Efficient beaming of self-collimated light from photonic crystals

Abstract

In this thesis, we have studied highly efficient beaming of self-collimated light from two-dimensional photonic crystals. From the calculations using the plane wave expansion and the finite-difference time-domain methods, we obtain the emission properties such as the spatial distributions of the electric fields and the transmission coefficients of power as a function of the distance of beam propagation as well as the angular distributions of power transmitted. We show that both enhanced transmission and highly directional emission of self-collimated beams from photonic crystals are achieved by using the bending and splitting of self-collimated beams in photonic crystals, and also by introducing an antireflection coating-like photonic crystal collimator to the exit surface of the structure. We also have investigated the device sensitivity to the transverse alignment error and the tilt error of the ARC-like PC collimator. We consider two-dimensional square lattice photonic crystals consisting of dielectric rods in air and restrict our consideration to the case of the TE modes (the electric field parallel to the rod axis). The dielectric constant and the radius of rods in PC 1 and 2 are $\epsilon = 12.0$ and $\it{r} = 0.35 a$, respectively. Here $\it{a}$ is the lattice constant of PC 1 and 2. The frequencies of self-collimated light beams which propagate along the $\Gamma \textrm{M}$ direction, around $\it{f} = 0.194 \it{c/a}$ are obtained from the equifrequency contours in the first band of PC 1 and 2. To improve the power transmission via the optimal minimization of the impedance mismatch between the photonic crystals and air, we have introduced the antireflection coating structures composed of the smaller surface rods which are of the radius $r_s = 0.2054 \it{a}$ and of the distance $d_s = 0.748 \it{a}$ at the end surfaces of the photonic crystals. We have carried out three kinds of studies for achieving highly efficient beaming of self-collimated light...