The method of multiple scales is used to develop a procedure for obtaining coupled-mode equations in low-contrast nonlinear photonic crystals periodic in one, two, or three dimensions. Coupled-mode equations for three coupled modes in a two-dimensional (2D) hexagonal lattice are obtained in this way and solved numerically. We show that 2D low-contrast nonlinear photonic crystals support optical...

We present a theoretical analysis of wave propagation in rectangular- and square-lattice photonic crystals by approximating the arbitrary refractive-index function with a staircase profile. This profile has a number of tunable parameters that allow one to fit the band structures of the staircase and the desired structure over a large frequency range. The staircase profile is such that its corre...

A suspension of monodisperse colloids has an interesting property of selfassembling into a three-dimensional ordered structure. This crystalline material has attracted significant interest on the implementation of photonic crystals, which have practical applications in reflectors, filters, resonators, and waveguides. In this thesis, self-assembly of colloidal crystals and photonic crystal techn...

Using the finite-difference time-domain method, based on the numerical simulation of oscillating dipole radiation, we analyze band structures in two-dimensional Kerr-nonlinear photonic crystals. This method is more thorough at calculating band structures in two-dimensional Kerr-nonlinear photonic crystals than approaches proposed earlier. We find that the band structures calculated for both TE ...

I studied experimentally the beam self-collimation and splitting in two-dimensional microwave photonic crystals. Using a microwave photonic crystal fabricated from alumina rods, I present an experimental proof of principle for an earlier theoretical proposal [A. Matthews et al., Opt. Commun. 279, 313 (2007)] of a photonic crystal beam splitter based on the self-collimation effect.

The performance of a polarizing beam splitter based on the one-dimensional photonic crystals (1D-PCs), is theoretically investigated. The polarizing beam splitter consists of a symmetric stack of the low-index quarter-wave plates and the high-index half-wave plates with a central defect layer of air. The linear transmission properties of the polarizing beam splitter are numerically simulat...

We present the use of a liquid crystal spatial light modulator to correct for the refractive-index mismatch induced spherical aberration in a high refractive-index lithium niobate crystal when a low repetition rate amplified laser is used for the direct fabrication of three-dimensional micro-structures. By correcting the aberration based on experimentally determined values, we show that the siz...