Wave-front propagation by Gaussian superposition

Abstract

A linear superposition of Gaussians is proposed for representing and propagating a plane or defocused scalar wave-front with an arbitrary amplitude distribution in a linear, homogeneous and isotropic medium. A comparison is made against a wave-front that is propagated using the discrete Fresnel diffraction integral. At distances of propagation where the quadratic phase in the discrete Fresnel integral oscillates slowly, both techniques give similar results. At distances where the quadratic phase undergoes a large number of oscillations, the number of samples when using the discrete Fresnel integral must be increased to fit within Nyquist criteria. In comparison, the wave-front expressed as a linear Gaussian superposition can be calculated precisely, without any approximation, making unnecessary to increase the number of samples. Then, shorter processing time can be attained without losing the resolution in computing the propagated field. Thus, the Gaussian superposition technique becomes especially efficient when complex multistage optical systems are analyzed.