Solenoidal optical forces from a plasmonic Archimedean spiral

The optical forces generated by a right-handed plasmonic Archimedean spiral (PAS) have been mapped and analyzed. By changing the handedness of the circularly polarized excitation, the structure can switch from a trapping force profile to a rotating force profile. The Helmholtz-Hodge decomposition method has been used to separate the solenoidal component and the conservative component of the force and quantify their relative magnitude. It is shown that the for right-hand circularly polarized excitation, the PAS creates a significant amount of solenoidal forces. Using the decomposed force components, an intuitive explanation of the motion of micro- and nanoparticles in the force field is presented. Vector field topology is used to visualize the force components. The analysis is found to be consistent with numerical and experimental results. Due to the intuitive nature of the analysis, it can be used in the initial design process of complex laboratory-on-a-chip systems where a rigorous analysis is computationally expensive.

Figure 1

Schematic of a plasmonic Archimedean spiral.

Figure 2

Geometry of the plasmonic Archimedean spiral. (a) Top view ($xy$ plane). (b) Cross-sectional view ($yz$ plane).

Figure 3

Field-intensity enhancement for LHCP incident light. (a) $z=10\mathrm{nm}$ plane view, (b) $y=0$ plane view, and (c) $x=0$ plane view.

Figure 4

Field-intensity enhancement for RHCP incident light. (a) $z=10\mathrm{nm}$ plane view, (b) $y=0$ plane view, and (c) $x=0$ plane view.

Figure 5

Force profile for LHCP excitation at the $z=660\mathrm{nm}$ plane. (a) $x$ component of the force $F_x$, (b) $y$ component of the force $F_y$, (c) force lines in the $xy$ plane, and (d) $z$ component of the force $F_z$. Equations (3) and (4) were used to calculate the force.

Figure 6

Force profile for RHCP excitation at the $z=660\mathrm{nm}$ plane. (a) $x$ component of the force $F_x$, (b) $y$ component of the force $F_y$, (c) force lines in the $xy$ plane, and (d) $z$ component of the force $F_z$. Equations (3) and (4) were used to calculate the force.

Figure 7

$z$ component of the force at the $x=0$ plane for (a) LHCP excitation and (b) RHCP excitation. The plots share the same color bar. Equations (3) and (4) were used to calculate the force.

Figure 8

Components of the optical force for LHCP excitation at the $z=660\mathrm{nm}$ plane. (a)–(d) The conservative component and (e)–(g) the solenoidal component. (a), (b), (e), and (f) share the same color bar. (d) is a visualization obtained using the vector-field topology method. The different colored points correspond to different types of critical points as described in the legend below (d). Equations (5), (6), and (7) were used on the LHCP force data to calculate force components.

Figure 9

Components of the optical force for RHCP excitation at the $z=660\mathrm{nm}$ plane. (a)–(d) The conservative component and (e)–(h) the solenoidal component. (a), (b), (e), and (f) share the same color bar. (d) and (h) are visualizations obtained using the vector-field topology method. The different types of critical points are represented using the color scheme mentioned in Fig. 8. Equations (5), (6), and (7) were used on the RHCP force data to calculate force components.

Figure 10

The $z$ component of the torque experience by the particle for RHCP excitation. (a) Torque calculated from the total force field and (b) torque calculated from the solenoidal component of the force. The axis of rotation is assumed to be the $z$ axis. The plots share the same color bar.

Figure 11

For a PAS excited by 1545-nm LHCP light, (a) the position probability density of a particle calculated from the optical potential and (b) the final position of 25,000 Brownian trajectories.

Figure 12

For a PAS excited by 1545-nm RHCP light, (a) the position probability density of a particle calculated from optical potential and (b) the final position of 25,000 Brownian trajectories.