Calculation of Ultrashort Pulse Propagation based on Rational Approximations for Dispersion

Ultrashort pulses contain only a few optical cycles and exhibit broad spectra. Their carrier frequency is therefore not well defined and their description in terms of the standard slowly varying envelope approximation (SVEA) becomes questionable. Existing modeling approaches can be divided in two classes, namely generalized envelope equations, that stem from the nonlinear Schrödinger equation (NSE), and non-envelope equations which treat the field directly. Based on fundamental physical rules we will present an approach that effectively interpolates between these classes and provides a suitable setting for accurate and highly efficient numerical treatment of pulse propagation. I. ENVELOPE MODELS The traditional approach to the description of few-cycle optical pulses is the extension of the well-established theory of envelope equations. These models are related to the nonlinear Schrödinger equation (NSE) for the electric field envelope and several generalizations of it [1], e..g.,