Characterization of Finite Photonic Crystals with Defects

A simple computational approach is proposed to obtain the dispersion characteristics that could be observed outside of general finite-extent photonic crystals with defects. Since introducing and tailoring defects in photonic crystals are crucial for designing practical devices, the proposed method may play an important role in characterization and optimization of such defects. The method uses reflection data, due to an incident plane wave at a given frequency, collected at the front interface of a photonic crystal. It is simple and applicable for general photonic crystals, that is, photonic crystals with any periodicity, 1D, 2D, and 3D, and even with any kind of defects. The validity of the method was tested and verified on 1D and 2D finite photonic crystals, for which the reflection coefficient data at the front interface can be easily obtained by analytical means and numerical simulations, respectively. In addition, different types of defects, like random and periodic defects, were studied and it has been shown that the method is capable of providing information pertinent to the outside world on the defect modes.