Opto-thermophoretic trapping of micro and nanoparticles with a 2 m Tm-doped fiber laser

We propose a method for opto-thermophoretic trapping with a 2 µm Tm-doped fiber laser. The infrared continuous-wave laser beam is directly and strongly absorbed by water solution, and some local temperature gradient is generated around a focus. The particles are migrated along the temperature gradient, and form a hexagonal close-packed structure at a bottom-glass solution interface. On the other hand, the particles are not trapped in heavy water which does not absorb 2 µm light. The fact indicates that the local temperature elevation is the origin of this phenomenon. We have investigated the dependence of the phenomenon on the material, particle size, and laser power. To the best of our knowledge, 2 µm is the longest wavelength used for the opto-thermophoretic trapping.


Supplemental information 1
We adjusted mirrors before the objective lens, and shifted the laser focus to a left-bottom position in a field of view. The dark shade is observed at the left-bottom when the laser is on, as shown in Fig.   S1(b-e). We wait until the particle appears in the right-top position in the field of view, as the edge of the particle is observed in Fig. S1(a). When the laser is switched on, the particle is pulled toward the laser focus diagonally. The diagonal direction is about 125 μm which is the longest distance we can measure in our system (field of view). Namely, the particle is at least gathered 125 μm far away from the focus when the laser power is 10 mW.

Supplemental information 2
We carried out the opto-thermophoretic trapping without adding the NaCl to water solution. In fact, all the particles were pushed along the laser propagation direction and assembly formation was not observed as shown in the Fig. S2(a-f).

Supplemental information 3
When the laser power increases to 40 mW, the particles in heavy water start to be trapped but the speed of accumulation is much slower compared to the trapping in water solvent with laser power of 10 mW. The laser is turned on at 0 s. The length of the black bar is 5 μm.

Supplemental information 4
We also measured the laser power before and after the water and heavy water sample chambers to estimate how much of the laser power is absorbed by the solvent. The thickness of the chamber solution is about 120 μm. This estimation shows that the laser is absorbed to the water about 2.2 times compared to heavy water. These experimental facts clearly indicate that the temperature elevation is indeed the origin of the accumulation of the particle at the focus.

Supplemental information 5
We estimated the trapping potential and the trapping stiffness for higher laser power. For 2 μm polystyrene particles, the maximum trapping stiffness we observed in the present study is about 1.0 pN/μm.

Supplemental information 6
We calculated the optical force exerted on 500 nm, 1 μm and 2 μm polystyrene particles by 1956 nm continuous Gaussian laser beam. The NA of the objective lens used in the calculation is 0.5 which is the same as the experiment. Practically, we used an optical tweezers Toolbox based on Mie theory for the force calculation [1]. As shown in Fig. S6(b), the sign of the optical force along the z-axis is positive. This means the scattering force is stronger than the gradient force and the particle cannot be trapped around the focus. Due to the low NA of the objective lens (0.5), the optical gradient force is not sufficiently large enough to overcome the optical scattering force. Therefore, the present trapping phenomenon we observed cannot be explained by the optical force. While, the optical gradient force in lateral direction (r-direction, along the interface, Fig. S6(c)) may have a contribution for collecting the particle to the focus. and blue curves correspond to the particle diameter of 2 μm, 1 μm and 500 nm, respectively. The red and blue curves are magnified by 4 and 16 times. Numerical aperture, refractive index of water and particle are set to 0.5, 1.31 and 1.56, respectively. The laser power is 10 mW and laser wavelength is 1956 nm.

Supplemental information 7
Fig.7S demonstrates the spacer dependency of this study. When spacer thickness between two substrates is 30 μm, the tracked particle denoted inside the red circle moved merely 3.5 μm toward focusing spot in 1 second under 36 mW laser power. In contrast, the particle in the spacer with the thickness of 120 μm moved 16.7 μm, more than 4 times larger than the former.
As a sample space becomes thinner, the convection flow becomes weaker (see Visualization 6 and 7). This indicates the convection flow contributes to the gathering process. The focused 2 μm laser is efficiently absorbed into the water, which produces a temperature gradient around the laser focus, inducing the convection flow which accumulates the particle toward the focus.

Visualization 1
Video of opto-thermophoretic trapping of 1 μm polystyrene particles in the water with NaCl (referring to Fig. 2(a-f)).

Visualization 2
Video of opto-thermophoretic trapping of 200 nm polystyrene particles in the water with NaCl (referring to Fig. 5(a)).

Visualization 3
Video of opto-thermophoretic trapping of 500 nm polystyrene particles in the water with NaCl (referring to Fig. 6(a-f)).

Visualization 4
Video of opto-thermophoretic trapping of 500 nm PMMA particles in the water with NaCl (referring to Fig. 6(g-l)).

Visualization 5
Video of opto-thermophoretic trapping of 500 nm silica particles in the water with NaCl (referring to Fig. 6(m-r)).

Visualization 6
Video of opto-thermophoretic trapping of 1 μm polystyrene particles in the 120 μm spacer under 36 mW laser power.

Visualization 7
Video of opto-thermophoretic trapping of 1 μm polystyrene particles in the 30 μm spacer under 36 mW laser power.