Calculation of diffraction of laser radiation by a two-dimensional (cylindrical) axicon with the high numerical aperture in various models

Abstract

We consider the diffraction of Gaussian beams by a cylindrical axicon whose numerical aperture (NA) is close to or higher than a limiting value (when the incident wave is assumed not to pass through an element). Three models of diffraction were considered: the ray approach, the vector wave theory with a thin optical element approximation and the solution of Maxwell’s equations by the finite elements method. Although in the ray approach the limiting NA corresponds to the total internal reflection (TIR), the analysis of the ray path has shown that with increasing NA (narrowing axicon’s angle) a proportion of energy leaks through the lateral sides, forming a diverging beam. In the wave theory, energy dissipation in lateral directions also occurs, but evanescent waves play a special role in the element’s near-field zone. In this case, the analytical estimations for the electric field components have been obtained in a thin element approximation. Application of the finite element method to Maxwell’s equations has shown that for optimal concentration of energy at the refractive element’s tip its NA should be increased (by narrowing the axicon’s angle or by increasing the material refractive index) only until the TIR occurs. The further increase of the NA results in both the reflection of rays from the flat surface and their output from the lateral sides.