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 between centers of adjacent mirrors equals (m+1/2) radians at resonance frequencies m, with m an integer. The mirror reflectances Rj, j= 1, ..., N, are chosen such that the transmittance T() of the filter is 1 at the resonance frequencies, and terms in the power series expansion of T() of order less than ( -m)2(N-1) are eliminated. This ensures that T() 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.
Henry F. Taylor, "Design of Multireflector Resonant Bandpass Filters for Guided Wave Optics," J. Lightwave Technol. 19, 866- (2001)