Complete confined bases for beam propagation in Cartesian coordinates

TL;DR

This paper introduces a new set of spatially confined basis functions for beam propagation in Cartesian coordinates, constructed from Gaussian polynomials, enabling analytical modeling and consistent initial spatial extent.

Contribution

The paper proposes a novel complete basis based on Gaussian polynomials that are spatially confined at the initial plane, improving beam propagation modeling.

Findings

Basis functions are spatially confined at initial plane.

Analytical paraxial propagation of basis elements is possible.

Optimal scaling parameter is independent of truncation order.

Abstract

Complete bases that are useful for beam propagation problems and that present the distinct property of being spatially confined at the initial plane are proposed. These bases are constructed in terms of polynomials of Gaussians, in contrast with standard alternatives such as the Hermite-Gaussian basis that are given by a Gaussian times a polynomial. The property of spatial confinement implies that, for all basis elements, the spatial extent at the initial plane is roughly the same. This property leads to an optimal scaling parameter that is independent of truncation order for the fitting of a confined initial field. Given their form as combinations of Gaussians, the paraxial propagation of these basis elements can be modeled analytically.