## Abstract

We present a fast and general iterative design method for both diffractive and nondiffractive two-dimensional optical elements. The method is based on a finite-thickness model in combination with the Yang–Gu phase-retrieval algorithm. A rigorous electromagnetic analysis (boundary element method) is used to appraise the designed results. We calculate the transverse-intensity distributions, diffraction efficiency, and spot size of the designed microlenses at the focusing plane for microlenses designed using the presented method and the conventional zero-thickness model. The main findings show the superiority of the presented method over the conventional method, especially for nondiffractive optical elements.

© 2007 Optical Society of America

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### Equations (6)

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(1)
$$\psi \left({\mathbf{r}}_{2}\right)=-{\int}_{\Gamma}\left[{\psi}_{1}^{\mathrm{inc}}\left({\mathbf{r}}_{\Gamma}\right)\frac{\partial {G}_{2}^{\mathrm{RS}1}({\mathbf{r}}_{2},{\mathbf{r}}_{\Gamma})}{\partial \widehat{y}}\right]\mathrm{d}l,$$
(2)
$$\psi \left({\mathbf{r}}_{2}\right)=\widehat{G}({\mathbf{r}}_{\Gamma},{\mathbf{r}}_{2}){\psi}_{1}^{\mathrm{inc}}\left({\mathbf{r}}_{\Gamma}\right),$$
(3)
$${\varphi}_{2}^{\left(n\right)}\left({x}_{2}\right)=\mathrm{arg}\left\{\widehat{G}{\rho}_{1}^{\left(n\right)}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}\left[\mathrm{i}{\varphi}_{1}^{\left(n\right)}\right]\right\},$$
(4)
$${\varphi}_{1}^{(n,m+1)}\left({x}_{1}\right)=\mathrm{arg}\mathbf{\left(}{\widehat{A}}_{D}^{-1}\{{\widehat{G}}^{\u2020}{\rho}_{2}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}\left(\mathrm{i}{\varphi}_{2}\right)-{\widehat{A}}_{ND}{\rho}_{1}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}\left[\mathrm{i}{\varphi}_{1}^{(n,m)}\right]\}\mathbf{\right)}.$$
(5)
$$\mathrm{\Delta}y=\frac{{\varphi}_{1}\left(x\right)}{{k}_{0}({n}_{1}-{n}_{2})}.$$
(6)
$${\rho}_{2}^{\left(n\right)}\left({x}_{2}\right)=w\left({x}_{2}\right)\mid {\widehat{G}}_{{\rho}_{1}}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}\left(i{\varphi}_{1}^{\left(n\right)}\right)\mid .$$