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Journal of the Optical Society of America B

Semiclassical quantization of the electromagnetic field confined in a Kerr-effect nonlinear cavity

Jose C. Martinez, Anton

Published Aug 1, 2006• 3 citations
Publisher

Abstract

We obtain stationary solution for optical solitons propagating in a Kerr-effect nonlinear cavity using elliptic functions and quantize them semiclassically. On invoking box boundary conditions, a constraint relating the number of particles, wavelength, and a parameter associated with the elliptic function emerges. This constraint fundamentally modifies the binding energy of the soliton and lends the system a rich plethora of solution types with diverse behavior as a function of excitation number. We also speculate on how the bright soliton can thermalize through a path of frequency conversion.

DOI
10.1364/josab.23.001644

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We construct a quantum theory of light in nonlinear dielectric media with dispersion and absorption. We employ a mesoscopic model for the light-matter interaction that include a fourth-order nonlinearity in the material response. Quantization is performed by constructing an effective action in a path-integral formalism by integrating out matter and bath degrees of freedom. We show how a nonlinear response function associated with Kerr nonlinearity is obtained through the model and, after full field quantization, we derive the Feynman rules from this theory.