Spectral properties of multiple grating structures

Spectral characteristics of multiple periodic gratings in planar dielectric waveguides are investigated using a coupled-mode theory. Gratings are modeled as periodic perturbations in the refractive index profile about the core-cladding boundary of the waveguide. Power coupling between the forward and backward traveling fundamental modes are calculated for cascaded gratings with arbitrary lengths and separations but equal periods. It is shown that extremely narrow spectral widths, smaller than 0.1 nm, can be achieved from two or more cascaded gratings. Variations of power reflection coefficient with wavelength are examined for several cases. Applications of these gratings are also addressed.