SIMPLE APPROXIMATION SCHEME FOR DISPERSIVE PULSE PROPAGATION, WITH COMPARISON TO THE STATIONARY PHASE APPROXIMATION

A standard approximation for dispersive pulse propagation is the method of stationary phase. A new phase space approximation based on the joint position-wavenumber Wigner distribution has been developed, which is very simple to apply and moreover is more accurate than the stationary phase approximation, especially for small time. In addition, a modification to the stationary phase approximation has been developed that improves the accuracy of the approximation for small time. We compare the accuracy of these three approximations, by computing the spatial moments of the resulting pulse over time. In the large time limit, all three approximations approach the same answer. For small time, the Wigner approximation is the most accurate of the three, followed by the modified stationary phase approximation. One of the reasons why the Wigner approximation is so accurate is that it exactly preserves low-order spatial moments of the pulse.