The Optimization of a Woodpile Photonic Crystal and its Negative Refractive Behavior

Abstract

In this paper, three-dimensional woodpile photonic crystals (PhCs) are investigated for various applications. In order to obtain PhCs with maximal photonic band gap, we optimize the size of 3D woodpile PhC by employing design of experiments. From the response surface model, which is a function of geometric design parameters, the photonic band gap is readily predicted, and the size ratios can be optimized. In addition, the PhC exhibits a negative refractive behavior due to its highly-anisotropic and wavelength-dependent dispersion properties. In order to predict the refracting angles of light inside the PhG, we investigate equi-frequency surfaces throughout the Brillouin zone. To verify that the refracting angles from the band structure calculation are reasonable, we perform finite, difference time domain (FDTD) simulations. The tendency of the refracting angle with respect to wavelength and incident angle is examined by showing the wave propagation inside the PhC come from the FDTD simulations.