“…The optimal radius of the air column is r=0.21a, where a is the lattice constant. Once the external dc magnetic field is applied along the axis of the air column, the semiconductor becomes gyroelectrically anisotropic, whose (relative) permittivity has the form of [16,18,20] i i (where N, e, and m * are the density, charge and effective mass of the free carriers, respectively, and ε 0 is the vacuum permittivity) is the bulk plasma frequency, ν is the scattering frequency, eB m c 0 * w = / is the cyclotron frequency, and ε ∞ is the highfrequency (relative) background permittivity of the semiconductor. To analyze the dispersion properties of PhC as well as its edge mode, the semiconductor is first assumed to be lossless (i.e., v 0 = ), in order to distinguish the propagating mode (with real propagation constant) from the evanescent mode (with a complex propagation constant).…”