Reduced characterization of tunable linear photonic integrated circuits

Tunable linear photonic circuits are important elements in both classical and quantum information technologies. The scaling of such circuits is possible only in the integrated form, which complicates their characterization because of the impossibility of the reconstruction of each element individually. The existing methods of characterization of linear photonic circuits require multiple changes in the phases of transfer matrix elements at various values of control parameters, which provides significant experimental difficulties. In this work, a new approach is proposed: it is demonstrated that the measurement of only transmission coefficients for certain values of the control parameters of the photonic circuit allows the development of a mathematical model that can predicts transmission coefficients for arbitrary values of the parameters. This method has been successfully approved in a numerical experiment for a tunable four-channel interferometer implementing an arbitrary unitary transformation. The proposed method provides new possibilities to efficiently characterize and design tunable linear photonic circuits.