Optical media with an imaginary third-order nonlinearity analyzed by Hamiltonian systems

In this paper we study propagation of electromagnetic waves in media with an imaginary Kerr-type nonlinearity. We show numerically that the slowly varying envelope approximation can still be used. It is proved that theoretical problems described by this type of differential equations are Hamiltonian systems. This characteristic is used to predict the variation of the electromagnetic field in the nonlinear material. Furthermore, we find a closed expression for the electromagnetic waves in a nonlinear medium with a linear absorption and an imaginary Kerr-type nonlinearity, for both a localized and a diffusive nonlinearity. Calculating the transmission probability of light through a Fabry-Perot structure shows that the introduction of an imaginary Kerr-type nonlinearity describes an intensity-dependent optical gain or absorption in a nonlinear medium. This system also shows bistable behavior comparable to real Kerr-type nonlinear materials.