Design and spectral characteristics of multireflector etalons

A numerical technique for analyzing multireflector optical resonators with an arbitrarily large number of mirrors is applied to the design of ripple-free, flat-top bandpass filters. The algorithm determines unique values for the mirror reflectances R_j, j=1,...,N, subject to a constraint on a contradirectional coupling strength parameter Z defined as Z=σ_j=1^Nζ_j with ζ_j=tanh^-1(√R_j). The method is applied to the design of resonators with N as high as 12. Transmittance and dispersion spectra are presented for two cases that represent relatively weak and relatively strong contradirectional coupling. These spectra illustrate that, for a fixed -20-dB width of the transmittance spectrum, the -3-dB spectral widths increase monotonically with N, while the central portion of the group refractive-index spectrum becomes flatter and wider as N increases. These designs are compared with those obtained using a Chebyshev formula to determine the mirror reflectances. Application of these multireflector resonators as bandpass filters, slow-wave electrooptic modulators, and nonlinear optical devices are discussed.