Photonic properties of two-dimensional high-contrast periodic structures: Numerical calculations

The photon properties of two-dimensional periodic structures formed by infinite homogeneous dielectric cylinders packed in a square lattice have been investigated theoretically. Depending on the dielectric contrast between the cylinders and the surrounding medium, the photonic band structure, transmission spectra of crystals with a finite number of layers, and spectra of Mie scattering by an isolated cylinder have been calculated. The calculations have been performed for the TE polarization. The transformation of photonic stop-bands corresponding to Bragg and Mie resonances has been analyzed using the obtained data. The main effect consists in “castling” energy positions of the Bragg stop-bands and Mie stop-bands. For low-contrast photonic crystals, the low-frequency region of the energy spectrum is determined by Bragg stop-bands, and Mie stop-bands are located higher in energy. With an increase in the dielectric contrast, the energy of Mie stop-bands decreases, and they intersect the region of Bragg stop-bands weakly varying in the TE polarization and form the low-energy region of the spectrum.