Finite-element analysis of disorder effects in photonic crystals

The effects of structural disorder in feature position in finite two-dimensional photonic crystals are studied computationally. Under random variation in feature position some structures are not only resistant to disorder, but also show improved transmittance reduction. This apparent increase in band gap strength can be explained in terms of distributions of point defects within the photonic crystal structure. For certain photonic crystal geometries, point defects lead to scattering that reduces transmittance. Similarly, it is shown that some line defects reduce transmittance by acting as waveguides of a subcritical dimension, inhibiting transmission better than the corresponding perfect photonic crystal structures. The open square lattice photonic crystal structure is examined in depth, and other configurations are examined briefly for comparison. Further calculations on the effects of disorder on waveguide structures show that while the apparent photonic band gap effect may be enhanced by disorder, the waveguide quality is always degraded due to variations in the feature position. Calculations are done using the finite element method to solve the 2-D Maxwell's Equations in the frequency domain.