Coupled-mode theory of resonant-grating filters

An approximate closed-form expression for the loss in a planar phase grating is derived by using coupled-mode theory. It is shown that this loss expression can be used to determine the spectral and angular width of a resonant-grating filter. A resonant-grating filter is a free-space optic that takes advantage of grating resonances to create narrow-band reflection peaks. Design characteristics, such as bandwidth, have previously been determined by profiling the resonance in reflectivity with the use of numerically intensive vector-diffraction methods such as rigorous coupled-wave analysis. The coupled-mode approach described here, however, gives the resonant-filter width directly, without the need to profile the resonance. Therefore computation time and hence design time are reduced. In addition, it is shown that the coupled-mode approach provides physical insights into the factors contributing to filter bandwidth.