ZEMAX Application Note

ZEMAX Development Corporation

Modeling Axicons An axicon surface is like a cone, with the tip of the cone at the vertex of the surface. Axicons are rotationally symmetric about the z axis, and are described by a single parameter . The angle is measured between the plane normal to the z axis at the vertex of the cone and the axicon surface. For , the axicon is identical to a plane. Axicons are used as mirrors to create a "ring" focus in certain types of laser systems, although they have other uses. The surface sag of an axicon is given by where z is the surface sag and r is the radial coordinate in lens units. Axicons can be modeled with sequential surfaces, or with non-sequentail components. There are two ways to model an axicon using sequential surfaces: 1) using the "Standard" surface model, and 2) using the "Odd Asphere" surface model. The standard surface approach is preferred over the odd asphere because the ray tracing is much faster, and the standard surface avoids having a "cusp" at the vertex where the surface normal is undefined. (ZEMAX traps this special case in the odd asphere, but it should still be avoided.) The standard surface deviates from the slope of an axicon near the "cusp". This deviation can be made arbitrarily small by the technique discussed in the following paragraphs. The standard surface behaves like an axicon when the radius of curvature is set to a very small value (the curvature is then a large value) and the conic constant is less than -1.0. This can be seen by taking the limit of the standard surface sag as the curvature goes to infinity: Then the conic constant should be set according to The exact value of the radius of curvature does not matter, but it should be several times less than the smallest radial aperture you intend to use. For example, if the axicon has a diameter of 100 mm, the axial portion to be excluded is 5 mm in diameter, and the cone angle is 10 degrees, use k = -33.16 and a radius of curvature on the order of .1 mm or less. A smaller value will also be satisfactory, but do not use zero. To use the odd asphere model, simply set the radius of curvature to infinity, and the parameter 1 value to the tangent of the cone angle. See the Surface Types chapter for details on the odd asphere surface. Although it sounds simpler, this approach should not be used unless the standard surface model proves unsatisfactory. There are multiple ways to model an axicon using non-sequential components: 1) using the "Cone" NSC object, 2) using the "Cylinder Pipe" NSC object, or 3) using the "standard surface" NSC object with the standard surface approach discussed above. The NSC "Cylinder Pipe" and "Cone" objects form exact cones defined by three parameters: the length between the front and back ends of the cone, the radial height of the cone at the front end, and the radial height of the cone at the back end. The tip (with a radial height of zero) can not be modeled to avoid forming a cusp, however this region is not used in most applications. The length of the cone should be set according to the following equation: If the region near the axis needs to be used, a small spherical end-cap can be placed over the open end of the cone to model a blunt tip, or the standard surface approach can be used to model the axicon in the non-sequential editor. Rev. 8/12/1999 ZEMAX Development Corporation 3001 112th Avenue NE, Suite 202 Bellevue, WA 98004-8017 USA Sales: Support: Fax: (425) 822-3406 (425) 822-1295 (425) 889-4687 E-Mail: sales@zemax.com support@zemax.com Copyright 2007, All Rights Reserved, ZEMAX Development Corporation