Time Delay in Thin Slabs with Kerr-Type Nonlinearity

In this paper we analyzed the following model: a thin slab with Kerr nonlinearity placed between two semi-infinite samples of linear and nonmagnetic materials. A general relation between the bidirectional group delay and the dwell time is derived for the thin slab. It is shown that the group delay is equal to the dwell time plus a self-interference delay. Particular attention is given to solving the Helmholtz equation for this case. Detailed and rigorous treatment revealed that the solutions of the Helmholtz equation are given via elliptic functions of the first kind. The boundary conditions at the interfaces are determined precisely. Finally, we provide an overall procedure for numerical calculation of the dwell times.