Reconstruction of the transfer matrix for tunable linear-optical chips without need to measure the phases of the matrix elements

Tunable linear-optical interferometers are a key element of both classical and quantum information systems. During the manufacturing process, these interferometers are subject to various instrumental imperfections that are inevitably introduced. In this way actual chip's transfer matrix can deviate form the expected one. It is therefore crucial to be able to reconstruct the transfer matrix of a fabricated chip for each set of control signals applied to chip’s optical modulators. Existing methods for reconstructing tunable linear-optical interferometers require measuring the phase of chip’s transfer matrix elements at different values of control signals. This is a complex and time-consuming experimental procedure. However, in the method we propose here, it’s possible to construct a mathematical model that predicts the transfer matrix for a tunable linear-optical chip at any values of the control signals, based on measurements of the transmission coefficients of the chip only. Our method was successfully verified numerically on the example of linear-optical chips 4x4 based on the universal Clements and mixing layers architectures. In the case of a chip 4x4 based on the mixing layers, the method was experimentally tested with an average reconstruction fidelity of 96.78%.