Omnidirectional reflection from the one-dimensional photonic crystal containing anisotropic left-handed material

Abstract.

We study the transmission properties in the one-dimensional photonic crystal containing alternate anisotropic left-handed material (LHM) layers and regular isotropic right-handed material (RHM) layers. For such an anisotropic case, the dispersion relation from the Bloch theorem is derived and the Bragg gaps of the periodic structure are observed. It is found that in the m=0 Bragg gap, there is an omnidirectionally reflectional (ODR) region, which is also invariant with a change of scale length, similar with the $\bar{n}=0$ gap in isotropic one-dimensional photonic crystal. With the aid of effective medium theory (EMT), the analytic expressions of all six elements of the effective electric permittivity tensor and magnetic permeability tensor are obtained. By using these results, we investigate the ODR region in the m=0 Bragg gap in all the possible cases of both TE and TM modes. We find that with different choices of parameters, the m=0 Bragg gap has different transmission properties, and the ODR region in it changes, consequently. The edges of the ODR region are given out in these cases. To one's interest, these results predict a complete reflection region in the m=0 Bragg gap, which is able to omnidirectionally reflect waves in both TE and TM modes.