All optical dynamic nanomanipulation with active colloidal tweezers

Manipulation of colloidal objects with light is important in diverse fields. While performance of traditional optical tweezers is restricted by the diffraction-limit, recent approaches based on plasmonic tweezers allow higher trapping efficiency at lower optical powers but suffer from the disadvantage that plasmonic nanostructures are fixed in space, which limits the speed and versatility of the trapping process. As we show here, plasmonic nanodisks fabricated over dielectric microrods provide a promising approach toward optical nanomanipulation: these hybrid structures can be maneuvered by conventional optical tweezers and simultaneously generate strongly confined optical near-fields in their vicinity, functioning as near-field traps themselves for colloids as small as 40 nm. The colloidal tweezers can be used to transport nanoscale cargo even in ionic solutions at optical intensities lower than the damage threshold of living micro-organisms, and in addition, allow parallel and independently controlled manipulation of different types of colloids, including fluorescent nanodiamonds and magnetic nanoparticles.

Each domain was meshed using free tetrahedral meshing of maximum size 42 nm outside the plasmonic disc and maximum element size of 15 nm inside the disc to obtain optimal convergence.
We use direct solver to solve the wave equation and calculate the electric field distributions.
To obtain the total electromagnetic force exerted by the Ag nanodisk on the colloidal particle we have used Maxwell stress tensor ( ⃖� ⃗ ) derived from the fields. The average mechanical force on the particles can be written as: and, where, ε and μ are electric permittivity and magnetic permeability of the surrounding medium respectively. The trapping potential ( trap = 1 2 2 ) for the trapped particle (Relative permittivity = 2.56) at the Rayleigh limit was obtained from

Supplementary Note 2: Modelling of temperature rise
To find out temperature rise due to plasmon induced heating in Ag-nanodisks we need to know the absorbed thermal power density inside the nanostructures which can be written as, where ( ) is the complex amplitude of the electronic current density inside the Ag nanostructure, where light absorption in water and silica is ignored. The temperature distribution in ACT and its outside is governed by where ρ is mass density (kg m -3 ), κ is thermal conductivity (Wm -1 K -1 ) and is thermal heat capacity (J kg -1 K -1 ). The resulting temperature can be assumed to be uniform over the metallic region due to large contrast of thermal diffusivity D in metal (~10 −4 m 2 s -1 ) and surrounding dielectric (~10 −7 m 2 s -1 ). As � � silver >> � � water , heat flows faster inside particle compared to the surrounding medium and accumulates at the boundary before it diffuses away through water. So, it can be considered that the boundary maintains a constant temperature throughout when being continuously illuminated.
Next, we estimate at what timescale the uniform temperature approximation (UTA) is valid. The typical time scale τ required to reach the steady-state regime is where is the thermal diffusivity (m 2 s -1 ) and is typical experimental length scale. Since, the heat flow is orders of magnitude faster in metal than water, the surrounding medium governs the magnitude of transient time scale which is of the order of μs. Therefore, for a CW illumination we can consider steady-state heat equation 2 to find out the temperature distribution in water. We assumed the thermal conductivities of Ag and water to be 429 Wm −1 K −1 and 0.6 Wm −1 K −1 respectively.
In this simulation, we neglected the effect of convection on temperature rise. We considered the Rayleigh number = Δ 3 ⁄ , where is the acceleration due to gravity, is the volume thermal expansion coefficient of water, Δ is the simulated rise in temperature ignoring convection and therefore an upper limit for the temperature rise, is a characteristic length of the system, is the kinematic viscosity and is the thermal diffusivity of water. The value of ~10 −11 shows role of convection in the heat flow and therefore temperature rise under present experimental conditions can be neglected.

Supplementary Note 3: Measurement of temperature rise
The temperature measurement was based on measuring the fluorescence efficiency of a water-soluble dye Rhodamine B which has a high temperature sensitivity. The fluorescence intensity ( ) as a function of temperature can be written as 3 ln ( ) In the same figure we have also plotted the simulated temperature rise for both ACT and isolated nanodisk in water, corresponding to illumination wavelength of 1064 nm. The simulated temperature rise for the ACT including metallic and dielectric parts (red solid line) is slightly smaller than the isolated nanodisk (without the SiO 2 structure, dotted green line). This was due to the higher thermal conductivity of glass than water which is taken to be 1.38 Wm −1 K −1 in all the calculations. The difference between simulated and experimental values can be attributed to the fact that the experimental measurements have been performed while the ACTs were immobilized on glass surface of the fluidic chamber which has higher thermal conductivity than water (0.6 Wm −1 K −1 ).
Accordingly, we considered ACTs located at the interface between two media, where we assumed an average thermal conductivity, avg = water + glass 2 . We assume avg = 1 Wm −1 K −1 in eqn.8 then the calculated temperature rise (dashed blue line) is close to and slightly less than the experimentally measured values. The overall agreement between the experimental measurements and the numerical models is encouraging.
We must stress the lower temperature rise in our experiments is to a large extent due to use of Ag as the plasmonic material, as opposed to Au commonly used for thermoplasmonic experiments. For example, higher temperature rise (~33 K at 10 mWμm -2 ) was found in literature 4 for similar disk geometry (288 nm dimeter, 40 nm thickness) fabricated on glass substrate and immersed in water but where the discs were made with gold (which is a better absorber than Ag). Also, in a separate plasmonic trapping experiment 37 K rise in temperature above ambient was reported for Au disk nanoantenna 5 . The heating of a silver nanoparticle has been compared with gold in a previous literature which also predicted lower temperature rise for Ag (see Supplementary information of Ref# 6) at IR wavelengths 6 .