Calculation of annular beam propagation in beamconverting annular resonator with a fast finite difference method

Beam-converting annular resonator(BCAR) possesses outstanding caracteristics of high extraction efficiency and near-diffractive beam quality.But the numerical simulation of BCAR is a hard work,for the thin annular beam propagating calculation will cost much computer work with conventional methods.In this paper a clever finite difference method based on coordinates transform is presented.This method can largely reduce the time for calculating annular beam propagation,it also has higher precision than W.D.Murphy's approximation method does．