Derivation of a wave equation for pulse propagation beyond a slowly varying envelope approximation

Abstract

An iterative method is used to derive an accurate wave equation that governs ultrashort pulse propagation in a single mode fibre. In the derivation, the slowly varying envelope approximation (SVEA) is not required. Therefore, the wave equation can be used to describe the propagation of an ultrashort pulse of a few optical cycles. It is found that, compared with the wave equation obtained by making an SVEA, an accurate wave equation has the same coefficients of the linear dispersion terms and different coefficients of the high-order time derivatives of the non-linear terms.