Transvers Mode Calculations in Unstable Resonators Using Fast Fourier Transform Method

A spherically diverging or converging beam propagation code using the fast Fourier transform (FFT) method, is presented. Because of adoption of a new spherical co-ordinate system, the code needs no co-ordinatetransformation for the same equally spaced sampling points at two transverse planes. The code is applied to calculations of unstable resonator modes and beam focusing characteristics. Incalculating unstable resonator modes with large Fresnel number, some techniques are employed, such asinterpolation of the mode between two differently scaled grid spacing by sampling theorem, and averagingvalue of the transfer function over one grid spacing. Results of unstable resonator calculations performed for a high power CO2 laser by FFT propagation codeare shown to demonstrate the effects of mirror misalignment on mode patterns, power outputs, and focusingcharacteristics.