## Abstract

Binary optics processing methods were applied to a silicon substrate to generate an array of small pillars in order to enhance transmission. The volume fraction of the silicon in the pillars was chosen to simulate a single homogeneous antireflection layer, and the pillar height was targeted to be a quarter-wave thickness. A mask was generated, using a graphics computer-aided design system; reactive-ion etching was used to generate the pillars. An improvement in long-wavelength infrared transmission is observed, with diffraction and scattering dominating at shorter wavelengths.

© 1992 Optical Society of America

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### Equations (14)

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(1)
$${n}_{\Vert}={(1-f+f{{n}_{s}}^{2})}^{1/2},$$
(2)
$${n}_{\perp}={(1-f+f/{{n}_{s}}^{2})}^{1/2},$$
(3)
$$n={\left|\frac{[1-f+f{{n}_{s}}^{2}][f+(1-f){{n}_{s}}^{2}]+{{n}_{s}}^{2}}{2[f+(1-f){{n}_{s}}^{2}]}\right|}^{1/2},$$
(5)
$$t=\mathrm{\lambda}/(4n),$$
(6)
$$f={a}^{2}/{b}^{2}.$$
(7)
$$b<\mathrm{\lambda}/{n}_{s}.$$
(8)
$$x=0.65+0.289\hspace{0.17em}y,$$
(10)
$$T=\frac{{T}_{a}{T}_{b}D}{1-(1-{T}_{a})(1-{T}_{b}){D}^{2}},$$
(11)
$$D=\text{exp}(-\mathrm{\alpha}d),$$
(12)
$${T}_{b}=\frac{4{n}_{s}}{{(1+{n}_{s})}^{2}}.$$
(13)
$$D=\frac{{\{[{{T}_{b}}^{4}+4{(1-{T}_{b})}^{2}{{T}_{0}}^{2}]\}}^{1/2}-{{T}_{b}}^{2}}{2{(1-{T}_{b})}^{2}{T}_{0}}.$$
(14)
$${T}_{a}=\frac{[1-(1-{T}_{b}){D}^{2}]T}{[{T}_{b}D-(1-{T}_{b}){D}^{2}T]}.$$