Photonic Binding in Silicon-Colloid Microcavities

Photonic binding between two identical silicon-colloid-based microcavities is studied by using a generalized multipolar expansion. In contrast with previous works, we focus on low-order cavity modes that resemble low-energy electronic orbitals. For conservative light intensities, the interaction between cavity modes with moderate $Q$ factors produces extremely large particle acceleration values. Optical forces dominate over van der Waals, gravity, and Brownian motion, and they show a binding-antibinding behavior in analogy to electronic binding. As these photonic forces are associated with relatively broad Mie mode resonances and they are not strongly influenced by sample absorption, our study opens a plausible avenue towards manipulation of high-refractive-index colloidal assemblies.

Figure 1

Contour plot of the scattering cross section $\sigma$ per sphere as a function of the size parameter $\alpha =2\pi r/\lambda$ and the distance between the spheres for (a) $p$ polarization and (b) $s$ polarization. Insets: Schematic representation of the dielectric-sphere dimer under consideration, along with the $a$ and $b$ Mie modes of the individual particles. The color scale is given for particles of radius $r=750\mathrm{nm}$.

Figure 2

(a) Scattering cross section of the dimer (right scale and thick black/lower curve) and photonic-force-induced acceleration (in units of the acceleration of gravity $g$) along the dimer-axis $z$ direction (left scale and red/upper curve) for $p$ polarization as a function of size parameter $\alpha =2\pi r/\lambda$ (bottom axis) and wavelength $\lambda$ (top axis). The scattering cross section for an individual sphere is also plotted (thin black/lower curve). The spheres radius is $r=750\mathrm{nm}$ and the surface-to-surface distance is $S=r/20$. The inset shows the scattering configuration. (b) Electric-field intensity distribution in the $x\mathrm{\text{−}}z$ plane for some of the dimer modes (upper panels), and the corresponding single-sphere modes (lower panels).

Figure 3

Same as Fig. 2 for $s$ polarization (i.e., incoming electric field perpendicular to dimer axis).

Figure 4

Attractive photonic force in the dimer for different modes and light polarizations ($p$ and $s$) as a function of the separation $S$ between the spheres. The photonic force for a light intensity of ${10}^{-4}\mathrm{W}/\mu {\mathrm{m}}^2$ is compared to the van der Waals force. The vertical dashed line corresponds to a distance $S=r/20$.