Nonlinear Scattering and Its Transfer Matrix Formulation in One Dimension

Abstract

We present a systematic formulation of scattering theory for nonlinear interactions in one dimension and develop a nonlinear generalization of the transfer matrix that has a composition property similar to its linear analog's. We offer alternative characterizations of spectral singularities, unidirectional reflectionlessness and invisibility, and nonreciprocal transmission for nonlinear scattering systems, and examine the application of our general results in addressing the scattering problem for nonlinear single- and double-$\delta$-function potentials.

9 pages, 3 figures

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• Green's Function Formulation of Multiple Nonlinear Dirac $\delta$-Function Potential in One Dimension
• Spectral Singularities with Directional Sensitivity
• Low coherence-induced resonance in double-layer structures having parity-time symmetry
• Blowing up Light: A nonlinear amplification scheme for electromagnetic waves
• Modeling Nonlinear Optics with the Transfer Matrix Method