Optimality of optical forces and torques on nanoparticles via illumination/scattering channels

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 incident field: plane waves, with infinite power, can be decomposed into multipolar orders with finite powers proportional to $\lambda^2$. In this Letter, 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 simplifies the reverse problem: computing optimal "holographic" incident beams, for a fixed collection of scatterers. We analyze structures and incident fields that approach the bounds, which for nonspherical, wavelength-scale bodies show a rich interplay between scattering channels. This framework should enable optimal mechanical control of nanoparticles with light.