Periodic gratings in waveguides act as frequency selective mirrors making them very useful as spectral filters for wavelength division multiplexing applications and as end mirrors for narrow linewidth lasers. A study of the spectral characteristics of both single and double gratings in planar dielectric waveguides is presented. The analysis of light propagation in a planar dielectric waveguide with sinusoidal boundary perturbations is carried out using coupled-mode theory. Power reflection and transmission coefficients are calculated for single gratings as well as two gratings of the same period and depth but arbitrary lengths and separated by a specified distance. The spectral response is examined for several cases. The influence of grating period, depth, and length in the single-grating case as well as separation of the gratings in the case of a double grating is investigated. Numerical results for example cases are presented. The results of this study are valuable for designing grating devices which are becoming increasingly attractive to broadband fiber-optic communication systems. / Master of Science