Azimuthal Imaginary Poynting Momentum Density

The momentum of light beams can possess azimuthal densities, circulating around the beam axis and inducing intriguing mechanical effects in local light-matter interaction. Belinfante’s spin momentum loops in circularly polarized beams, while the canonical momentum spirals in helically phased beams. However, a similar behavior of their imaginary counterpart, the so-called imaginary Poynting momentum (IPM), has not yet emerged. The foremost purpose of the present work is to put forward the discovery of this IPM vortex. We show that a simple superposition of radially and azimuthally polarized beams can form an IPM of completely azimuthal density. Additionally, the azimuthal IPM density can exist with a donut beam-intensity distribution and even with a vanishing azimuthal component of all other momenta. This uncovers the existence of a new mechanical effect which broadens the area of optical micromanipulation by achieving optical rotation of isotropic spheres, in the absence of both spin and orbital angular momenta. Our findings enrich the local dynamic properties of electromagnetic fields, highlighting the rotational action of their IPM, and thus its mechanical effect on microparticles and nanoparticles.

Figure 1

Illustration for different optical momentum vortices. (a) Canonical momentum in helically phased beams. (b) Belinfante’s spin momentum in circularly polarized beams. (c) Imaginary Poynting momentum in cylindrical vector beams.

Figure 2

Simulated field transversal spatial distribution at the waist plane of a cylindrical vector beam. (a) Intensity distribution with arrows indicating the polarization direction. (b) CM density. (c) Radial, azimuthal, and axial components of the IPM density versus the radial position. (d) IPM vortex.

Figure 3

Radial variation of the optical forces on a silicon sphere (diameter: 140 nm), located at the waist plane of the cylindrical vector beam shown in Fig. 2. The illumination wavelength is $\lambda =600\mathrm{nm}$.