Synthesis of coherent two-port lattice-form optical delay-line circuit

A method is presented for synthesizing a coherent two-port lattice-form optical delay-line circuit that is composed of optical delay lines, directional couplers, and phase shifters. The two bases of the method are the use of a unimodulus para-unitary matrix as a transfer matrix and the division of the transfer matrix into basic component transfer matrices. We succeeded in obtaining a set of recurrent equations with which to calculate circuit parameters to use for designing an optical delay-line circuit with a desired cross-port (through-port) transfer function. In the developed method, it is shown that two-port optical delay-line circuits can have the same transmission characteristics as finite impulse response digital filters with complex expansion coefficients. Three synthesis examples for optical frequency filters are described: a linear-phase Chebyshev filter, a multi-channel selector, and a group-delay dispersion equalizer. It is confirmed that transmission characteristics with a maximum transmittance of 100% can be always synthesized. The allowable parameter error for the synthesized linear-phase Chebyshev filter is also discussed