Abstract

The resonance effect associated with waveguide gratings is due to coupling between the propagating diffracted waves and the modes of the waveguide. Efficient narrow-line reflective filters can be designed using this principle. These filter elements do not require Bragg conditions or Fabry–Perot resonances for their operation. By identifying the effective waveguide-grating propagation constant, approximate design relations for the resonant filters can be established using the theory of dielectric slab waveguides.¹ In this paper, quantitative description of the parametric resonance regions of slanted and unslanted waveguide grating filters with small modulation will be presented. Expressions for the upper bounds of the filter linewidths are given. The validity of the formulas found is tested with the rigorous coupled-wave theory with respect to the grating modulation amplitude. The polarization characteristics of these structures are discussed. Design examples employing the analytical relations will be presented with final filter characteristics calculated numerically. This work was partly supported by the Texas Advanced Technology Program under grant no. 003656-023 and by the National Science Foundation under grant no. ECS9120856. 1. R. Magnusson and S. S. Wang, Appl. Phys. Lett. 61, 1022 (1992).

© 1993 Optical Society of America