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Optical Properties of Dielectric and Magnetic Photonic Crystals in the Low-Frequency Limit

Published online by Cambridge University Press:  01 February 2011

Arkady Krokhin ,
Jesús Arriaga  and
Edgar Reyes
Arkady Krokhin
Affiliation:
Department of Physics, University of North Texas, Denton, TX 76203, U.S.A. Instituto de Física, Universidad Autónoma de Puebla, Pue., 72570, Mexico
Jesús Arriaga
Affiliation:
Department of Physics, University of North Texas, Denton, TX 76203, U.S.A.
Edgar Reyes
Affiliation:
Department of Physics, University of North Texas, Denton, TX 76203, U.S.A.
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Abstract

We consider the long-wavelength limit for two-dimensional photonic crystals - periodic arrangement of magneto-dielectric rods with dielectric and magnetic constant εa and μa embedded in a magneto-dielectric background (εb,βb). Using the Fourier expansion method in the low-frequency limit (ω → 0 ) we develop an effective medium theory and give a rigorous proof that, in this limit, a periodic medium behaves like a homogeneous one. We derive compact analytical formulas for the effective index of refraction of a 2D photonic crystal. These formulas are very general, namely the Bravais lattice, the cross-sectional form of cylinders, their filling fractions and the dielectric and magnetic constants are all arbitrary. For non-magnetic materials, μa = μb = 1, we show how to introduce index ellipsoid and demonstrate that the E-mode is an ordinary wave and the H -mode is an extraordinary wave. For magnetic materials the both modes turn out to be extraordinary. This unusual property is unknown for natural crystals.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 797: Symposium W – Engineered Porosity for Microphotonics and Plasmonics , 2003 , W5.3
Copyright
Copyright © Materials Research Society 2004

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References

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