Optimal Nanoparticle Forces, Torques, and Illumination Fields

Abstract

A universal property of resonant subwavelength scatterers is that their optical cross-sections are proportional to a square wavelength, λ 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 incident field: plane waves, with infinite power, can be decomposed into multipolar orders with finite powers proportional to λ 2 . In this article, we identify λ 2 /c and λ 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. Keywords: optomechanics; optical force; optical torque; illumination fields; fundamental limits