Distortions of Gaussian pulses transmitted through a transparent isotropic layer

Abstract

Lasers can operate in two regimes: continuous-wave mode or pulsed mode. In the simplest case, the former mode corresponds to monochromatic beams with Gaussian distribution of amplitudes (beam limited in space); whereas the latter mode corresponds to polychromatic beams with Gaussian distribution of frequencies (pulse limited in time). When the pulsed beams are reflected and refracted in different types of interfaces, they undergo peculiar distortions that bear some parallelism with those found for beams limited in space. These effects, as shown in a previous work, correspond to time delay (first order) and change of pulse width (second order). The distortions are clearly limited by the principle of causality and their interpretation, while not straightforward, emerges clearly when the associated fields are expressed in magnitude and phase. Since the analytical expressions are not simple even for the case where the pulse is transmitted through a single layer of linear, homogeneous, isotropic and transparent material, it makes it difficult to solve the inverse problem. In this work, we present an alternative analytical development that makes it possible to explicitly determine these distortion effects when a pulse impinges normally on a transparent isotropic layer immersed in a medium of analogous characteristics.

Keywords

• Gaussian pulses
• Geometric Optics
• Phase shift