## Abstract

The optical arrangement of a spectral filter without an intermediate polarizer that was developed based on optical rotatory dispersion and test measurement results are presented and described. The filter uses three dispersive polarization rotators as the key elements in combination with two additional quarter-wave retarders, and it is wavelength tunable with a spectral transmission equivalent to that of a standard Lyot two-stage filter.

© 2006 Optical Society of America

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### Equations (5)

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(1)
$$T(\lambda )=\frac{1}{2}\{1\text{\hspace{0.17em}}\mathrm{cos}2[{P}_{2}+\rho (\lambda )]\mathrm{sin}2[{P}_{2}+\rho (\lambda )]0\}\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& {\mathrm{cos}}^{2}\hspace{0.17em}2{\theta}_{2}& \mathrm{sin}2{\theta}_{2}\text{\hspace{0.17em}}\mathrm{cos}2{\theta}_{2}& -\mathrm{sin}2{\theta}_{2}\\ 0& \mathrm{sin}2{\theta}_{2}\text{\hspace{0.17em}}\mathrm{cos}2{\theta}_{2}& {\mathrm{sin}}^{2}\text{\hspace{0.17em}}2{\theta}_{2}& \mathrm{cos}2{\theta}_{2}\\ 0& \mathrm{sin}2{\theta}_{2}& -\mathrm{cos}2{\theta}_{2}& 0\end{array}\right]\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& {\mathrm{cos}}^{2}\text{\hspace{0.17em}}2{\theta}_{1}& \mathrm{sin}2{\theta}_{1}\text{\hspace{0.17em}}\mathrm{cos}2{\theta}_{1}& -\mathrm{sin}2{\theta}_{1}\\ 0& \mathrm{sin}2{\theta}_{1}\text{\hspace{0.17em}}\mathrm{cos}2{\theta}_{1}& {\mathrm{sin}}^{2}\text{\hspace{0.17em}}2{\theta}_{1}& \mathrm{cos}2{\theta}_{1}\\ 0& \mathrm{sin}2{\theta}_{1}& -\mathrm{cos}2{\theta}_{1}& 0\end{array}\right]\left[\begin{array}{c}\begin{array}{c}1\\ 1\\ 0\\ 0\end{array}\end{array}\right]\text{}=\frac{1}{2}\{1+\mathrm{cos}2[{P}_{2}+\rho (\lambda )-{\theta}_{2}]\mathrm{cos}2{\theta}_{1}\mathrm{cos}2({\theta}_{2}-{\theta}_{1})+\mathrm{sin}2{\theta}_{1}\text{\hspace{0.17em}}\mathrm{sin}2[{P}_{2}+\rho (\lambda )-{\theta}_{2}\left]\right\}\mathrm{.}$$
(2)
$${T}_{c}(\lambda )=\mathrm{\xbd}\{1+{\mathrm{cos}}^{3}2[\rho (\lambda )+{\phi}_{1}]-{\mathrm{sin}}^{2}2[\rho (\lambda )+{\phi}_{1}]\}={\mathrm{cos}}^{2}[\rho (\lambda )+{\phi}_{1}]{\mathrm{cos}}^{2}2[\rho (\lambda )+{\phi}_{1}]$$
(3)
$${T}_{s}(\lambda )=\mathrm{\xbd}\{1-{\mathrm{cos}}^{3}2[\rho (\lambda )+{\phi}_{1}]-{\mathrm{sin}}^{2}2[\rho (\lambda )+{\phi}_{1}]\}={\mathrm{sin}}^{2}[\rho (\lambda )+{\phi}_{1}]{\mathrm{cos}}^{2}2[\rho (\lambda )+{\phi}_{1}]\mathrm{.}$$
(4)
$${T}_{r}(\lambda )=\{\begin{array}{l}{\mathrm{cos}}^{2}[45\xb0+{\rho}_{f}(\lambda )]{\mathrm{cos}}^{2}2[45\xb0+{\rho}_{f}(\lambda )]{\mathrm{cos}}^{2}[45\xb0-{\rho}_{f}(\lambda )]{\mathrm{cos}}^{2}2[45\xb0-{\rho}_{f}(\lambda )]\phantom{\rule[-0.0ex]{15q}{0.0ex}}{\phi}_{1}=45\xb0,{\phi}_{2}=90\xb0,{P}_{2}=45\xb0,\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\\ {\mathrm{sin}}^{2}[45\xb0+{\rho}_{f}(\lambda )]{\mathrm{cos}}^{2}\text{\hspace{0.17em}}2[45\xb0+{\rho}_{f}(\lambda )]{\mathrm{sin}}^{2}\text{\hspace{0.17em}}[45\xb0-{\rho}_{f}(\lambda )]{\mathrm{cos}}^{2}\text{\hspace{0.17em}}2[45\xb0-{\rho}_{f}(\lambda )]\phantom{\rule[-0.0ex]{17q}{0.0ex}}{\phi}_{1}=45\xb0,{\phi}_{2}=0\xb0,{P}_{2}=-45\xb0,\end{array}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$$
(5)
$$P(\lambda )=\frac{9.5639}{{\lambda}_{2}-0.0127493}-\frac{2.3113}{{\lambda}^{2}-0.000974}-0.1905,$$