A conjugate gradient minimisation approach to generating holographic traps for ultracold atoms

TL;DR

This paper introduces a conjugate gradient minimisation method for generating holograms, offering a versatile and efficient alternative to traditional iterative Fourier transform algorithms, with applications in optical trapping of ultracold atoms.

Contribution

It presents a novel conjugate gradient approach with carefully designed cost functions for hologram generation, improving control and efficiency over existing methods.

Findings

Effective in generating a wide range of light distributions

Can circumvent optical vortex formation during hologram calculation

Applicable to optical trapping of ultracold atoms

Abstract

Direct minimisation of a cost function can in principle provide a versatile and highly controllable route to computational hologram generation. However, to date iterative Fourier transform algorithms have been predominantly used. Here we show that the careful design of cost functions, combined with numerically efficient conjugate gradient minimisation, establishes a practical method for the generation of holograms for a wide range of target light distributions. This results in a guided optimisation process, with a crucial advantage illustrated by the ability to circumvent optical vortex formation during hologram calculation. We demonstrate the implementation of the conjugate gradient method for both discrete and continuous intensity distributions and discuss its applicability to optical trapping of ultracold atoms.