## Abstract

The ordinary and extraordinary complex refractive indices, *n*
_{o} - *j*κ
_{o} and *n*
_{e} - *j*κ
_{e}, of a nematic liquid crystal were measured in the infrared region at 3.0–11.5-µm wavelength. The complex refractive indices were evaluated in terms of the angular dependence of the reflectance. Semicylindrical CsI prisms and a goniometer were used for measurement of the reflectance in a wide incident-angle range and throughout the wide infrared spectral region. Refractive indices *n*
_{o} and *n*
_{e} changed notably near the absorption wavelength. Negative birefringence, i.e., *n*
_{e} < *n*
_{o}, was observed in the vicinity of 6.6 µm, where *n*
_{e} changed more than did *n*
_{o}.

© 2003 Optical Society of America

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### Equations (5)

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(1)
$${R}_{p}\left(\mathrm{\theta}\right)={\left|\frac{{\left({n}_{o}-j{\mathrm{\kappa}}_{o}\right)}^{2}cos\mathrm{\theta}-{n}_{G}{\left[{\left({n}_{o}-j{\mathrm{\kappa}}_{o}\right)}^{2}-n_{G}{}^{2}{sin}^{2}\mathrm{\theta}\right]}^{1/2}}{{\left({n}_{o}-j{\mathrm{\kappa}}_{o}\right)}^{2}cos\mathrm{\theta}+{n}_{G}{\left[{\left({n}_{o}-j{\mathrm{\kappa}}_{o}\right)}^{2}-n_{G}{}^{2}{sin}^{2}\mathrm{\theta}\right]}^{1/2}}\right|}^{2},$$
(2)
$${R}_{s}\left(\mathrm{\theta}\right)={\left|\frac{{n}_{G}cos\mathrm{\theta}-{\left[{\left({n}_{e}-j{\mathrm{\kappa}}_{e}\right)}^{2}-n_{G}{}^{2}{sin}^{2}\mathrm{\theta}\right]}^{1/2}}{{n}_{G}cos\mathrm{\theta}+{\left[{\left({n}_{e}-j{\mathrm{\kappa}}_{e}\right)}^{2}-n_{G}{}^{2}{sin}^{2}\mathrm{\theta}\right]}^{1/2}}\right|}^{2}$$
(3)
$$\overline{{R}_{p}\left(\mathrm{\theta}\right)}={R}_{p}+{R}_{p}{\left(1-{R}_{p}\right)}^{2}{\mathrm{\tau}}^{2}+R_{p}{}^{3}{\left(1-{R}_{p}\right)}^{2}{\mathrm{\tau}}^{4}+R_{p}{}^{5}{\left(1-{R}_{p}\right)}^{2}{\mathrm{\tau}}^{6}+\cdots =\frac{1+\left(1-2{R}_{p}\right)exp\left\{-8\mathrm{\pi}{\mathrm{\kappa}}_{o}d/\left[\mathrm{\lambda}{\left(1-n_{G}{}^{2}{sin}^{2}\mathrm{\theta}/n_{o}{}^{2}\right)}^{1/2}\right]\right\}}{1-R_{p}{}^{2}exp\left\{-8\mathrm{\pi}{\mathrm{\kappa}}_{o}d/\left[\mathrm{\lambda}{\left(1-n_{G}{}^{2}{sin}^{2}\mathrm{\theta}/n_{o}{}^{2}\right)}^{1/2}\right]\right\}}{R}_{p},$$
(4)
$$\overline{{R}_{s}\left(\mathrm{\theta}\right)}=\frac{1+\left(1-2{R}_{s}\right)exp\left\{-8\mathrm{\pi}{\mathrm{\kappa}}_{e}d/\left[\mathrm{\lambda}{\left(1-n_{G}{}^{2}{sin}^{2}\mathrm{\theta}/n_{e}{}^{2}\right)}^{1/2}\right]\right\}}{1-R_{s}{}^{2}exp\left\{-8\mathrm{\pi}{\mathrm{\kappa}}_{e}d/\left[\mathrm{\lambda}{\left(1-n_{G}{}^{2}{sin}^{2}\mathrm{\theta}/n_{e}{}^{2}\right)}^{1/2}\right]\right\}}{R}_{s}.$$
(5)
$$\mathrm{\sigma}=\frac{1}{N}{\left\{\sum _{i=1}^{N}{\left[\overline{R\left({\mathrm{\theta}}_{i}\right)}-I\left({\mathrm{\theta}}_{i}\right)/{I}_{0}\right]}^{2}\right\}}^{1/2},$$