Scattering-matrix analysis of periodically patterned multilayers with asymmetric unit cells and birefringent media

The paper deals with a theoretical analysis of two-dimensional photonic crystals realized in multilayer structures composed of anisotropic media. Fourier analysis has been successfully applied before to study optical properties of photonic crystal structures, usually composed of optically isotropic media. In a commonly used formulation [D. M. Whittaker and I. S. Culshaw, Phys. Rev. B 60, 2610 (1999)], inversion symmetry of the unit cell is required. Here, we extend the treatment of Whittaker and Culshaw to structures with asymmetric unit cells that can be composed of birefringent media. As applications we consider a high-refractive-index membrane with a triangular lattice of triangular holes, where the presence of a TE-like gap at omega and of a TM-like gap at 2*omega is established, and a slot waveguide made of birefringent porous silicon, where coupling of guided modes to radiative modes is achieved through a one-dimensional periodic grating. Interesting applications may arise when, e.g., birefringent liquid crystals are infiltrated in photonic media and controlled by an external electric field for optical switching purposes. The work arises from a collaboration between the theoretical groups at the University of Pavia and the University of Toronto.