29 December 2003 Extreme anisotropy of two-dimensional photonic crystals due to mode degeneracy and crystal symmetry
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Abstract
It is common to assume that, for small wavenumbers, the phase and group velocities of a propagating wave in a photonic crystal coincide. This is the consequence of a simple mathematical fact: if the frequency is an analytic function of the small wavenumber, it must depend only on its magnitude but not on its direction. We have found an important exception to this rule: if a mode is doubly-degenerate for the vanishing wavenumber (at the Γ-point of the photonic dispersion curve), it can be strongly anisotropic even for small wavenumbers. The anisotropy can be so strong that, for certain propagation directions, the group velocity may oppose the phase velocity. For the other propagation directions the group and phase velocities may be co-linear. The unusual band structure of the extremely anisotropic photonic crystal results in counter-intuitive refractive properties, such as the total internal reflection for small incidence angles. Whether such extreme anisotropy is manifested is determined by the symmetry of the photonic crystal. Analytic theory based on group-theoretical considerations and the supporting results of the finite element electromagnetic simulation are presented, and several potential applications listed.
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Yaroslav A. Urzhumov, Yaroslav A. Urzhumov, Gennady Shvets, Gennady Shvets, } "Extreme anisotropy of two-dimensional photonic crystals due to mode degeneracy and crystal symmetry", Proc. SPIE 5184, Physics, Theory, and Applications of Periodic Structures in Optics II, (29 December 2003); doi: 10.1117/12.510230; https://doi.org/10.1117/12.510230
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