Inverse design of gradient-index volume multimode converters

TL;DR

This paper introduces a gradient descent-based algorithm for designing 3D graded-index optical devices capable of complex light manipulation, suitable for fabrication with laser manufacturing techniques.

Contribution

It presents a novel computational method for creating 3D graded-index optical elements with smooth refractive index variations for advanced photonic applications.

Findings

Designs successfully perform mode sorting, photonic lantern functions, and beam shaping.

Refractive index variations are within feasible manufacturing ranges.

The approach enables compact, complex 3D optical components.

Abstract

Graded-index optical elements are capable of shaping light precisely and in very specific ways. While classical freeform optics uses only a two-dimensional domain such as the surface of a lens, recent technological advances in laser manufacturing offer promising prospects for the realization of arbitrary three-dimensional graded-index volumes, i.e. transparent dielectric substrates with voxel-wise modified refractive index distributions. Such elements would be able to perform complex light transformations on compact scales. Here we present an algorithmic approach for computing 3D graded-index devices, which utilizes numerical beam propagation and error reduction based on gradient descent. We present solutions for millimeter-sized elements addressing important tasks in photonics: a mode sorter, a photonic lantern and a multimode intensity beam shaper. We further discuss suitable cost functions for all designs to be used in the algorithm. The 3D graded-index designs are spatially smooth and require a relatively small refractive index range in the order of $10^{-2}$, which is within the reach of direct laser writing manufacturing processes such as two-photon polymerization.