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

Abstract

Abstract Exploiting light’s phase dimension opened multiple avenues in photonics, from phase-contrast microscopy to coherent optical communications. Phase-sensitive measurements usually utilize interferometric techniques to extract the optical phase. However, in some cases, when the feature space of an electromagnetic field is highly degenerate or inherently low dimensional, the vast majority of field distribution parameters, including wavefront, can be extracted from intensity measurements only. But even the fastest of previously published intensity-only methods have too high a computational complexity to be applicable at the speeds used in optical communications and, most importantly, require data from CCD cameras, which are generally very 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. It 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 telecom-grade photodetectors. This opens the avenue for ultra-fast applications of intensity-only mode decomposition methods, including the pulse-to-pulse beam complete characterization of lasers with spatio-temporal modelocking, providing an essential tool for experimental exploration of the modal dynamics in such systems. It can also be applied to ultra-fast sensing in few-mode fibers and for coherent mode division-multiplexed receivers using quadratic detectors only.