1. Introduction

Since Ashkin observed the acceleration and trapping of particles by optical trap in 1970 [1], optical tweezers have been developed from two-dimension to three-dimension [2]. The number of optical traps is also extended from single trap to dual-optical traps [3], even multi-optical traps [4–6]. At the beginning, the optical trap is formed by TEM₀₀ mode Gaussian laser beam, then various kinds of modes such as hollow beam [7], Laguerre-Gaussian beam [8] and vector beam are adopted [9,10]. These special modes give the optical trap some new characters, like orbital angular momentum, larger trap stiffness and trap depth. A variety of objects can be trapped such as organelles in cells [11], gold nanoparticles [12] and carbon nanotubes [13]. Gold nanoparticles, which support local surface plasmon resonance (SPR) [14] modes, are considered to have great applications in nanophotonics, medicine and many other areas [15, 16]. Gold spheres with diameters ranging from 18 to 254nm have been trapped steadily in three-dimensions in experiment [17], and the spectroscopy of a single trapped gold particle has been measured [18]. Optical trapping of gold nanorods and nanowires were also reported [19]. Two-photon absorption of gold was observed as the optical trap is formed by pulsed laser [20], and the optical trap formed by pulsed laser can split due to the strong absorption of the trapped gold spheres [21]. As a tool of micro manipulation, optical tweezers can array gold particles on certain substrate [22].

One important issue in optical tweezers is the quantification of trapping parameters for different objects. The trap stiffness, escape distance, maximum lateral optical force of a single particle can be determined by forced oscillation, escape velocity, and Brownian motion [23–28]. The potential of a particle in optical trap could be calibrated by thermal noise analysis [29]. The trapping potential of multiple trapped dielectric spheres could be measured by the force balance between repulsive osmotic and confining gradient-force pressures [30].

In this paper, we studied the optical trapping and light scattering properties of multiple trapped gold spheres with a setup composed of DF imaging and optical tweezers system. We measured the trapping potential for a single gold nanosphere by trapping an ensemble of gold nanospheres with a focused laser beam. In section 2, we illustrated the setup in our experiment. In section 3, we used both DF imaging and scattering spectra to count the trapped gold spheres and measured the trapping potential. In section 4 we gave a summary.

2. Experimental setup

The optical tweezers setup in our experiments is based on a microscopy (Leica DMIRB), as is schematically shown in Fig. 1. The wide red line represents 1064nm laser, and the thin green line represents visible light emitted from tungsten lamp. The laser beam was expanded by lens L1 and L2, and then focused by an objective (N.A 0.7-1.4 OIL) and formed the optical trap. There is a rotating module right behind the condenser (N.A. 1.4 OIL), which can change the status from bright field (BF) to DF. We usually set the objective’s N.A to be 0.9 in order to balance the DF imaging and optical trapping performance. When the microscopy works at the DF imaging mode, the trapped gold spheres can be observed by eyepiece and CCD camera (Cool snapfx). The scattering spectra of the trapped gold spheres can be measured by the spectrometer (Ocean Optics, QE 65000). As the CCD camera and spectrometer were placed at the same place, they could not work simultaneously.

 

Fig. 1 Schematic diagram of the experimental setup. The wide red line represents 1064nm laser, and the thin green line represents the visible light emitted from the tungsten Lamp. A beam of 1064nm laser was expanded by lens L1 and L2, and then focused by the objective to form the optical trap. DF imaging system was mainly formed by condenser and objective. The DF image of the trapped spheres can be observed by eyepiece and CCD camera.

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3. Optical trapping of multiple gold spheres

The gold spheres used in this experiment are bought from STREM (79-6045), and the diameter of the spheres is 50nm and the standard deviation is 2nm. In this experiment, the laser power was 204mW at the input threshold of the objective, and the transmission of the objective is about 60%. Similar to micron dielectric spheres, optical trap can trap a single or multiple gold spheres steadily. Usually, the more the trapped spheres the larger the intensity of the scattering light from the trapped spheres. There should be some relationship between the scattering intensity and the number of the trapped gold spheres. We diluted the bought gold sphere solution, so that the spheres entered the trap one by one most of the time. We recorded the intensity change of the images captured by the CCD camera. Figure 2(a) is one of the images captured by the CCD. We summed the gray scales of all the pixels included in the red rectangle and obtained its change with the time. The result is shown in Fig. 2(b). The numbers marked in the figure represent the particle quantity in the trap. It can be seen that the intensity change is stepwise and the step sizes are integer multiples of certain value, which implies that only one gold sphere enters or escapes from the trap in most cases. As the size of the gold spheres (50 ± 2nm) is not exactly the same, the scattering intensity of each trapped sphere is a little different from each other. That’s why the size of the steps in Fig. 2(b) is a little different from each other. In addition, the depth sometimes is nearly double of the others. We think there should be two gold spheres entering the trap at the same time. This technique of scattering intensity measurement provides a good method to monitor the number of gold spheres trapped in the trap in the real time.

 

Fig. 2 (a)A typical pseudo color image of the trapped gold spheres captured by the CCD.(b)Measured scattering intensity change with the time. Numbers indicated in the figure represent the gold sphere quantity in the trap.

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We substituted the CCD with a spectrometer and measured the scattering spectra of the trapped gold spheres. Figure 3(a) shows the spectra measured at ten different time points. We found that the peak positions of all the spectra are the same as that for only one gold sphere in the trap, but the amplitudes of the spectra increase with the number of gold spheres in the trap. This means that there is no interparticle coupling among trapped gold spheres [31]. Because the peak intensities of these spectra have nearly stepwise change, so it’s reasonable to guess that the peak intensity of the spectra is proportional to the number of the trapped gold spheres. Figure 3(b) is the scattering peak intensities obtained from Fig. 3(a) versus the estimated number of gold spheres. The black dots are the experimental data, and the red curve is the fitting result. It can be seen that the scattering amplitude of gold sphere is linearly proportional to the number of gold spheres in the trap. In order to compare these spectra in detail, we normalized them as seen in inset of Fig. 3(a). We can see that there is no interparticle coupling when the spheres in the trap are not dense enough.

 

Fig. 3 (a)Several spectra of the trapped gold spheres captured at ten different time points. Inset is the normalized spectra of scattering intensity. (b) Peak intensities of the spectra in (a) versus the estimated number of the trapped gold spheres. The black dots are the experimental data, and the red curve is the linear fitting one.

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The above experiments were done with diluted concentration of gold spheres. We also measured the scattering intensity of the undiluted solution (with a concentration of$2.36\times {10}^{-2}/\mu m^3$). To comparison, we normalized the spectra of single and multiple trapped gold spheres and displayed in one figure as shown in Fig. 4. From Fig. 4, we can see that the peak frequency is a little red shift and broadened. This is because while the concentration of solution becomes high, lots of gold spheres run into the optical trap simultaneously, there exists interparticle coupling when distance among the particles is short. It has been well proven that the interparticle coupling can bring about red-shifting and broadening of the spectrum [32]

 

Fig. 4 The normalized scattering spectra of the trapped single and multiple gold nanoparticles.

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In order to know the trapping potential of a single gold nanosphere, we use the similar method as mentioned in Ref. 30 to obtain potential energy of gold nanospheres. Firstly, we measured the relative enhancement △N of the particle number density N in the trap with the increase of laser intensity I for various particle concentations N as shown in Fig. 5. It can be seen that the relative enhancement of the particle is linearly related to the trapping intensity. Then we plot (2 × initial slope in Fig. 5)⁻¹ as a function of the initial number density N as shown in Fig. 6. The N = 0 intercept of the curve is k_BT/β, which yields β = 0.16 × 10⁻¹⁰ k_BT m²/W. Where β = U₀/I, U₀ is the depth of the potential energy. According to the obtained value of β, we give U₀ = 0.023 k_BT at 1mW laser power. We also calculated the potential energy of the gold sphere in optical trap by using Mie theory [33]. The parameters we used are the same as what we used in our experiment. The results showed that the potential energy along z axis is weakest. The value is U₀ = 0.067 k_BT at 1mW laser power, which is higher than experimental one. This discrepance comes from the fact that in the experiment, there inevitably exist spherical aberration of microscopy objective and mechanical instability of the setup, and so on, all of which can result in a smaller experimental value than theoretical one.

 

Fig. 5 The dependence of △N/N on the trapping intensity at five different particle concentrations.

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Fig. 6 (2 × initial slope of △N/N vs. I)⁻¹ for different particle concentrations.

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4. Summary

In summary, we have discussed the trapping of gold spheres by optical tweezers experimentally. As gold particle has large scattering and absorption cross section, only gold spheres with smaller size can be trapped. We developed two methods based on the setup of DF imaging and optical trap system to analyze the number of the trapped gold spheres in the situation when the concentration of the trapped spheres is low. One is counting the scattering intensity of the DF image of the trapped spheres, and the other is measuring the peak value of the scattering spectra of the trapped spheres. When there are lots of spheres in the optical trap, the scattering spectra broadens because of the interparticle coupling among the spheres. The potential energy of single trapped nanosphere is obtained by trapping an ensemble of nanaspheres. From the potential energy we obtained (0.023 k_BT at 1mW laser power), it looks that trapping efficiency is a little low, this is due to the fact that the N.A. is low in order to get good dark field image. The successful optical trapping of single and multiple gold spheres by optical tweezers is expected to open up a new way to study the plasmonic properties of metal nanoparticle ensembles in situ and in real time.