Maximally localized modes of a multimode fiber

TL;DR

This paper introduces an optimization technique to find highly localized modes in multimode fibers, revealing spontaneous organization into concentric rings and enabling targeted mode bundle design.

Contribution

It develops a novel method to identify maximally localized fiber modes and demonstrates their spontaneous organization and customizable bundle geometries.

Findings

Modes organize into concentric rings without geometric constraints.

Spot sizes and ellipticities vary predictably across rings.

The method enables designing mode bundles with specific geometries.

Abstract

This article presents an optimization method to find the most spatially concentrated basis of a multimode fiber, obtained by minimizing the sum of the spatial spreads of the individual modes over all unitary transformations of a given orthonormal mode set. The resulting modes are the optical analogue of maximally localized Wannier functions in solid-state physics. We apply the method to the Laguerre-Gaussian basis of a graded-index fiber for mode counts ranging from 6 to 55. In all cases, the modes spontaneously organize into concentric rings without any geometric constraint being imposed. The spot sizes and ellipticities evolve from one ring to the next in ways that geometric packing approaches cannot predict. For large mode counts, the optimizer finds solutions where neither the number of spots per ring nor the spots within a given ring follow a regular pattern, indicating that the fully symmetric arrangement is no longer a minimum of the spread functional. A constrained variant of the method enables the optimizer to target any prescribed bundle geometry while quantifying its localization cost, opening a route to physically grounded photonic lantern design.