Multi-Degree-of-Freedom Stabilization of Large-Scale Photonic-Integrated Circuits

We present and elaborate the principles of a novelcontrol and calibration(C&C) systematic approach, aiming at feedback stabilization of large scalephotonic-integrated circuits(PIC) to their nominal operating points inD-dimensional spaces of tuning parameters, based on refinement ofextremum-seeking(ES) real-time optimization techniques. The novel methodology enables, in principle, stabilizing a large numberDof tuningdegrees of freedom(DOF) of PICs, with just one optical power monitoring (probe) point. The proposed C&C digital controller ports multidimensional ES stabilization concepts to photonics for the first time and further introduces novel improvements to known ES techniques, proposing a new frame-baseddiscrete-multitonemethod of actuation signals generation and probe signals detection, akin to anorthogonal-frequency-division multiplexingmodulation format. Another novel element is that the iterative digital algorithm adaptively selects between gradient- versus Newton-based descent and between various methods of line search. This approach enables real-time application of unconstrained optimization techniques for C&C of photonic circuits with multiple tuning DOFs. The new technique is exemplified by numeric simulations of the stabilization of a Silicon photonic microring modulator withD= 2 tuning DOFs, concurrently tuning both resonant phase and a second coupling phase parameter, optimizing critical coupling into the microring based on observing the optical power at single low-frequency monitoring point.