Dissipative quadratic solitons supported by a localized gain

Abstract

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.

arXiv comment24 pages, 9 figures, to appear in PRA

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Cited by in corpus (5)

• Spatial solitons and stability in self-focusing and defocusing Kerr nonlinear media with generalized PT-symmetric Scarff-II potentials
• Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrodinger equation
• Localized solutions of Lugiato-Lefever equations with focused pump
• Fundamental and vortex dissipative quadratic solitons supported by spatially localized gain
• One- and two-dimensional solitons supported by singular modulation of quadratic nonlinearity