The equivalent structure and some optical properties of the periodic-defect photonic crystal

Abstract

The concept of the effective medium is used to deal with problems of defects in photonic crystals (PhCs) throughout this paper. First, scattering phenomena in PhCs with defects are investigated and can be very well replaced by those in an effective medium with effective defects in interesting frequency region. It is based on the fact that the Bloch wave in the defect-free PhC very approximates to the wave in the effective medium. Then a periodic-defect PhC created by adding periodic defects into the defect-free PhC is proposed. It can be replaced with an effective PhC by utilizing the concept of effective periodic defects embedded into an effective medium. We verify the equivalence between the periodic-defect PhC and the effective PhC by comparing their photonic band structure (PBS) and photonic band gaps (PBGs) as well as transmissions. Next, the effective PhCs instead of the periodic-defect PhCs are used to investigate the variance of the PBGs by applying different periodic defects. The substitution allows us successfully predicting the negative refraction in the periodic-defect PhC through the PBS of the effective PhC. Finally, the field distributions and Fourier coefficients of waveguide modes in the effective PhC and the periodic-defect PhC are equivalent by the supercell method confirmations. (C) 2011 American Institute of Physics. [doi:10.1063/1.3567296]