Optical devices based on self-collimation phenomenon in two-dimensional photonic crystals

Abstract

In this study, we suggest two types of optical filters based on the self-collimation phenomenon in two-dimensional photonic crystals (2D-PCs). The PC structure considered in this study is a square array of circular alumina rods with the radius $\It{r} = 2 mm, the lattice constant $\It{a}$ = 5 mm, and the dielectric constant of $\epsilon \appprox$ 9.7. In this square lattice PC lights of frequencies around $\It{f}$ = 12.50 GHz have flat equi-frequency contours and thereby can exhibit self-collimation phenomenon when they propagate along the (11) direction of the lattice. The finite-difference time-domain simulations and also the experimental measurements demonstrate that the self-collimated beam can propagate without spread in PCs. The measured transmissions are compared with the experimental results in microwave range. We have carried out three kinds of studies for achieving optical filters based on self-collimation phenomenon in 2D-PCs. First, the bending and splitting of the self-collimated beams are investigated. From the equi-frequency 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 the 2D-PCs and air. A line-defect created by removing a few rods in a row can totally reflect the incoming self-collimated beams. Using this method line-defect mirrors can be realized and we can effectively bend the self-collimated beams. Also a line-defect created by reducing the radius of defect rods in a row gives rise to the splitting of the self-collimated beams. Besides, the power ratio of two split self-collimated beams can be controlled systematically by changing the radii of rods in the line-defect. We also show that the self-collimated beams can be effectively steered by employing the line-defect mirrors and beam splitters. Second, we study the Goos-H$\ddot{a}nchen (GH) shift which is a small shift in the plane containing the incident and reflected beams wh...