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 φ between centers of adjacent mirrors equals (m+1/2)π radians at resonance frequencies ν_m, with m an integer. The mirror reflectances R_j, j=1,…,N, are chosen such that the transmittance T(ν) of the filter is 1 at the resonance frequencies, and terms in the power series expansion of T(ν) of order less than (ν-ν_m)^2(N-1) are eliminated. This ensures that T(ν) 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