## Abstract

The performance characteristics of focusing diffractive mirrors designed with various methods are evaluated by using the rigorous boundary element method. Quantitative results are presented for (1) conventional-zero-thickness mirror designs, (2) alternative-zero-thickness designs that incorporate an off-axis correction factor and (3) finite-thickness designs. For TM polarization, the mirrors designed by using the alternative-zero-thickness method perform considerably worse than those designed by using the conventional-zero-thickness method, which contradicts predictions made in an earlier paper [J. Opt. Soc. Am. A **17**, 1132 (2000)].

© 2001 Optical Society of America

Full Article |

PDF Article
### Equations (9)

Equations on this page are rendered with MathJax. Learn more.

(1)
$${x}_{m}^{\pm}={x}_{0}+[-m{\mathrm{\lambda}}_{1}sin\alpha \pm ({m}^{2}{\mathrm{\lambda}}_{1}^{2}+2m{\mathrm{\lambda}}_{1}fcos\alpha {)}^{1/2}]{sec}^{2}\alpha .$$
(2)
$${h}^{\mathrm{zt}}(x)=\frac{1}{\gamma}\{xsin\alpha +[(x-{x}_{f}{)}^{2}+{f}^{2}{]}^{1/2}-f(cos\alpha +tan\beta sin\alpha )-m{\mathrm{\lambda}}_{1}\}$$
(3)
$$\mathrm{for}\hspace{0.5em}\hspace{0.5em}\left\{\begin{array}{c}{x}_{m}^{+}\le x\le min({x}_{m+1}^{+},D/2)\hspace{1em}\hspace{0.5em}\hspace{1em}\mathrm{if}\hspace{0.5em}x\ge {x}_{0}\\ max({x}_{m+1}^{-},-D/2)\le x\le {x}_{m}^{-}\hspace{1em}\hspace{1em}\mathrm{if}\hspace{0.5em}x\le {x}_{0}\end{array}.\right.$$
(4)
$${h}^{\mathrm{ft}}(x)=\frac{-B-\sqrt{{B}^{2}-4\mathit{AC}}}{2A},$$
(5)
$$A={sin}^{2}\alpha $$
(6)
$$B=-2f(1+{cos}^{2}\alpha )-2(cos\alpha )(ftan\beta sin\alpha -xsin\alpha +m{\mathrm{\lambda}}_{1}),$$
(7)
$$C=(x-ftan\beta {)}^{2}+{f}^{2}-(fcos\alpha +ftan\beta sin\alpha -xsin\alpha +m{\mathrm{\lambda}}_{1}{)}^{2}.$$
(8)
$${\varphi}^{\mathrm{inc}}({\mathbf{r}}_{1})={\varphi}_{0}w(x)exp(-{\mathit{jk}}_{1}xsin\alpha )exp({\mathit{jk}}_{1}ycos\alpha ),$$
(9)
$${\mathbf{r}}_{1}\in {S}_{1},$$