Abstract

The Ginzburg–Landau equation (GLE) is in general not integrable by the inverse scattering method and supports solitary-wave solution, typically called Pereira–Stenflo (PS)-type dissipative soliton (DS). We numerically demonstrate that, in an active dissipative system, the DS can radiate dispersive waves (DWs) when third-order dispersion (TOD) is present. We propose a silicon-based active waveguide that excites PS solitons. In the presence of TOD the stable DSs are perturbed and energy can be transferred to linear DWs when a resonance condition is achieved. The dynamics of the DS is governed by the complex GLE, which we solve numerically for different operational parameters. Numerical solution of the perturbed GLE exhibits multiple radiations, when the DS is allowed to propagate through a large distance. We theoretically derive a special phase-matching relation that can predict the frequencies of these multiple radiations, which are found numerically. The energy of the radiated wave is also calculated semi-analytically by adopting the plane wave superposition technique. In our theoretical and numerical calculations we include the role of free carriers, which appear inside semiconductor waveguides as a consequence of two-photon absorption (TPA). We demonstrate that apart from TOD, TPA and gain dispersion are two additional parameters that can control the energy and frequency of the radiation emitted by DSs. The DS-mediated radiation inside an active dissipative system is characteristically different from ordinary Kerr-soliton-mediated radiation and demands an insightful understanding. In this work we try to provide detailed insights of this fascinating phenomenon by adopting elaborate analytical and numerical calculations.

© 2018 Optical Society of America

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