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Overview of an effective‐medium approach to the reflection and refraction of light at a turbid colloidal half‐space
Author(s) -
GutiérrezReyes Edahí,
GarcíaValenzuela Augusto,
Barrera Rubén G.
Publication year - 2012
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.201100735
Subject(s) - integral equation , reflection (computer programming) , optics , plane wave , refraction , amplitude , reflection coefficient , electromagnetic field , total external reflection , physics , mathematical analysis , electric field , field (mathematics) , total internal reflection , mathematics , computer science , quantum mechanics , pure mathematics , programming language
It has been recently shown that the effective electromagnetic bulk response of a dilute colloidal system, composed by a large collection of identical big spheres, located at random, is spatially dispersive (non‐local). Here, we extend this effective‐medium approach to the calculation of the reflection and transmission amplitudes of the same system but with a flat interface. We use an integral‐equation approach for the calculation of the average electric field. The integral equation is solved within the effective‐field approximation, by proposing a plane‐wave solution with effective parameters that are calculated by solving a set of consistency equations. We obtain explicit expressions for the transmission and reflection amplitudes as a function of the filling fraction, the radius of the inclusions and the angle of incidence. We show and discuss numerical results for a system of silver particles.