Transmission of p- and s-polarized light through a prism and the condition of minimum deviation

Abstract

The condition of minimum deviation (MD) by a transparent optically isotropic prism is re-derived, and expressions for the intensity transmittances $T_p\left(\theta \right)$ and $T_s\left(\theta \right)$ of an uncoated prism of refractive index n and prism angle α for incident p- and s-polarized light and their derivatives with respect to the internal angle of refraction θ are obtained. When the MD condition $\left(\theta =\alpha /2\right)$ is satisfied, $T_s$ is maximum and $T_p$ is maximum or minimum. The transmission ellipsometric parameters ${\psi }_t,{\Delta }_t$ of a symmetrically coated prism are also shown to be locally stationary with respect to θ at $\theta =\alpha /2$. The constraint on $\left(n,\alpha \right)$ for maximally flat transmittance (MFT) of p-polarized light at and near the MD condition is determined. The transmittance $T_p$ of prisms represented by points that lie below the locus $\left(n,\alpha \right)$ of MFT exhibits oscillation as a function of θ. No similar behavior is found for the s polarization. Magnitudes and angular positions of the maxima and minima of the oscillatory $T_p$-versus-θ curves are also calculated as functions of α for a ZnS prism of refractive index $n=2.35$ in the visible.

© 2010 Optical Society of America

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