Figure 5.10 — Orbital angular momentum on a sphere Figure 5.10 — Orbital angular momentum on a sphere. Optical forces produced on a particle (np = 1.50) with radius a = 300 nm (solid line in (a)) in water (nm = 1.33) near the focus of a Laguerre–Gaussian beam with (a) l = +1and (b) l = −1(p = 1, w0 = 4mm). One can observe how the force fields bend because of the transfer of orbital angular momentum from the light beam to the particle. When the size of the focal spot is increased by decreasing the beam waist to w0 = 1.2 mm, the particle is attracted towards the annular region where the focal intensity is maximum, as can be seen in (c) for l = +1and (d) for l = −1 (p = 1). All beams have wavelength λ0 = 632 nm, are focused by a 1.20 NA water-immersion objective with aperture radius 4 mm and have power 10 mW after the aperture.