Measurement of the radial mode spectrum of photons through a phase-retrieval method

TL;DR

This paper introduces a straightforward phase-retrieval based protocol to accurately measure the radial index of Laguerre-Gaussian modes by transforming them into a fundamental mode compatible with single-mode fibers, enabling efficient radial profile characterization.

Contribution

The authors develop a simple, phase-retrieval based method to determine the radial mode index of LG modes, preserving orthogonality and reducing crosstalk, which improves radial mode characterization.

Findings

Successfully converts high-order LG modes into Gaussian modes for fiber coupling

Achieves high coupling efficiency for transformed radial modes

Protocol is potentially free of mode crosstalk

Abstract

We propose and demonstrate a simple and easy-to-implement projective-measurement protocol to determine the radial index 'p' of a Laguerre-Gaussian (LGlp) mode. Our method entails converting any specified high-order LG0p mode into a near-Gaussian distribution that matches the fundamental mode of a single-mode fiber (SMF) through the use of two phase-screens (unitary transformations) obtained by applying a phase-retrieval algorithm. The unitary transformations preserve the orthogonality of modes and guarantee that our protocol can, in principle, be free of crosstalk. We measure the coupling efficiency of the transformed radial modes to the SMF for different pairs of phase-screens. Because of the universality of phase-retrieval methods, we believe that our protocol provides an efficient way of fully characterizing the radial spatial profile of an optical field.