Analytical expressions for the clipping of Laguerre– and Hermite–Gauss modes by circular apertures

Abstract

We present a closed-form analytical expression that describes the effect of clipping by circular apertures on laser beams, described in terms of an expansion in eigenmodes of the paraxial wave equation, in either the Laguerre–Gauss or Hermite–Gauss bases. This result provides a faster and more accurate way to compute the coupling between higher-order modes, compared to commonly used grid-based numerical integration.