Accuracy of linear transformations performed on a nonideal Mach–Zehnder interferometer

Abstract

We consider a mathematical model of a planar Mach–Zehnder interferometer with nonideal beam splitters. For this model, we obtain two fidelity estimates of the matrix–vector multiplication in the form of dependences of the multiplication error on the beam splitting error in directional couplers. The first estimate is obtained as a measure of the difference between the transfer matrices implemented by interferometers and is presented in the form of the norm of the difference between two unitary matrices corresponding to ideal and non-ideal interferometers. The second estimate is obtained as a measure of the difference in output intensities. It is shown that in the latter case the fidelity depends both on the beam splitter error and on the parameters of the input signals. We verified the second estimate using computer simulations of MZI in COMSOL Multiphysics.