Focal-plane wavefront sensing with photonic lanterns I: theoretical framework

TL;DR

This paper develops a mathematical framework for photonic lantern wavefront sensors, enabling analysis and optimization of their performance in various optical applications, including telescope coupling and nulling interferometry.

Contribution

It introduces a comprehensive theoretical model for PLWFS, including linear and nonlinear reconstruction methods, and demonstrates initial numerical verification.

Findings

Framework allows performance quantification in linear and nonlinear regimes

Numerical simulations validate the theoretical models

Framework adaptable to additional optical components

Abstract

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 (VFN). 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 the photonic lantern wavefront sensor (PLWFS), deriving linear and higher-order reconstruction models as well as metrics through which sensing performance -- both in 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 is generalizable to other wavefront sensing architectures. Lastly, we provide initial numerical verification of our mathematical models, by simulating a 6-port PLWFS. In a companion paper, 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.