Effective Index Method in Modeling of High Index Contrast Planar Photonic Crystals

摘要

In this paper, a novel effective index method for modeling high index contrast planar photonic crystals is introduced. In this effective index method, the frequency axis is divided into many regions, and the effective index for each region is obtained using the central frequency of this region. Dispersion relationship in a wide frequency region can then be calculated using the effective index for each region to obtain the states in this region with a 2-D simulation and integrating all states in all frequency regions. The validity of this effective index method in approximating an intense three-dimensional (3-D) simulation required by the finite thickness of planar photonic crystals with a less intense two-dimensional simulation is examined. As an example, this method is applied to calculate the band diagram of a planar photonic crystal waveguide. By comparing with the results obtained with the full 3D simulation, we find that this method is valid for all states below the light cone in many bands, and the wider the waveguide, the more the number of bands, which agree with the full 3D results.