Chiral near fields generated from plasmonic optical lattices

Plasmonic fields are usually considered nonchiral because of the transverse magnetic polarization of surface plasmon modes. We, however, show here that an optical lattice created from the intersection of two coherent surface plasmons propagating on a smooth metal film can generate optical chirality in the interfering near field. We reveal in particular the emergence of plasmonic potentials relevant to the generation of near-field chiral forces. This draws promising perspectives for performing enantiomeric separation schemes within the near field.

Figure 1

Sketch of the plasmonic optical lattice. Two SPs are propagating along the two orthogonal $x$ and $y$ directions, on the same gold-water interface. The figure displays the total electromagnetic energy $W(x,y)$ on top of the metallic layer ($z=0^{+}$), normalized by $I_0/c$, with a vignetting of the two surface plasmons to show their respective propagation directions and reveal the interfering region, shown in the upper inset. In this evaluation, a 540-nm wavelength has been chosen in order to increase the plasmonic longitudinal exponential decay making the two orthogonal propagation directions more visible.

Figure 2

(a) Density of chirality $K\left(\mathbf{r}\right)$ as a function of position $(x,y)$ on top of the metallic layer ($z=0$), normalized by $\omega I_{1,2}/c^2$. The chirality density is minimized along lines $L_p^{-}$ (dashed white lines) and maximized along lines $L_p^{+}$ (solid white lines). The reactive chiral force defined from the gradient of $K\left(\mathbf{r}\right)$ will essentially be directed perpendicularly to the $L_p^{\pm }$ lines. (b) Direction and relative amplitude of the $x$ and $y$ components of the vector field $\mathit{\Phi }-\nabla \times \mathit{\Pi }/2$ given in Eq. (11), in the $z=0$ plane. The lines $L_p^{\pm }$ are displayed in red for comparison with (a). Both panels correspond to the scheme presented in Fig. 1 where two surface plasmons of identical intensities are launched perpendicularly from each other at a 780-nm wavelength on a gold-water interface, with no phase difference at the origin, i.e., with $\theta =0$.

Figure 3

(a) Gradient of the chirality density in the $z$ direction, normalized by ${\omega }^2{I}_{1,2}/c^3$. (b) $z$ component of the vector field $\mathit{\Phi }-\nabla \times \mathit{\Pi }/2$ in the $z=0$ plane, normalized by $\omega I_{1,2}/2c$. These patterns correspond to the scheme of orthogonal surface plasmons involved in Fig. 2. The lines $L_p^{\pm }$ are presented for comparison with Fig. 2. Panels (a) and (b) can be quantitatively compared since both figures are equivalent to a force density normalized by $\omega I_{1,2}/c^2$.