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.
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