Figure 2
From: Photon momentum transfer in inhomogeneous dielectric mixtures and induced tractor beams
Optical forces derived using different formulas. The parameters are n1=1.0, n2=1.33, n3=1.45 and Δ=0, unless otherwise specified. (a) The variation in the optical forces with the shape ry/rx at θ1=0. The forces are calculated using the ray-tracing method, in which the Minkowski approach is adopted for the photon momentum. (b) The variation in the optical forces with the incident direction θ1 for the p-polarization case, as calculated via the modified Einstein–Laub formula (MEL, circle line) proposed in this paper, volume integration of the Lorentz force density (Lorentz, triangle line), the Chu formula (Chu, asterisk line) and the Minkowski stress tensor (Minkowski, square line). The size of the scatterer is defined by rx=2.0 µm and ry=0.4 µm (as shown in (c)). (c) The field pattern for Hz in the case of θ1=−30°. (d) The variation in the optical forces with the incident direction θ1 for a circular scatterer of rx=ry=2.0 µm. The forces are calculated using the ray-tracing method. (e, f) The same as (b) and (c), respectively, except for ry=2.0 µm.
