Comparison of various diffraction formulas in a study of open resonators

A numerical evaluation of the modes and losses of open resonators allows us to compare different approximate diffraction formulas used in the kernel. We show that, in the case of a Fabry-Perot resonator the shape of the kernel has no practical influence on the results, at least for Fresnel numbers ranging up to 42.25. For the confocal resonator large differences are found even at small Fresnel number N, of the order of 1. In addition, neglecting the angular dependence gives rise to results with no physical meaning (negative losses), and raises the question of the accuracy of the results obtained by using the different diffraction formulas.