# Eigenmode beam optimisation for optical micro-manipulation

## TL;DR

This paper introduces an eigenmode-based method for optimizing optical trapping beams in micro-manipulation, leveraging Mie scattering theory to identify the best beam profiles for specific particle and system parameters.

## Contribution

It presents a novel application of optical eigenmodes combined with Mie scattering theory to optimize beam profiles for micro-manipulation tasks.

## Key findings

- Eigenmodes provide a natural basis for describing momentum transfer.
- The method allows for the calculation of optimal trapping beams for different parameters.
- The approach enhances the efficiency and stability of optical micro-manipulation.

## Abstract

Optical micro-manipulation and trapping of micro-particles delivers a mechanical system in direct interaction with a beam of light. In this interaction, the optical properties such as polarisation, beam profile and wavelength of the trapping beam are important. Different beams are associated with different momentum transfer, trap stiffness and stabilisation properties, for example. One method to determine the best beam profile is through the use of the optical eigenmode approach. To use this method, we employ Mie scattering theory which enables the exact determination of the scattered field as a function of the incident field. More precisely, this approach allows us to calculate the Hermitian relationship between the incident field and the optical forces acting on the scattering objects. This Hermitian relationship defines also a set of orthogonal optical eigenmodes which deliver a natural basis to describe momentum transfer in light-matter interactions. This relationship defines also a set of orthogonal optical eigenmodes. Using these modes it is possible to define, for each numerical aperture, particle size or geometry, the optimal trapping beam.