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Spotlight on Optics


  • October 2013

Optics InfoBase > Spotlight on Optics > Complex reflection coefficients of p- and s-polarized light at the pseudo-Brewster angle of a dielectric–conductor interface

Complex reflection coefficients of p- and s-polarized light at the pseudo-Brewster angle of a dielectric–conductor interface

Published in JOSA A, Vol. 30 Issue 10, pp.1975-1979 (2013)
by R. M. A. Azzam

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Spotlight summary: Brewster angle is an important concept, well known to all those who have studied at least one introductory Optics course. When an unpolarized light beam is incident on a dielectric-dielectric interface at the Brewster angle, the reflected beam is fully polarized since the Fresnel reflection coefficient for one of the polarizations (p-polarization) vanishes. The concept of pseudo-Brewster angle (PBA) is a generalization of this concept. When the relative permittivity of a medium with respect to another is a complex quantity (e.g. due to material absorption), the Fresnel reflection coefficient does not vanish in general but achieves a minimum magnitude at a certain angle, which is known as the PBA. With the optics of metals gaining tremendous importance in recent years due to areas such as plasmonics, metamaterials, etc., concepts such as PBA need to be revisited, as is accomplished in the present paper by Azzam.

In this paper the author focuses on metal-dielectric interfaces and provides a detailed analysis of PBA. Several general curves are provided that, for example, trace the loci of complex values of the Fresnel reflection coefficient for p and s polarizations for a given value of PBA, the locus of all possible values of complex permittivity for given values of PBA, phase shifts associated with reflection at PBA, complex plane trajectories of the ratio of Fresnel reflection coefficients for p and s polarizations, etc. The importance of these plots is that, besides providing a complete analysis of behavior of light waves at PBA, they can be thought of as design curves when researchers aim to engineer materials with exotic optical properties.

--Kedar Khare

Technical Division: Light–Matter Interactions
ToC Category: Physical Optics
OCIS Codes: (120.5700) Instrumentation, measurement, and metrology : Reflection
(240.0240) Optics at surfaces : Optics at surfaces
(260.0260) Physical optics : Physical optics
(260.3910) Physical optics : Metal optics
(260.5430) Physical optics : Polarization
(240.2130) Optics at surfaces : Ellipsometry and polarimetry

Posted on October 11, 2013

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