Modeling Axicons in FRED

Physical Axicon Lens

A Thorlabs Axicon Lens AX2520-UV model is used in this file to convert a plane wave input beam into a ring profile. Axicons are defined by the following parameters:

Axicon Parameters (Original image from Thorlabs)

To create the axicon surface shape a General Asphere surface is used on surface 2, with an R1 coefficient set by

Which for a physical angle of 20 deg requires an R1 coefficient of approximately -0.364:

Notes:

The raytrace is performed coherently using FRED’s Gaussian Beam Decomposition technique.
To minimize ray errors at the center point of the conic surface, a large number of rays need to be traced.
A grid of 201 x 201 is deemed sufficient.
The ring profile can be seen by plotting either the Irradiance, Energy Density, or Scalar Field profile at the Image Plane.

Associated FRED file: FRED_AxiconLensExample.frd

Idealized Axicon

It is also possible to model axicons as an idealized pure phase surface using a 2-point HOE (a diffraction grating) with radial phase terms. In this case the HOE parameters are nulled out, and to account for the missing material power the linear radial term R1 is calculated using:

Where n is the idealized refractive index. Which for n = 1.48 (fused silica @ 330nm) gives R1 = -0.175

Pure phase axicon equivalent to AX2520-UV