Helicity and Polarization Gradient Optical Trapping in Evanescent Fields

Optical traps using nonconservative forces instead of conservative intensity-gradient forces expand the trap parameter space. Existing traps with nonconservative helicity-dependent forces are limited to chiral particles and fields with helicity gradients. We relax these constraints by proposing helicity and polarization gradient optical trapping of achiral particles in evanescent fields. We further propose an optical switching system in which a microsphere is trapped and optically manipulated around a microfiber using polarization gradients. Our Letter deepens the understanding of light-matter interactions in polarization gradient fields and expands the range of compatible particles and stable trapping fields.

Figure 1

Helicity gradient optical trapping of particles in a total-internal-reflection (TIR) system. (a) Two plane waves with orthogonal polarizations are incident on the glass-water interface ($y<0$ is glass, and $y>0$ is water) both at an angle $\alpha$ from the normal. The planes of incidence intersect at an angle of $\gamma$. A polarization standing wave is produced in the transverse direction with spatially varying $x$-directed spin angular momentum (SAM) $s_x$. (b) Mechanism of helicity gradient optical trapping when the two incident beams have orthogonal linear polarizations. (c) Polarization distribution in the transverse ($z$) direction represented on the Poincaré sphere. (d),(e) $s_x$ (d) and transverse BSM $P_z^S$ (e) volume density distributions in the transverse plane. (f),(g) Lateral optical force (f) and trapping potential (g) of a polystyrene particle (diameter 200 nm) along the $z$ direction when varying the phase difference between the two beams. Black dotted lines in (f) indicate zero lateral force ($F_z=0$). Purple dots in (g) indicate trapping positions. The unit of the trapping potential is $k_{B}T$, where $k_B=1.38\times {10}^{-23}\mathrm{J}·{\mathrm{K}}^{-1}$ and $T=293.15\mathrm{K}$ are the Boltzmann constant and the temperature, respectively. For all simulations, $n_{\text{glass}}=1.52$, $n_{\text{water}}=1.33$, $\gamma =20°$, $\alpha =65°$, $\lambda =785\mathrm{nm}$, and $\text{intensity}=1\mathrm{mW}/\mathrm{\mu }{\mathrm{m}}^2$ per beam.

Figure 2

Helicity gradient optical trapping in the TIR system using two orthogonal circular polarizations with identical amplitudes ($\text{intensity}=1\mathrm{mW}/\mathrm{\mu }{\mathrm{m}}^2$ per beam). (a) Input and effective polarization distributions on the Poincaré sphere for a Mie particle. (b),(c) Lateral optical force (b) and trapping potential (c) of a silicon nanoparticle (diameter 200 nm) for different incident wavelengths. The nanoparticle supports electric and magnetic dipole resonances. Black dashed lines in (b) indicate $F_z=0$. Purple dots in (c) denote stable trapping positions. (d) Lateral optical force and trapping potential at the magnetic dipole resonance wavelength (768 nm).

Figure 3

Polarization gradient optical trapping in a microfiber-microsphere system for optical switching. (a) Schematic of an optical switching system. One input microfiber is surrounded by four output microfibers. The purple circle indicates a whispering-gallery mode. See the Supplemental Video [48] for a more detailed demonstration of the optical switching system. (b) Polarizations in the $y^{\prime }{z}^{\prime }$ coordinate system at different azimuth positions. The lateral direction is along the $y^{\prime }$ direction tangent to the input fiber. The input fiber and the microsphere are represented by the yellow circle and the blue partial circle, respectively. Four input polarizations (the polarization of the control light in the input fiber) are considered: RCP, LCP, and $\pm 45°$ diagonal polarizations. The polarization state in the $y^{\prime }{z}^{\prime }$ coordinate system varies with the microsphere’s azimuthal position when the input polarization is noncircular.

Figure 4

Simulation of polarization gradient optical trapping in the microfiber-microsphere system. (a),(b) Lateral optical force $F_t$ on the microsphere (a) and trapping potential (b) at different azimuthal positions when varying the control light polarization. The black dashed curves in (a) are the contour lines for $F_t=0$. The four purple dots indicate trapping sites when input linear polarizations are diagonal ($\pm 45°$). Red dots in (b) indicate local potential minima (trapping sites). The microfiber and microsphere radii are 0.8 and $8.0\mathrm{\mu }\mathrm{m}$, respectively. The control light wavelength is 1408.6 nm. (c) The transmission spectrum at the output fiber when the microsphere is in a trapping state. (d) Electric field distribution in the $xz$ cross section at $\lambda =1212.5\mathrm{nm}$, the peak transmittance wavelength [green star in (c)].