Tracking the transport of nanoparticles in a plasmonic optical lattice

In solid-state physics, when atoms are brought into close proximity their electrons can exhibit delocalized transport (i.e., they may move through the periodic potentials within the solid). This may produce a Bloch state, a specific wave function for a periodically repeating environment that enables description of electrons in a crystal structure. In a similar way, forcing microparticles and nanoparticles through periodic optical potentials, or an optical lattice (a spatially periodic polarization pattern formed by the interference of counter-propagating laser beams), has enabled many interesting statistical transport phenomena and applications.¹ For example, highly efficient sorting of microparticles has been achieved, based on either the index of refraction or the size of the particles in a 3D optical lattice within a microfluidic environment.² Such particle sorting could have applications in the sorting of viruses, proteins, and other particles. However, if one attempts to shrink the spatial dimensions of these experiments, the size of the particles that can be trapped (i.e., manipulated or measured) is restricted by the diffraction limit. Specifically, the trapping efficiency for an object of radius a drops rapidly (i.e., following a cubic power law, a³).³

To overcome these diffraction limits, researchers have developed near-field optical trapping techniques—plasmonic optical tweezers—using plasmonic metallic nanostructures.^{4, 5} Unlike conventional optical tweezers, where focused laser beams with a strong electric field gradient attract dielectric particles, plasmonic optical tweezers form from the illumination of gold nanostructure arrays. When exposed to light, electrons in the nanostructures exhibit collective motions (known as localized surface plasmonic oscillations). The localized surface plasmonic oscillations confine the light at a sub-wavelength scale and generate an optical gradient force to trap nanoscale objects. To date, plasmonic trapping of a wide range of micro- and nano-objects (e.g., metallic and dielectric particles, bacteria, and molecules) have been reported.^{4, 5} To extend isolated plasmonic optical tweezers to a plasmonic optical lattice, one research group has used undulated gold film to support the transport of gold nanoparticles. Those researchers have also demonstrated negative refraction phenomena (i.e., cornerstones in the field of metamaterials).⁶

In our research we have sought to enable transport of nanoparticles in a plasmonic optical lattice. We pack many plasmonic nanostructures (in this case, nanodisks) into a unit cell. We also associate each cell with a simple square lattice to form a periodic potential (see Figure 1).⁷ This creates multiple sites that can optically tweeze the nanoparticles. It can also support delocalized transport, with the proper choice of lattice period, as well as depth and width of the trapping site.

Figure 1. A nanoplasmonic optical lattice . (Left) Electromagnetic field intensity distribution of a unit cell from a finite domain time difference simulation. (Right) A scanning electron microscope image of the plasmonic nanostructure array used in the experiment. The array consists of a 7×7square lattice of gold nanodisks. Each unit cell contains four nanodisks of diameter 200nm.

To test our plasmonic optical lattice approach, we have built an inversion microscope setup, which we modified from a commercial optical tweezer kit (using gold nanostructures fabricated through electron beam lithography). In our first experiment, we illuminated the nanoplasmonic array of gold nanodisks using a semiconductor diode laser to loosely focus a Gaussian beam that had a wavelength in the near-IR regime (980nm). Then, using fluorescent image video microscopy, we tracked the transport of polystyrene nanoparticles dispersed on the nanoplasmonic array.

The results of our experiments showed that the optical lattice conferred delocalized transport on nanoparticles as small as 100nm in diameter (see Figure 2). The Gaussian beam produced a gradient, which caused the nanoparticles to roam from the edge of the array to the center. We thus found that larger nanoparticles (diameter 500nm) formed predominantly hexagonal close-packed clustering (see Figure 2). We also conducted further analysis on single particle trajectories that we collected. As such, we were able to confirm that particle transport in our experiments was indeed faster than in free diffusion.⁷

Figure 2. Multiple particle trapping of nanospheres with diameters of (a) 500nm and (b) 100nm. Nanoparticles in (a) accumulate to form predominantly (hexagonal) close-packed structures. These larger nanoparticles tend to be tightly trapped by the nanoplasmonic array. Nanoparticles in (b) accumulate in the central regions, but are only loosely trapped because of the weaker trapping forces.

It may be appropriate, in the future, for our plasmonic optical lattice approach to be used for probing the quantum mechanical interactions of atoms. For instance, the consequences of shrinking the dimensions of an optical lattice have already been calculated.⁸ It was found that it is possible to enhance the quantum mechanical tunneling effect between trapped atoms by several orders of magnitude. We are therefore interested in realizing this effect experimentally, with the use of our plasmonic optical lattice/trapping techniques (e.g., with silver nanoplasmonic arrays). Another possible application of our approach (in biology) is to support the optofluidic cultivation of photosynthetic bacteria, through an enhanced evanescent plasmonic field. This could allow the production of biofuels through carbon fixation.⁹ To develop these concepts further, it may be necessary to consider the possibility of forcing nanoparticles of different size or refractive index into a properly designed plasmonic optical lattice (i.e., such that they follow different trajectories to facilitate sorting in microfluidic environments).¹⁰ Photothermal heating (heat retained from the absorbed light), however, causes convection that can adversely disrupt the transport of nanoparticles. Several groups have attempted to characterize such effects by measuring either the temperature increase or the convectional flow of the nanoplasmonic array.^{11, 12} Indeed, one research group have shown that substrates of high thermal conductivity (e.g., copper) can serve as heat sinks in the nanostructure.¹³ As such, they can offer a potential solution to the problem of excess heat.

In summary, we have created a plasmonic optical lattice that enables optical tweezing of nanoparticles and that supports their delocalized transport. Our approach has several potential applications, for example, in the fields of nanotechnology, atomic physics, and biofuel production. We are currently focused on elucidating the contribution of thermal convection in our technique. Our aim is to identify an optimal engineering strategy that can be used to counter photothermal effects and therefore fully exploit the potential of plasmonic optical lattices.