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Energy flux pattern of inverse Goos-Hanchen shift in photonic crystals with negative index of refraction

The energy flux patterns of inverse Goos-Hanchen (GH) shift around the interface between air and negatively refractive photonic crystal (NRPhC) with different surface terminations is investigated. Results show that NRPhC exhibits inverse GH shift in TM and TE polarization, and the localization and pattern of energy flux differ in TM and TE polarizations and are strongly affected by surface termination. This is different to the condition of negative permittivity materials (i.e., metal), which only presents inverse GH shift in TM polarization. In the case of TE polarization, the energy flux pattern exhibits the flux of backward wave whose localization changes from the surface to inside of NRPhC with the variation of surface termination. In the case of TM polarization, the energy flux pattern is always confined within the surface of NRPhC, whereas its pattern changes from the flux of backward wave to vortices at the surface of NRPhC, which is different to the energy flux of TM polarization of metal. By properly truncating the surface of NRPhC we can control the magnitude of inverse GH shift for TM and TE polarized light.