Error analysis of the virtual-source method

The virtual source method (VSM) is well known as a very efficient approach in generating the mode profile of unstable resonators (UR). However, as far as we know, the error of this method has rarely been examined in details. In this paper, we compare the formula in VSM with the uniform asymptotic solution of the Fresnel-Kirchhoff diffraction integral for a two-aperture model. It is shown that, the accuracy of edge wave functions is sensitive to both the equivalent Fresnel number (Neq) and the geometrical magnification (M) of UR, the error becomes Intolerable when they become very small. A criterion is presented to exam the validity of VSM for specific combination of Neq and M. The origin of the so-called “mask effect” is also discussed, it may be caused by treating all the geometric boundary of EWs emitted from different virtual source as the same.