Effective medium parameters for 1D photonic crystal containing single-negative material layers using the envelope function approach

Abstract

Nonlinear wave propagation in a 1D photonic crystal containing single-negative layers is investigated using the multiple-scale method. In this approach, the electric field is decomposed into a slowly varying envelope function and a fast Bloch-like function to obtain the analytic expressions of the effective parameters of an equivalent medium. The periodic structure has an equivalent left-handed medium for the envelope function. Gap soliton formation is discussed and compared with that associated with the Bragg gap.