The photonic crystals possess complex dispersion relation and the unusual dispersion leads to negative refraction. Based on negative refraction, three main physical phenomena, negative Goos–Hänchen displacement, inverse Doppler effect and abnormal Cherenkov radiation have been proposed. In this work, two abnormal physical phenomena are discussed. Firstly, the negative Goos–Hänchen shift displacement is simulated by using common FDTD method. The negative displacement is measured experimentally at the wavelength of 10.6 μm. Secondly, a novel phenomenon, the dual Doppler effect, in the simultaneous occurrence of both normal and inverse Doppler effect in one moving two-dimensional wedge-type photonic crystal with negative index is investigated by using spatial Fourier Transformation. This phenomenon is also simulated by an improved FDTD method. The results have potential applications in precision measurement, cloaking, sensor, radar deception and so on.
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