Photonic Crystal Wave guides
The wave propagation in or along periodic structures such as photonic crystal waveguides produces many interesting features that are absent for uniform structures. These features can then provide large variety of applications ranging from integrated optics [1–3], microwave filters and gratings , and DFB lasers  in the early 1970s to the study of photonic band gap structures and photonic crystals in the late 1980s [5–7] and artificial metamaterial in the middle 2000s, to name a few. The first comprehensive study of wave-propagation in periodic structures was done by Brillouin  in 1953. Tamir et al. in 1964  provided the complete exact solution to the case of TE wave propagation in a sinusoidally stratified (periodic) dielectric medium. In 1965, Yeh et al.  gave the complete exact solution to the case of TM wave propagation in a sinusoidally stratified (periodic) dielectric medium. Casey et al.  also found the exact solution for the case of wavepropagation in a sinusoidally varying plasma medium. Elachi and Yeh in 1973  gave a formal solution to the problem of wave propagation along a periodic dielectric waveguide.
KeywordsDispersion Relation Photonic Crystal Periodic Structure Dielectric Medium Stop Band
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