  Programmable photonic integrated circuits (PICs), offering diverse signal
processing functions within a single chip, are promising solutions for
applications ranging from optical communications to artificial intelligence.
While the scale and complexity of programmable PICs is increasing, the
characterization, and thus calibration, of them becomes increasingly
challenging. Here we demonstrate a phase retrieval method for programmable PICs
using an on-chip fractional-delay reference path. The impulse response of the
chip can be uniquely and precisely identified from only the insertion loss
using a standard complex Fourier transform. We demonstrate our approach
experimentally with a 4-tap finite-impulse-response chip. The results match
well with expectations and verifies our approach as effective for individually
determining the taps' weights without the need for additional ports and
photodiodes.
