Band Structure for a One-dimensional Photonic Crystal

Photonic Crystals, also known as Photonic Band Gap materials, are periodic dielectric structures that forbid propagation of EM waves in a certain frequency range defining forbidden frequency bands. The ability of PCs to control the light with amazing way gives rise to distinct optical phenomena offering a rich background for both theoretical and experimental research. The 1D periodic system is explained in terms of a generalized analytical expression for the transmission coefficient through N unit cells involving the Chebyshev polynomial of second kind using the time reversal symmetry through the transfer matrix method. Propagation of EM waves in the superlattice structure consisting of alternating plasma and dielectric material, is studied for normal and oblique incidence. The results of PBG characteristics are discussed in terms of plasma density, plasma width, incident angle and number of unit cells. Complete photonic band gaps are found in 1D ternary photonic crystals composed of an ordinary dielectric and single negative metamaterials.