Synthesis of diffractive axicons for partially coherent light based on asymptotic wave theory

Abstract

A general, noniterative method for designing diffractive axicons is derived. This new technique clarifies the earlier phenomenological design principle that was used for coherent light and extends it to the domain of partial coherence. The approach is based on the method of stationary phase in fluctuating diffracted wave fields, and it applies to arbitrary axially symmetric radiation of the Schell-model type. It is shown that the general design equation can be solved numerically, in a straightforward way, for any reasonable illumination and image specifications.

Transverse variation of partially coherent axicon lines

“…An arbitrary multiplicative constant should be included to make the integral ful®l both boundary conditions z…r 1 †ˆd 1 and z…r 2 †ˆd 2 . This is the main result of [6], where also a more general form that applies to any incident illumination of the Schell-model type is derived. Equation (5) can easily be solved numerically for z…» †; and then the phase function can be found through numerical integration using the de®nition of the stationary point ' 0 …» c †ˆ¡» c =z.…”

“…This means that, for beams of relatively high degrees of coherence, both the on-axis intensity pro®le [6] and the width pro®le, which describes the linewidth as a function of z, can be found. This provides an excellent tool for characterizing the focal lines of axicons in partially coherent illumination, as produced by commonly available multimode laser sources.…”

“…Since many light sources used today, such as diode lasers or excimer lasers, produce partially coherent beams, there is a need for the design and characterization of di ractive elements for partially coherent illumination [1±3]. We have previously developed a noniterative inverse design method of di ractive axicons [4] for partially coherent light, by application of the stationary-phase method to the Fresnel di raction integral [5,6]. In the approach, the on-axis intensity I…z †, where z is the distance from the axicon, is designed to follow a desired pro®le (e.g.…”

Depth of focus and intensity distribution of a lensacon illuminated by a partially coherent Gaussian Schell vortex beam

“…The diffracted field u(ρ, z) at z distance from the source plan of the PCGSMV beam lensacon in the Huygens-Fresnel (H-F) integral approach is written as [26,27]: where k = 2π λ and k is the wave number with wavelength λ and A(ρ ′ ) defined as:…”