Photonic Crystal Optics and Homogenization of 2D Periodic Composites
We study the long-wavelength limit for an arbitrary photonic crystal (PC) of 2D periodicity. Light propagation is not restricted to the plane of periodicity. We proved that 2D PC’s are uni-axial or bi-axial and derived compact, explicit formulas for the effective (“principal”) dielectric constants; these are plotted for silicon - air composites. This could facilitate the custom design of optical components for diverse spectral regions and applications. Our method of “homogenization” is not limited to optical properties, but is also valid for electrostatics, magnetostatics, DC conductivity, thermal conductivity, etc. Thus our results are applicable to the Physics of Inhomogeneous Media where exact, compact formulas are scarce. Our numerical method yields results with very high accuracy, even for very large dielectric contrasts and filling fractions.
KeywordsPhotonic Crystal Filling Fraction Phononic Crystal Electric Field Parallel Apartado Postal
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