Sparse intensity sampling for ultrafast full-field reconstruction in low-dimensional photonic systems.

Phase-sensitive measurements usually utilize interferometric techniques to retrieve the optical phase. However, when the feature space of an electromagnetic field is inherently low dimensional, most field parameters can be extracted from intensity measurements only. However, even the fastest of the previously published intensity-only methods have too high a computational complexity to be applicable at high data rates and, most importantly, require data from CCD cameras, which are generally slow. This paper shows how a few intensity measurements taken from properly placed photodetectors can be used to reconstruct the complex-valued field fully in systems with low-dimensional feature space. The presented method allows full-field characterization in few-mode fibers and does not employ a reference beam. This result is 3 orders of magnitude faster than the fastest previously published result and uses 3 orders of magnitude fewer photodetectors, allowing retrieval of mode amplitudes and phases relative to the fundamental mode using only several photodetectors. This approach enables ultrafast applications of intensity-only mode decomposition method, including pulse-to-pulse laser beam characterization, providing an essential tool for experimental exploration of the modal dynamics in spatiotemporal modelocked systems. It can also be applied to ultrafast sensing in few-mode fibers and for coherent mode division-multiplexed receivers using quadratic detectors only.