Time-domain finite-difference BPM with Padé approximants in time axis for analysis of circularly symmetric fields
A Padé (2,2) approximant is applied to the time axis in the time-domain beam propagation method for circularly symmetric fields. By virtue of a multistep procedure, the Padé (2,2) operator is factored into a series of two Padé (1,1) operators. The present method offers substantial improvement in the analysis of pulse propagation. An upper limit of the time step is also discussed using the analysis of a fibre grating.