COUPLED-MODE THEORY OF RESONANT-GRATING FILTERS

An approximate closed-form expression for the loss in a planar phase g rating is derived by using coupled-mode theory. It is shown that this loss expression can be used to determine the spectral and angular widt h of a resonant-grating filter. A resonant-grating filter is a free-sp ace 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 describe d here, however, gives the resonant-filter width directly, without the need to profile the resonance. Therefore computation time and hence d esign time are reduced. In addition, it is shown that the coupled-mode approach provides physical insights into the factors contributing to filter bandwidth. (C) 1997 Optical Society of America.