulses in a photonic nanowire by a higher order nonlinear Schrodinger equation with an additional effect relating to the nonlinear change of group velocity.
Abstract: In this paper, we generate bright as well as dark soliton type ultrashort laser pulses in a photonic nanowire. The pulse evolution in the photonic nanowire is described by higher order nonlinear Schrodinger equation with an additional effect relating to the nonlinear change of group velocity, which, in turn, is proportional to the field intensity. The pulse evolution equation is solved by coupled amplitude-phase method. Further, we calculate the minimum power required for realizing the ultrashort laser pulses. The main crux of this work stems from the generation of ultrashort pulses by an entirely new nonlinear effect involving change of group velocity.
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TL;DR: In this paper, the problem of nonlinear pulse propagation in optical fibers, as governed by the nonlinear Schrodinger equation, is reformulated as a variational problem and approximate solutions are obtained for the evolution during propagation of pulse width, pulse amplitude, and nonlinear frequency chirp.
Abstract: The problem of nonlinear pulse propagation in optical fibers, as governed by the nonlinear Schr\"odinger equation, is reformulated as a variational problem. By means of Gaussian trial functions and a Ritz optimization procedure, approximate solutions are obtained for the evolution during propagation of pulse width, pulse amplitude, and nonlinear frequency chirp. Comparisons with results from inverse-scattering theory and/or numerically obtained solutions show very good agreement.
867 citations
TL;DR: In this paper, solitary wave solutions of the higher order nonlinear Schrodinger equation for the propagation of short light pulses in an optical fiber are studied. And conditions for the existence of $N$-soliton solutions are determined; when these conditions are met the equation becomes the modified Korteweg-de Vries equation.
Abstract: We study solitary wave solutions of the higher order nonlinear Schr\"odinger equation for the propagation of short light pulses in an optical fiber. Using a scaling transformation we reduce the equation to a two-parameter canonical form. Solitary wave (1-soliton) solutions always exist provided easily met inequality constraints on the parameters in the equation are satisfied. Conditions for the existence of $N$-soliton solutions ( $N\ensuremath{\ge}2$) are determined; when these conditions are met the equation becomes the modified Korteweg--de Vries equation. A proper subset of these conditions meet the Painlev\'e plausibility conditions for integrability.
285 citations
TL;DR: The higher order nonlinear Schrödinger equation describing the propagation of ultrashort pulses in optical fibers is solved and by means of the coupled amplitude-phase formulation fundamental (solitary wave) dark soliton solutions are found.
Abstract: We solve the higher order nonlinear Schrodinger equation describing the propagation of ultrashort pulses in optical fibers. By means of the coupled amplitude-phase formulation fundamental (solitary wave) dark soliton solutions are found.
111 citations
TL;DR: In this paper, a set of new unidirectional evolution equations for photonic nanowires with sub-wavelength core diameter is derived, which leads to the discovery of new, previously unexplored nonlinear effects which have the potential to affect soliton propagation considerably.
Abstract: We derive a set of new unidirectional evolution equations for photonic nanowires, i.e. waveguides with sub-wavelength core diameter. Contrary to previous approaches, our formulation simultaneously takes into account both the vector nature of the electromagnetic field and the full variations of the effective modal profiles with wavelength. This leads to the discovery of new, previously unexplored nonlinear effects which have the potential to affect soliton propagation considerably. We specialize our theoretical considerations to the case of perfectly circular silica strands in air, and we support our analysis with detailed numerical simulations.
15 citations
TL;DR: In this article, the authors investigated the nonlinear pulse propagation through the fiber Bragg grating structure where the pulse dynamics are governed by nonlinear-coupled mode (NLCM) equations.
Abstract: We investigate the nonlinear pulse propagation through the fiber Bragg grating structure where the pulse dynamics are governed by the nonlinear-coupled mode (NLCM) equations. Using multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. To construct the bright and dark Bragg solitons in the upper and lower branches of the dispersion curve, we solve the PNLS equation using the coupled amplitude-phase method.
9 citations
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