## Abstract

A very efficient numerical tool to electromagnetically analyze random structures is proposed. The principle is treating random structure as superposition of diffraction gratings. Then, influence of each component grating can be computed with any electromagnetic grating theory which is well established for its accuracy and computation speed. This article explains how to treat obtained data in detail. Applied to single-tiered scatteres, the proposed method gives comparable results with a standard way based on FDTD method in far shorter time.

© 2008 Optical Society of America

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### Equations (7)

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(1)
$${C}_{m}(i,k)={\mathrm{DFT}}_{t}\left\{{F}^{n}(i,k)\right\},$$
(2)
$${A}_{l}\left(k\right)={\mathrm{DFT}}_{s}\left\{{C}_{1}(i,k)\right\},$$
(3)
$$\eta \left(\theta \right)=\{\begin{array}{c}\frac{{\eta}_{m}\left({d}_{j}\right)}{\sum _{j}{\gamma}_{j}},\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\left(m\ne 0\right),\\ \frac{\sum _{j}{\eta}_{0}\left({d}_{j}\right)}{\sum _{j}{\gamma}_{j}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\phantom{\rule{.2em}{0ex}}\left(m=0\right),\end{array}$$
(4)
$$p\left(x\right)=\mathrm{exp}\left(\frac{-{x}^{2}}{{a}^{2}}\right),$$
(5)
$$q\left(x\right)=\mathrm{exp}\left(\frac{-{x}^{2}}{{b}^{2}}\right),$$
(6)
$$f\left(x\right)={\int}_{-\infty}^{\infty}p\left(\xi \right)q\left(x-\xi \right)d\xi =\frac{\mathrm{ab}}{\sqrt{{a}^{2}+{b}^{2}}}\sqrt{\pi}\mathrm{exp}\left[\frac{-{x}^{2}}{\left({a}^{2}+{b}^{2}\right)}\right],$$
(7)
$$\phantom{\rule{.9em}{0ex}}\phantom{\rule{.9em}{0ex}}\phantom{\rule{.2em}{0ex}}\simeq b\sqrt{\pi}\mathrm{exp}\left(\frac{-{x}^{2}}{{a}^{2}}\right).$$