• Anisotropic left-handed materials;
  • wave propagation;
  • left-right coupling;
  • helicity inversion.


Some physically interesting properties and effects (including the quantum effects) of wave propagation in biaxially anisotropic left-handed materials are investigated in this paper: (i) we show that in the biaxially gyrotropic left-handed material, the left-right coupling of circularly polarized light arises due to the negative indices in permittivity and permeability tensors of gyrotropic media; (ii) it is well known that the geometric phases of photons inside a curved fiber in previous experiments often depend on the cone angles of solid angles subtended by a curve traced by the direction of wave vector of light, at the center of photon momentum space. Here, however, for the light propagating inside certain anisotropic left-handed media we will present a different geometric phase that is independent of the cone angles; (iii) the extra phases of electromagnetic wave resulting from the instantaneous helicity inversion at the interfaces between left- and right-handed (LRH) media is also studied in detail by using the Lewis-Riesenfeld invariant theory. Some interesting applications (e.g., controllable position-dependent frequency shift, detection of quantum-vacuum geometric phases and helicity reversals at the LRH interfaces etc.) of above effects and phenomena in left-handed media is briefly discussed.