| This dissertation is concerned with the design of optical waveguide filters for potential application in communication systems. Each filter consists of a single mode waveguide which contains N reflectors separated by a distance L, with N ≥ 2---a multireflector etalon with equal mirror spacing. The transmittance of the etalon is periodic in optical frequency, provided that the reflector dimension DeltaL is infinitesimal. Ideally, the transmittance is 100% within band and 0% out-of-band. The analysis considers both etalons with infinitesimal reflectors and with reflectors of finite extent, for N ≤ 12.; The most challenging aspect of the research is to obtain values for the contradirectional coupling parameters zetaj, j =1,..., N, which provide transmittance spectra which most closely approximate the ideal case described above. Here, zetaj is defined as zetaj = tanh-1 (rj) for discrete reflectors, with rj the amplitude reflection coefficient. For distributed reflectors zeta j = kappajDeltaL, with kappaj the contradirectional coupling constant and DeltaL the extent of the reflector. It is shown that, although the mathematical description for the two cases is very different, the transmittance spectra for a given set of the zetaj's are the same in the limit that DeltaL → 0. For the discrete analysis, the two independent variables are N and Z, with Z = j=1N zj . For distributed reflectors, an additional independent variable F, given by F = DeltaL/L, must also be specified. The zetaj's corresponding to different filter designs, calculated by an iterative technique, are compiled in tabular form. Polynomial coefficients for calculating the zeta j's from a fitted curve are also given. Transmittance spectra for representative designs are plotted, as are the corresponding dispersion spectra.; For the case of infinitesimal reflectors, the calculated transmittance spectra are periodic in optical frequency, approaching the ideal more closely as N increases, while the width of the transmittance peaks decreases with increasing Z. For coupling regions of finite extent, the transmittance is still 100% at the center of the central peak, but the transmittance spectra are no longer periodic and the transmittance minima increase with separation from the central peak. |
