## Abstract

Polarization-independent trap detectors, in which light is strongly absorbed through multiple reflections, are generically described in terms of the symmetry planes of a cube. The detailed design of a four-element transmission trap with coaxial input and output beams is presented. It is shown that such a trap retains polarization-dependent loss and that six detectors are required for a polarization independent transmission trap with coaxial beams.

© 1994 Optical Society of America

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### Equations (13)

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(1)
$$n\phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}sin\theta \phantom{\rule{0em}{0ex}}(-cos\theta ,d\phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}r\phantom{\rule{0.3em}{0ex}}-\phantom{\rule{0.3em}{0ex}}cos\theta ,sin\theta \phantom{\rule{0em}{0ex}})\phantom{\rule{0.1em}{0ex}},$$
(2)
$$n\phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}sin\phantom{\rule{0em}{0ex}}\theta (d\phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}r\phantom{\rule{0.3em}{0ex}}-cos\theta ,-cos\theta ,sin\theta \phantom{\rule{0em}{0ex}})\phantom{\rule{0.1em}{0ex}},$$
(3)
$$d\phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}r=({cos}^{2}\theta +\phantom{\rule{0.3em}{0ex}}1)\phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}2cos\theta ,$$
(4)
$${E}^{\prime}={T}_{r}E\phantom{\rule{0.1em}{0ex}},$$
(5)
$$E=\left[\begin{array}{c}{E}_{p}\\ {E}_{s}\end{array}\right]$$
(6)
$${T}_{r}=\left[\begin{array}{cc}{r}_{p}& 0\\ 0& {r}_{s}\end{array}\right]$$
(7)
$${T}_{\alpha}=\left[\begin{array}{cc}cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{array}\right]\phantom{\rule{0.3em}{0ex}}.$$
(8)
$$cos\alpha =2cos\theta \phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}(1\phantom{\rule{0.3em}{0ex}}+\phantom{\rule{0.3em}{0ex}}{cos}^{2}\theta \phantom{\rule{0em}{0ex}})\phantom{\rule{0.1em}{0ex}}.$$
(9)
$$T={T}_{-90}{T}_{\mathit{\text{ro}}}{T}_{\alpha}{T}_{\mathit{\text{ri}}}{T}_{90}{T}_{\mathit{\text{ri}}}{T}_{\alpha}{T}_{\mathit{\text{ro}}}\phantom{\rule{0.1em}{0ex}}.$$
(10)
$$T={r}_{\mathit{\text{so}}}{r}_{\mathit{\text{po}}}{r}_{\mathit{\text{si}}}{r}_{\mathit{\text{pi}}}\phantom{\rule{0.1em}{0ex}}\left[\begin{array}{cc}{r}_{\mathit{\text{po}}}\phantom{\rule{0em}{0ex}}/{r}_{\mathit{\text{so}}}sin2\phantom{\rule{0em}{0ex}}\alpha & cos2\phantom{\rule{0em}{0ex}}\alpha \\ -cos2\phantom{\rule{0em}{0ex}}\alpha & {r}_{\mathit{\text{so}}}\phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}{r}_{\mathit{\text{po}}}sin2\phantom{\rule{0em}{0ex}}\alpha \end{array}\right]\phantom{\rule{0.3em}{0ex}}.$$
(11)
$$(r\phantom{\rule{0.3em}{0ex}}+\phantom{\rule{0.3em}{0ex}}d\phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}2)\phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}wsin\theta .$$
(12)
$$1\phantom{\rule{0.3em}{0ex}}-\phantom{\rule{0.3em}{0ex}}(1\phantom{\rule{0.3em}{0ex}}+\phantom{\rule{0.3em}{0ex}}2r\phantom{\rule{0em}{0ex}}/\phantom{\rule{0em}{0ex}}d)cos\theta .$$
(13)
$$(\phantom{\rule{0em}{0ex}}cos\theta +\phantom{\rule{0.3em}{0ex}}1)\phantom{\rule{0.1em}{0ex}}(\phantom{\rule{0em}{0ex}}cos\theta -\phantom{\rule{0.3em}{0ex}}\sqrt{2}\phantom{\rule{0.3em}{0ex}}+\phantom{\rule{0.3em}{0ex}}1)\phantom{\rule{0.1em}{0ex}}(\phantom{\rule{0em}{0ex}}cos\theta +\phantom{\rule{0.3em}{0ex}}\sqrt{2}\phantom{\rule{0.3em}{0ex}}+\phantom{\rule{0.3em}{0ex}}1)=0\phantom{\rule{0.1em}{0ex}}.$$