## Abstract

Rugate filters reflectance spectra were calculated for various index profiles with half-Gaussian modulation; graded-index as well as step-index profiles were used. The results show excellent sidelobe suppression around the stopbands, relatively high optical density, and good flatness in the reflectance band.

© 1993 Optical Society of America

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### Equations (5)

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(1)
$$n\left(x\right)={n}_{a}+\frac{1}{2}{n}_{p}\phantom{\rule{0.2em}{0ex}}\text{sin}\left(\frac{2\pi x}{p}\right),$$
(2)
$$\text{BW}=\frac{\Delta \lambda}{\lambda}=\frac{{n}_{p}}{2{n}_{a}},$$
(3)
$$\begin{array}{ll}\text{OD}\hfill & ={\text{log}}_{10}\left(\frac{1}{1-R}\right)\hfill \\ \hfill & =\left(1.36\times \text{BW}\times N\right)-{\text{log}}_{10}\left(4/{n}_{s}\right),\hfill \end{array}$$
(4)
$$n\left(x\right)={n}_{L}+\frac{1}{2}{n}_{p}\left[1+\text{sin}\left(\frac{2\pi x}{p}\right)\right]\text{exp}\left(-\alpha {x}^{2}\right)$$
(5)
$$n\left(x\right)={n}_{a}+{\scriptscriptstyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{n}_{p}\left[1+{\left(-1\right)}^{i}\right]\text{exp}\left({{-\alpha x}_{i}}^{2}\right),$$