The Photonic Band Structure

In this paper, firstly, eigenvalue equations of 2D and 3D in plane wave method are obtained. Secondly, program is written to solve the equation of 2D. Finally, two-dimensional square lattice photonic crystal behaving in the electromagnetic zones is fabricated and the transmission spectra of the photonic crystal with and without defects were measured.The results of caculations are:(1) Photonic band gap tend to appear in triangular lattices rather than square lattices. And complete band gap(the band gap for both polarizations overlaps) can be obtained if proper parameters are selected.(2) At a fixed filling factor, the lager the difference of the two dielectric constants is ,the wider the band gap will be.(3) At fixed dielectric constants and crystal lattice constant, firstly, the larger the filling factor is , the lower the band will be. Secondly, the widest band gap appears at optimal filling factor, but the optimal filling factor is different for the two polarizations.Experiment shows that band gap really exists in the fabricated 2D square lattices photonic crystal. And defect states appears when several cylinders are removed.