What is the theoretical basis for total reflection at quadratic band edges in 1D?
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The theoretical basis for total reflection at quadratic band edges in 1D photonic crystals is studied in the papers by Zhao et al. and D'Aguanno et al. Zhao et al. analyze the reflection phase of photonic bands in finite bi-directional 1D dielectric photonic crystals using an interference model. They show that their model works well for the photonic bands, except near the band edges . D'Aguanno et al. theoretically study quadratic interactions in finite 1D photonic band gap structures with deep gratings. They find that above a certain input intensity, a competitive, multi-wave mixing process occurs, resulting in mostly reflected pump field and balanced forward and backward generation. They also observe resonance-like effects in transmission and reflection as functions of input second harmonic power .
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