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PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2011-06-22
Dispersion Relation and Band Gaps of 3D Photonic Crystals Made of Spheres
By
Francisco Guller,

    Dr. Francisco Guller

    Centro Atomico Constituyentes

    Argentina

    Homepage

Marina E. Inchaussandague,

    Dr. Marina E. Inchaussandague

    Universidad de Buenos Aires

    Argentina

    Homepage

Ricardo Depine

    Dr. Ricardo Depine

    Dept Fis, GEA

    Univ Buenos Aires, Fac Ciencias Exactas & Nat

    Argentina

    Homepage

Progress In Electromagnetics Research M, Vol. 19, 1-12, 2011
doi:10.2528/PIERM11051405 | Google Scholar

Abstract
In this paper, we introduce a dispersion equation for 3D photonic crystals made of parallel layers of non-overlapping spheres, valid when both wavelength and separation between layers are much larger than the distance between neighbouring spheres. This equation is based on the Korringa-Kohn-Rostoker (KKR) wave calculation method developed by Stefanou et al.~and can be used to predict the spectral positions of bandgaps in structures made of dispersive spheres. Perfect agreement between the spectral positions of bandgaps predicted with our simplified equation and those obtained with the numerical code MULTEM2 was observed. We find that this simplified relation allows us to identify two types of bandgaps: those related to the constitutive parameters of the spheres and those related to the three dimensional periodicity (distance between layers). Bandgaps of the first type are independent of the frequency and the distance between layers, while those of the second type depend only on these two quantities. We then analyze the influence of the constitutive parameters of the spheres on the spectral position of bandgaps for spheres immersed in dielectric or magnetic homogeneous media. The number and positions of the bandgaps are affected by the permitivity (permeability) of the host medium if the spheres have dispersive permitivity (permeability).
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Citation
Francisco Guller, Marina E. Inchaussandague, and Ricardo Depine, "Dispersion Relation and Band Gaps of 3D Photonic Crystals Made of Spheres," Progress In Electromagnetics Research M, Vol. 19, 1-12, 2011.
doi:10.2528/PIERM11051405
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