Unusually Strong Optical Interactions between Particles in Quasi-One-Dimensional Geometries

A theoretical analysis of the optically induced interaction between small particles in a quasi-one-dimensional system is presented. The total reflection of light modes near a geometric resonance leads to strong radiation pressure on a single particle. The presence of the two particles splits the resonance leading to a nontrivial oscillating interaction. The existence of stable, optically bound dimers under two counterpropagating (noncorrelated) light modes is also discussed.

Figure 1

Normalized total forward force [$F_z/|F_{z_{\mathrm{m}\mathrm{a}\mathrm{x}}}|=(1-T)$] vs $\omega$ on a single particle (single peak) and on the two particle system (double peak) at $k_{1}L/\pi =7.4$. Dashed and dot-dashed curves corresponds to the approximated expressions (9) and (13) (with no fitting parameters). (Top: sketch of the particle-waveguide system. Bottom: Patterns of the real part of the total electric field at the resonant frequencies (${\omega }_{-},{\omega }_{+}$).

Figure 2

(a) Contour plot of the normalized total forward force ($F_z=F_{z2}+F_{z1}$) and (b) normalized interaction force between particles ($F_{12}=F_{z2}-F_{z1}$) in a frequency-distance ($\omega -k_{1}L$) map. Contour lines in (b) correspond to $F_{12}=0$ separating bonding and antibonding regions. Vertical lines at $k_{1}L/\pi =7.4$ and $k_{1}L/\pi =4.3$ correspond to the $F_z$ vs $\omega$ curves in Figs. 1, 3, respectively [circles on the lines in (b) are at the resonant peaks in (a)].

Figure 3

Normalized forces vs frequency for the two particles system at $k_{1}L/\pi =4.3$. The continuous line represents the total forward force $F_z$. Dotted and dashed lines correspond to $F_{z1}$ and $F_{z2}$, respectively. Dot-dashed curve represents the interaction force between particles $F_{12}$.

Figure 4

Optically induced interaction potential between two particles at a distance $L$ for three different frequencies (corresponding to the horizontal lines of Fig. 2).