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The general eigen-mode equation of microscopic nonlocal response theory has been applied to infinite 3-dimensional (3D) crystals. This leads to a simple and general dispersion equation containing several known results as limiting cases. This result unifies various situations, such as the polaritons with Bragg scattering, the X-ray dynamical scattering with resonance, and photonic bands, in a single transparent formalism.
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Kikuo Cho (1997) studied this question.
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