Focal-plane wavefront sensing with photonic lanterns: theoretical framework

The photonic lantern (PL) is a tapered waveguide that can efficiently couple light into multiple single-mode optical fibers. Such devices are currently being considered for a number of tasks, including the coupling of telescopes and high-resolution, fiber-fed spectrometers, coherent detection, nulling interferometry, and vortex-fiber nulling. In conjunction with these use cases, PLs can simultaneously perform low-order focal-plane wavefront sensing. In this work, we provide a mathematical framework for the analysis of a PL wavefront sensor (PLWFS), deriving linear and higher-order reconstruction models as well as metrics through which sensing performance—in both the linear and nonlinear regimes—can be quantified. This framework can be extended to account for additional optics such as beam-shaping optics and vortex masks, and can be generalized for other wavefront sensing architectures. Finally, we provide initial numerical verification of our mathematical models by simulating a six-port PLWFS. In a forthcoming companion paper (Lin and Fitzgerald), we provide a more comprehensive numerical characterization of few-port PLWFSs, and consider how the sensing properties of these devices can be controlled and optimized.