Optimal nanoparticle forces, torques, and illumination fields

TL;DR

This paper develops a theoretical framework to determine the maximum optical forces and torques on nanoparticles, identifies fundamental constants related to these forces, and explores optimal illumination fields for controlling nanoparticle mechanics.

Contribution

It introduces a quadratic scattering-channel framework for upper bounds on optical forces and torques, and computes optimal holographic incident beams for nanoparticle manipulation.

Findings

Maximum cross-sections proportional to λ^2 for resonant scatterers.

Derived λ^2/c and λ^3/c as force and torque constants.

Spherical symmetry limits reaching force/torque bounds.

Abstract

A universal property of resonant subwavelength scatterers is that their optical cross-sections are proportional to a square wavelength, $\lambda^2$, regardless of whether they are plasmonic nanoparticles, two-level quantum systems, or RF antennas. The maximum cross-section is an intrinsic property of the \emph{incident field}: plane waves, with infinite power, can be decomposed into multipolar orders with finite powers proportional to $\lambda^2$. In this Article, we identify $\lambda^2/c$ and $\lambda^3/c$ as analogous force and torque constants, derived within a more general quadratic scattering-channel framework for upper bounds to optical force and torque for any illumination field. This framework also solves the reverse problem: computing globally optimal "holographic" incident beams, for a fixed collection of scatterers. We analyze structures and incident fields that approach the bounds, which for wavelength-scale bodies show a rich interplay between scattering channels, and we show that spherically symmetric structures are forbidden from reaching the plane-wave force/torque bounds. This framework should enable optimal mechanical control of nanoparticles with light.