To Study the Effect of Grating Length on Propagating Modes in Bragg Filters with AlxGa1-xN/GaN Material Composition

In this paper, the forward and backward propagating modes in an optical waveguide structure namely the fiber Bragg filter also considered as a one dimensional photonic crystal, are analytically computed as a function of grating length for coupled optical modes. AlxGa1-xN/GaN material composition is considered as a unit block of the periodic organization, and refractive index of AlxGa1-xN/GaN is taken to be dependent on material composition, bandgap and operating wavelength following Adachi's model. Expressions of propagating wave are derived using coupled mode theory. Simulated results help us to study the propagation of forward and backward wave propagating modes inside fiber and waveguide devices.Comment: 17 pages,15 figures. This paper is similar except the reflectivity discussion with arXiv:1312.444