## Abstract

The reflectance of an absorbing medium *R*_{θ}(*ϕ*) for incident light of an arbitrary state of polarization is considered as a function of the compex dielectic constant *ɛ; ϕ* is the angle incidence and *θ* is an incident polarization parameter, for which cos^{2}*θ* and sin^{2}*θ* give the power fractions of incident radiation that are *p*- and *s*-polarized, respectively. Our objective is to explore the complex *ɛ*-plane and define the domains for which the different types of *R*_{θ}(*ϕ*) vs *ϕ* curves (monotonic, single minimum, and secondary maximum and minimum) occur. An ethanolic solution of Rhodamine B, an organic laser dye luminofor with a well-defined resonance absorption spectrum, was chosen as the absorbing medium. We were able to define the criteria for three distinctly different types of behavior of *R*_{θ}(*ϕ*).

© 1990 Optical Society of America

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### Equations (8)

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(1)
$$\begin{array}{l}{r}_{p}=\frac{\varepsilon \hspace{0.17em}\text{cos}\varphi -{(\varepsilon -{\text{sin}}^{2}\varphi )}^{1/2}}{\varepsilon \hspace{0.17em}\text{cos}\varphi +{(\varepsilon -{\text{sin}}^{2}\varphi )}^{1/2}},\\ {r}_{s}=\frac{\text{cos}\varphi -{(\varepsilon -{\text{sin}}^{2}\varphi )}^{1/2}}{\text{cos}\varphi +{(\varepsilon -{\text{sin}}^{2}\varphi )}^{1/2}},\end{array}$$
(2)
$${R}_{p}={r}_{p}{r}_{p}^{*},\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}{R}_{s}={r}_{s}{r}_{s}^{*}$$
(3)
$${R}_{q}=q{R}_{p}+(1-q){R}_{s}.$$
(4)
$${R}_{\theta}=({\text{cos}}^{2}\theta ){R}_{p}+({\text{sin}}^{2}\theta ){R}_{s}.$$
(5)
$$\partial {R}_{\theta}/\partial \varphi =0.$$
(6)
$$\text{Re}[({\text{cos}}^{2}\theta ){r}_{p}^{\prime}{r}_{p}^{*}+({\text{sin}}^{2}\theta ){r}_{s}^{\prime}{r}_{s}^{*}]=0,$$
(7)
$$\varepsilon ={\varepsilon}^{\prime}+\text{j}{\varepsilon}^{\u2033}={N}^{2}=({n}^{2}-{k}^{2})+\text{j}2nk,$$
(8)
$$n({\omega}^{\prime})={n}_{1}+\frac{1}{\pi}\text{P}.\text{V}.{\int}_{-\infty}^{\infty}\frac{k(\omega )}{(\omega -{\omega}^{\prime})}d\omega ,$$