“…We consider a simple two-phase photonic crystal that consists of a homogeneous anisotropic dielectric matrix containing 1.5mm holes, periodically spaced 4mm apart in both the x 1 -and x 2 -directions. Using thermoplastic co-extrusion fabrication or other methods, low-loss dielectric composites of various degrees of anisotropy can be fabricated; see, e.g., (Zhang et al 2008), (Wing et al 2006). Here, for illustration, we use a matrix with dielectric constants of M I = 9.6 and M II = 90, where the superimposed M denotes the matrix dielectric tensor.…”