Influence of Kerr nonlinearity on the band structures of two-dimensional photonic crystals

Dynamic modifications of the band structures of two-dimensional photonic crystals composed of Kerr-nonlinear dielectric rods in air forming hexagonal, square and honeycomb lattices are investigated. Calculations are carried out by the method based on the finite-difference time-domain (FDTD) technique for both TM and TE polarizations. The bands in all cases are observed to red-shift with the introduction of nonlinearity. Inspection of the variation of the mid-gap frequencies with source intensity reveals that the red-shift increases as gap number increases, in a manner proportional to the mid-gap frequency in linear regime. The red-shift of mid-gap frequencies is also found to follow the adopted saturable model for the change of relative permittivity with source intensity. Either the so-called dielectric or the air band edges of the gaps are found to be more sensitive to nonlinearity resulting in broadening or shrinking of the gaps. Possible utilizations of the present observations for all-optical device applications, such as wavelength multiplexing, are discussed.