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In this paper, we have studied the photonic band structure of function photonic crystals in which the dielectric constant of the scattering centers (rods) is a function of space coordinates. The under-studied lattice is hexagonal and cross section of rods has a circular symmetry embedded in the air background. Photonic band structures for both electric and magnetic polarizations of the electromagnetic waves are calculated. The obtained results show the existence of the forbidden frequency region (photonic band gap). It is considered that the dielectric rods are made of the Kerr type materials. Therefore, by considering different distributions of light intensity, different function forms will be obtained for the dielectric constants of rods, which are called function photonic crystals. The influence of the function coefficient (corresponding to the Kerr coefficient) on photonic band structures has been theoretically investigated. The results show that the width and number of photonic band gaps are more controllable than the conventional photonic crystals. These results can be very useful in designing the optical devices.

Using the Dirichlet-Neumann mapping method, we were able to calculate the photonic band structure of the annular metal photonic crystals. The surveyed grid is square and scattering centers (bars) are in the form of air rings located on the metal surface, as well as metal rings located in the air. The photonic band structure is calculated for both polarizations E and H for electromagnetic waves. The results indicate that there are frequency bands (photon strips) plus flat bands at low light speeds. The effect of the size of the air and metal rings on photonic tape structures has been theoretically investigated

In this paper we studied the focusing effect of electromagnetic wave in the two-dimensional graded photonic crystal consisting of Silicon rods in the air background with gradually varying lattice constant. The results showed that graded photonic crystal can focus wide beams on a narrow area at frequencies near the lower edge of the band gap, where equal frequency contours are not concave. For calculation of photonic band structure and equal frequency contours, we have used plane wave expansion method and revised plane wave expansion method, respectively. The calculation of the electric and magnetic fields was performed by finite difference time domain method.

In this paper, using plane ware expansion method the polarization-dependent band structures are investigated in two dimensional photonic crystal waveguide with a square lattice composed of GaAs elliptic elements in air background. Then, the changes of the band structure with changing ellipticity of the elliptic elements are discussed. It is observed that by increasing the ellipticity of elements the size of the photonic band gap and the guiding eigen frequency will increase

In this paper the effect of photonic band gap on the group velocity of reflected pulse from a dielectric slab doped with two-level or three-level atoms has been investigated. It is assumed that the slab is sandwiched between a uniform medium (like vacuum) and a one-dimensional photonic crystal. It is shown that the reflected pulse from the slab doped with two-level (three-level) atoms will be superluminal (subluminal) if the carrier frequency of the incident Gaussian pulse is in the photonic band gap. In contrast, for the incident pulse with the carrier frequency at the edge of photonic band gap, the reflected pulse from the slab doped with two-level (three-level) atoms is subluminal (superluminal).