Design of multireflector resonant bandpass filters for guided wave optics

A design algorithm for ripple-free flat-top bandpass filters in optical waveguides containing N equally spaced, lossless mirrors is described. The algorithm assumes that the propagation phase shift /spl phi/ between centers of adjacent mirrors equals (m+1/2)/spl pi/ radians at resonance frequencies /spl nu//sub m/, with m an integer. The mirror reflectances R/sub j/, j=1,...,N, are chosen such that the transmittance T(/spl nu/) of the filter is 1 at the resonance frequencies, and terms in the power series expansion of T(/spl nu/) of order less than (/spl nu/-/spl nu//sub m/)/sup 2(N-1)/ are eliminated. This ensures that T(/spl nu/) approaches an ideal rectangular profile with increasing N, as illustrated by calculated transmittance spectra for N=2, 4 and 6. The dispersion of these multimirror etalons has also been explored. For the higher N values, it is found that the group refractive index is a minimum at the resonance frequencies, in contrast to the case N=2 for which the group index is a maximum at the resonances.