Propagation of self-collimated lights in two-dimensional photonic crystals

Abstract

In this thesis, we present a study on the propagation of self-collimated beams in two-dimensional photonic crystals for the future applications to implement photonic integrated circuits based on the self-collimation effect. We analyze the equifrequency contours of a two-dimensional square lattice photonic crystal which is composed of dielectric rods with the dielectric constant $\epsis = 12$ and the radius $\it{r} = 0.35 a$. Lights of frequencies around $\it{f} = 0.194 \it{c/a}$ have flat equifrequency contours and thereby can exhibit self-collimation phenomenon when they propagate along the (11) direction of square lattice. Finite-difference time-domain simulations demonstrate that self-collimated beam can be well guided in photonic crystals without the use of any physical boundary. Bending and splitting of self-collimated beams are investigated. From the equifrequency contour analysis, we find that the concept of total internal reflection at the interfaces between two dielectrics can be also applied to the interfaces between two-dimensional photonic crystals and air. We show that a line-defect created by removing a few rods in a row can totally reflect the incoming self-collimated beams. Also a line-defect created by reducing the radius of rods in a row gives rise to the splitting of self-collimated beams. Moreover, the power ratio between two split self-collimated beams can be controlled systematically by varying the radii of rods in the line-defect. It is shown that self-collimated beams can be effectively routed by employing the line-defect mirrors and beam splitters. We propose a method to design antireflection structures to minimize the reflection of light beams at the interfaces between a two-dimensional photonic crystal and a homogeneous dielectric. The design parameters of the optimal structure to give zero reflection can be obtained from the one-dimensional antireflection coating theory and the finite-difference time-domain simulations....