Matrix methods for the systematic analysis of fiber optic bidirectional birefringent networks

A great variety of methods for network analysis have been developed both in the frequency domain and in the time domain. The analysis methods in the frequency domain are applicable both to coherent sources as in incoherent sources and they also make the analysis of the most complex structures possible. In this communication several matricial methods in the frequency domain, such as the scattering matrix in conjunction with the graph theory, the Yeh 4 X 4 matrices, and the transfer matrices are introduced and compared. They permit the exact and systematic analysis of the birefringent bi-directional concatenated photonic two- port and four-port networks. This analysis technique has been applied to the design and simulation of the polarization-based in-line wavelength filters made by directional couplers and hi-bi optical fibers, such as all- fiber Fabry-Perot resonators, and Lyot-Ohman, Solc-fan, and Solc-folded all-fiber filters. The use of these matricial analysis methods gives the precise optical spectral response.