Colloquium: Gripped by light: Optical binding

The light-matter interaction has been at the heart of major advances from the atomic scale right to the microscopic scale over the past four decades. Confinement by light, embodied by the area of optical trapping, has had a major influence across all of the natural sciences. However, an emergent and powerful topic within this field that has steadily merged but not gained much recognition is optical binding: the importance of exploring the optically mediated interaction between assembled objects that can cause attractive and repulsive forces and dramatically influence the way they assemble and organize themselves. This offers routes for colloidal self-assembly, crystallization, and organization of templates for biological and colloidal sciences. In this Colloquium, this emergent area is reviewed looking at the pioneering experiments in the field and the various theoretical approaches that aim to describe this behavior. The latest experimental studies in the field are reviewed and theoretical approaches are now beginning to converge to describe the binding behavior seen. Recent links between optical binding and nonlinearity are explored as well as future themes and challenges.

Figure 1

Experimental setup of the first experiment with lateral optical binding. Ar laser of $10\mathrm{W}$ power and wavelength of $541.5\mathrm{nm}$ transformed into line focus was used. From 20.

Figure 2

Lateral optical binding in a line focus. The separation of two polystyrene spheres shown of diameters $1.43\mu \mathrm{m}$ placed in water and illuminated with laser wavelength $541.5\mathrm{nm}$. Left: Time development of interparticle separation distance. Right: Histogram of the particle separation distances. From 20.

Figure 3

Longitudinal optical binding in counterpropagating beam geometry. Experimental data for the arrays of (a) two, (b) three, and (c) seven spheres (each $3\mu \mathrm{m}$ in size). The diagrams on the right elucidate how the particles fill up the approximately harmonic potential well created by the two counterpropagating beams. From 133.

Figure 4

(Color online) Examples of the amplitude distribution of the electric field emitted by the oscillating dipole oriented along the $x$ axis (arrow). (a) The upper row shows the far field where the emitted field amplitude decreases much faster along the $x$ axis. (b) The bottom row shows the near field where in contrast the field amplitude decreases slowly along the $x$ axis. Black contours denote places of the same field intensity; field amplitudes on neighboring contours differ by one order of magnitude.

Figure 5

(Color online) Definition of variables used for the mathematical description (left). Simplified scheme of the interaction between two particles without multiple scattering between them which is equivalent to the description given by Eq. (11). Incident field induces dipoles ${\mathbf{p}}^I\left({\mathbf{r}}_A\right)={\overline{\alpha }}^A{\mathbf{E}}^I\left({\mathbf{r}}_A\right)$ or ${\mathbf{p}}^I\left({\mathbf{r}}_B\right)={\overline{\alpha }}^B{\mathbf{E}}^I\left({\mathbf{r}}_B\right)$ in particle $A$ or $B$, respectively. The field emitted by particle $A$ reaches particle $B$ and induces there the dipole component ${\mathbf{p}}^{A\to B}\left({\mathbf{r}}_A\right)=\overline{\mathbf{G}}{\overline{\alpha }}^A{\mathbf{E}}^I\left({\mathbf{r}}_A\right)$ which interacts with the incident field ${\mathbf{E}}^I\left({\mathbf{r}}_B\right)$. The second parallel path corresponds to the interaction of the emitted field by the dipole $A$ with the dipole induced in particle $B$ by the incident field ${\mathbf{E}}^I\left({\mathbf{r}}_B\right)$.

Figure 6

(Color online) Visualization of the forces acting on particle $B$ if particle $A$ is placed at the origin of the coordinate system. (a) The near- and (b) far-field cases, respectively. Curves at the background follow the trajectories of particle $B$ toward equilibrium positions (denoted by the dotted edges).

Figure 7

(Color online) Interaction between spherical nanoparticles $A$ and $B$ in the case of longitudinal binding. Sphere $A$ radiates toward sphere $B$ in the same direction as the incident field and with the same wave vector size. Therefore the phase of the incident and scattered field is independent of the interparticle distance $\mathbf{R}$ (left) if sphere $A$ is fixed. In contrast the sphere $B$ radiates backward against the incident wave propagation, thus the phase of the incident and scattered waves depends on the interparticle distance as $2kR$ and it results in oscillatory behavior of force $F_x^A$.

Figure 8

Optical binding of infinite cylinders under plane-wave illumination. Force along the $x$ axis (light propagation direction) acting on the right-hand side cylinder for a varying number of cylinders on the left. Case 1 corresponds to two cylinders; cases 2 and 3 are explained in the inset. The parameters used are the following: cylinder radius $a=0.3\lambda$, laser wavelength $\lambda =546\mathrm{nm}$, permittivity of polystyrene cylinder ${\epsilon }_p=2.56$, and water ${\epsilon }_m=1.69$. From 60.

Figure 9

Optical binding of infinite cylinders in the interference field of plane waves. Positions of 20 cylinders (white circles) and field distributions (background gray-scale images) for (a) random initial positions in a three-plane-wave interference pattern, background shows unperturbed incident field distribution; (b) organized final positions due to the trapping and binding forces, background shows unperturbed incident field distribution; (c) the same as (b) but final field distribution is shown at the background; and (d) organized final positions corresponding to another set of cylinders in initial positions. The parameters used are the following: $a=0.15\lambda$, $\lambda =546\mathrm{nm}$, ${\epsilon }_p=2.56$, and ${\epsilon }_m=1.69$. Adapted from 60.

Figure 10

Optical binding of spheres near a planar dielectric interface. Two glass spheres are placed at the same distance below the dielectric interface oriented along the $x$ axis. The incident beam $(\lambda =632.8\mathrm{nm})$ impinges perpendicularly to the interface and illuminates both spheres. The binding forces shown between these spheres for $s$ (marked +) and $p$ polarizations. Full curves denote the forces in the presence of the surface and dashed curves without it. Glass spheres have radii of (a) $10\mathrm{nm}$ and (b) $100\mathrm{nm}$. From 26.

Figure 11

(Color online) Stability of optical binding of multiple identical spheres. Examples of equilibrium configurations calculated for varying numbers of polystyrene $({\epsilon }_p=2.53)$ spheres of radius $a=0.414\mu \mathrm{m}$ placed in vacuum (air) and illuminated with horizontal polarization of the incident light with a wavelength $\lambda =0.52\mu \mathrm{m}$. Configurations (a)–(e) have all eigenmodes stable, (b) and (e) are in drifting equilibrium, and (f) and (g) have either stable or quasistable modes (see the text). From 106.

Figure 12

Short- and long-range particle organization in counterpropagating Bessel beams. Top: Formation of chains with multiple particles of diameter $802\mathrm{nm}$ (left) or $1070\mathrm{nm}$ (right). Bottom: Self-organization of $1070\mathrm{nm}$ particles in wider Bessel beam cores of radii ${\rho }_0=2.4\mu \mathrm{m}$ (left) and ${\rho }_0=3.7\mu \mathrm{m}$ (right). From [75]

Figure 13

Particle self-organization due to optical binding in the vicinity of a planar interface. Sequence of video frames of an array of $520\mathrm{nm}$ particles as a quarter-wave plate is rotated to change the polarization of one of the counterpropagating beams from $s$ $(\varphi =0°)$ to $p$ $(\varphi =45°)$. Hexagonal packing nucleating at the center of the array is seen at (b) and then the hexagonal crystalline structure grows outward toward the left- and right-hand sides of the array. From 96.

Figure 14

Particle self-organization due to the combination of optical binding and thermophoresis in the vicinity of a metal-coated planar interface. Increasing the incident light power in a thin chamber (with height of $10\mu \mathrm{m}$) formed above a metal-coated interface triggers lateral thermophoresis that results in the repulsion of particles (silica, with diameter of $5\mu \mathrm{m}$) from the center of the illuminated region where the SPPs are excited (hot to cold movement). Subsequently the repelled colloids arrange into linear arrays at the periphery of the region. Light scattered by the colloids (no additional white light illumination). The top and bottom insets are detailed views of the linear ordering of the accumulated particles acquired with additional white light illumination. From 48.

Figure 15

Formation of OSSs under unpatterned plane-wave illumination. The temporal evolution of the OSS created from polymer particles of diameter $410\mathrm{nm}$ formation for illuminating powers above the threshold. Each panel is a CCD image of the illuminated region at different times after the light has been coupled into the system. Bright-field imaging also confirms the presence of ordered colloids in regions of high intensity. From 120.