Bidirectionality in Bianistropic but Reciprocal Photonic Crystals and Its Usage in Active Photonics

We show that the bidirectionality of optical modes exists in general bianisotropic but reciprocal photonic crystals and related structures. Using this property, we obtain an alternative bidirectionality of modes with sources (gain) in active photonic crystals. In the former, we conclude that degeneracies of modes with complex anti-parallel wave vectors are always identical as long as the structure is reciprocal. With the latter, we setup an associated biorthogonality relation in the Rayleigh-Carson form for modes in active photonic crystals.