A comprehensive analysis of the coupling coefficients between plane waves in conventional dielectric media and Bloch waves of photonic crystals with effective negative refractions is performed by the layer Korringa-Kohn-Rostoker method. Employing the infinite layers refraction operator, semi-infinite size photonic crystals are considered. Some special coupling properties are discussed. In particular, the strong angular dependence of coupling coefficients is found even for an interface between air (n=1) and a photonic crystal with effective refractive index (n(eff)=-1). Thus, a negative refractive index defined by the radius of a circular equal-frequency contour does not guarantee an isotropic behavior.
Ruan, Z., Qiu, M., Xiao, S., He, S., & Thylen, L. (2005). Coupling between plane waves and Bloch waves in photonic crystals with negative refraction. Physical Review B Condensed Matter, 71(4), . https://doi.org/10.1103/PhysRevB.71.045111