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We show that an electromagnetic (EM) wave undergoes negative refraction at the interface between a positive and negative refractive index material, the latter being a properly chosen photonic crystal. Finite-difference time-domain (FDTD) simulations are used to study the time evolution of an EM wave as it hits the interface. The wave is trapped temporarily at the interface, reorganizes, and, after a long time, the wave front moves eventually in the negative direction. This particular example shows how causality and speed of light are not violated in spite of the negative refraction always present in a negative index material.
Foteinopoulou et al. (Thu,) studied this question.