Lateral optical force on chiral particles near a surface

Abstract

Light can exert radiation pressure on any object it encounters and that resulting optical force can be used to manipulate particles. It is commonly assumed that light should move a particle forward and indeed an incident plane wave with a photon momentum ħk can only push any particle, independent of its properties, in the direction of k. Here we demonstrate, using full-wave simulations, that an anomalous lateral force can be induced in a direction perpendicular to that of the incident photon momentum if a chiral particle is placed above a substrate that does not break any left-right symmetry. Analytical theory shows that the lateral force emerges from the coupling between structural chirality (the handedness of the chiral particle) and the light reflected from the substrate surface. Such coupling induces a sideway force that pushes chiral particles with opposite handedness in opposite directions.

Figure 1. Anomalous lateral force in the helix particle–substrate configuration.

(a) A linearly polarized plane wave pushes a normal spherical particle forward. A standalone RH helix (c) and a standalone LH helix (e) will be pushed forward by radiation pressure. When the normal spherical particle is put near a substrate, (b) it still moves forward while the helical particles (d,f) are shifted in opposite directions by an anomalous lateral force. The arrows associated with the helical particles indicate the handedness. The substrate has the dimensions of l × w × t. (g) Dimensions of the helix particle. It has inner radius r=50 nm, outer radius R=150 nm and pitch P=300 nm.

Figure 2. Numerically calculated lateral forces acting on the helical gold particles.

(a) Lateral forces F_y acting on the LH (blue lines) and RH (red lines) particles in the presence of metal (gold) and dielectric (ε_d=2.5) substrates. (b) Lateral forces as a function of the number of pitches for the LH (blue lines) and RH (red lines) particles in the presence (circles) and absence of (triangles) the gold substrate. (c) Lateral force acting on the LH particle as a function of the gap distance between the particle and the gold substrate. (d) Lateral force as a function of the thickness of the dielectric substrate for the LH particle. In the numerical simulations, the frequency is set at f=490 THz for case of the metallic substrate (b,c) and at f=380 THz for the case of the dielectric substrate.

Figure 3. Magnetic field distribution on the gold substrate.

(a) H_x field pattern for the RH particle on the gold substrate. (b) H_x field pattern for the LH particle on the gold substrate. Note the asymmetrical pattern and the different directions in which the RH and LH particles scatter EM fields. The plotted fields are on a plane just above the substrate and the frequency is set at f=420 THz.

Figure 4. Numerical results for a chiral sphere above a gold substrate.

Time-averaged Poynting vectors (a) for an isolated chiral sphere, (b) for a chiral sphere above a gold substrate and (c) for a chiral sphere sandwiched symmetrically by two gold substrates. We set κ=1 for the sphere. Time-averaged electric spin density ‹L_e› (d) for the isolated sphere, (e) for the sphere above a gold substrate and (f) for the sphere sandwiched by two gold substrates. The left–right asymmetry is obvious in panels (b) and (e). (g) Lateral force acting on the chiral sphere above a gold substrate (blue line) and sandwiched by two gold substrates (red line) as a function of the chirality parameter κ. The blue line shows that the sign of the lateral force F_y depends on κ and F_y=0 if κ=0. The red line indicates the lateral force vanishes in the sandwiched case. The frequency is set at f=500 THz.

Figure 5. Analytical results for a dipolar chiral particle above a substrate.

(a) Lateral force acting on a dipolar chiral particle ( a=30 nm, ε_r=2.0) as a function of its chirality when the particle is located 60 nm above a semi-infinite gold substrate. (b) Lateral force acting on the chiral particle (κ=−1) as a function of the thickness of a dielectric substrate (ε_d=2.5+0.001i), showing oscillating behaviour. (c) Magnitudes of the reflection coefficients for an evanescent channel k_//=10k₀ (red line) and a propagating channel k_//=0.5k₀ (green dotted line and blue line). The wavelength is set to be λ=600 nm.