Power monitoring in a feedforward photonic network using two output detectors

Programmable feedforward photonic meshes of Mach-Zehnder interferometers are computational optical circuits that have many classical and quantum computing applications including machine learning, sensing, and telecommunications. Such devices can form the basis of energy-efficient photonic neural networks, which solve complex tasks using photonics-accelerated matrix multiplication on a chip, and which may require calibration and training mechanisms. Such training can benefit from internal optical power monitoring and physical gradient measurement for optimizing controllable phase shifts to maximize some task merit function. Here, we design and experimentally verify a new architecture capable of power monitoring any waveguide segment in a feedforward photonic circuit. Our scheme is experimentally realized by modulating phase shifters in a 6 x 6 triangular mesh silicon photonic chip, which can non-invasively (i.e., without any internal "power taps ") resolve optical powers in a 3 x 3 triangular mesh based on response measurements in only two output detectors. We measure roughly 3% average error over 1000 trials in the presence of systematic manufacturing and environmental drift errors and verify scalability of our procedure to more modes via simulation.