Focal shift and focal switch of focused truncated elliptical Gaussian beams

It is shown that when a generalized astigmatic elliptical Gaussian beam (EGB) propagates in a focusing optical system with an elliptical aperture, the effect of focal shift and focal switch can appear. An analytical propagation expression for an EGB through an axially nonsymmetrical optical system with a thin lens and an elliptical aperture is derived. Some numerical simulations are illustrated for its focal shift and focal switch, and some physical explanations are also given.