Photokinetic analysis of the forces and torques exerted by optical tweezers carrying angular momentum

Abstract

The theory of photokinetic effects expresses the forces and torques exerted by a beam of light in terms of experimentally accessible amplitude and phase profiles. We use this formalism to develop an intuitive explanation for the performance of optical tweezers operating in the Rayleigh regime, including effects arising from the influence of light's angular momentum. First-order dipole contributions reveal how a focused beam can trap small objects, and what features limit the trap's stability. The first-order force separates naturally into a conservative intensity-gradient term that forms a trap and a non-conservative solenoidal term that drives the system out of thermodynamic equilibrium. Neither term depends on the light's polarization; light's spin angular momentum plays no role at dipole order. Polarization-dependent effects, such as trap-strength anisotropy and spin-curl forces, are captured by the second-order dipole-interference contribution to the photokinetic force. The photokinetic expansion thus illuminates how light's angular momentum can be harnessed for optical micromanipulation, even in the most basic optical traps.This article is part of the themed issue 'Optical orbital angular momentum'.

Optical orbital angular momentum

“…The generation of beams with OAM directly from lasers is the topic of the next paper [49]. Light carrying OAM has found a number of practical applications and we have papers describing two of these: the forces and torques induced by them [50] and the use of OAM in microscopy [51].…”

Kerker‐Type Intensity‐Gradient Force of Light

“…Additionally, because its curl ∇ × F r (Ki) ∝ ∇cos2 θ × ∇ I does not vanish in general, F r (Ki) represents a nonconservative mechanical property of the intensity gradients. In this connection, one may note that nonconservative optical forces are usually associated with the curl of spin or phase gradient of light …”

Tailoring Optical Gradient Force and Optical Scattering and Absorption Force

“…Based on a previously derived multipolar expression for optical forces acting on a spherical particle 19 , 36 , 47 , we derived in the supplemental material the analytical expression of F g and F k for the first few leading multipoles: where α′ , β ′, γ ′, γ ′ m , Ω′ and α ″ are the multipole moments obtainable from Mie theory and are tabulated in the supplemental material, k is the wavenumber, a is the particle radius, and E in and B in are the arbitrary incident electromagnetic fields. In principle, one may keep adding higher order terms (such as octopole moment and beyond) into the multipole expansion to derive more accurate expression, but in practice the mathematics can be prohibitive, especially when Toroidal moments are involved.…”

“…It has been fruitfully applied in a broad variety of areas, not only spanning the traditional scientific fields, but also in more applied fields 1 – 10 . It is customary and useful to theoretically split the optical force as F = F g + F k , where F g is the (conservative) gradient force and F k is the (non-conservative) scattering and absorption force 1 , 11 – 19 . Here, ∇ × F g = −∇ × ∇ U = 0 and ∇⋅ F k = ∇⋅∇ × g = 0.…”