SCATTERING MATRIX OF THE BIDIRECTIONAL X-COUPLER

Abstract

An analytical model for describing the operation of a fiber-optic X-shaped power divider implemented as a four-port device is presented. The main attention is paid to the construction of a scattering matrix (S-matrix) reflecting the distribution of the optical signal between the input and output ports, taking into account phase shifts, reflection coefficients and losses inside the device. The unitarity conditions of the matrix derived from the law of conservation of energy are considered, which allows us to establish the relationship between the power division coefficients at different ports. The proposed model can serve as a basis for optimizing the characteristics of optical dividers in integrated optical circuits.