Electromagnetic-field distribution in loaded unstable resonators

We describe a numerical algorithm for the evaluation of the electromagnetic-field distribution in a loaded unstable resonator. The storage requirements are minimized so that the resulting code can be used for large Fresnel numbers. Edge diffraction is accounted for by a recently developed continuous Fourier-transform algorithm. Use is made of a new gain formula that incorporates the effects of interference between the forward and backward waves. The present method yields improved accuracy over previous methods and enables one to perform calculations for systems with large Fresnel numbers on a medium-sized computer. Numerical results are presented for a loaded confocal unstable resonator to study the effect of the saturated gain on the mode profile. An important conclusion is that the saturated gain does not alter the number of peaks and their relative positions in the intensity distribution. This supports the simplified view that these features arise from edge diffraction and that the saturated gain amplifies each peak by a different amount depending on the peak intensities.