Paraxiality considerations of higher order gaussian modes

Abstract

Frequently, gaussian modes are used as free space wave equation solutions. This is not true since they are obtained assuming certain paraxial character in them. In this paper, we present an original study of the condition for paraxiality of higher order gaussian modes solutions of the wave equations in free space. A bound for the product of number (k) in free space and the beam waist of a family of modes is obtained, in terms of the mode indexes - the bound being more restrictive the larger the order of the mode.