Optical force on yeast cells generated from surface plasmon polaritons

The surface plasmon resonance phenomenon is widely used in sensing, near-field control, and nonlinear optics. In this paper, the optical near-field generated by the surface plasmon resonance phenomenon is applied to trap yeast cells. The effect of the relative axial distance between the gold film surface and the waist of the focused beam on the trap stiffness is studied. There is a maximized trap stiffness at a specific relative axial distance for trapping yeast cells. The trap stiffness is significantly higher than the value at other locations. This study can be applied to screening of particles with different sizes.


1.Introduction
Surface plasmon polariton (SPP) is a surface electromagnetic mode in which the incident electromagnetic wave and the collective oscillation of free electrons on the metal surface coupled at the interface between a metal and a dielectric layer.SPPs generate field localization and field enhancement on the metal surface and have the ability to break the diffraction limit.In 1902, Robert W. Wood observed that the reflected light of metal gratings was composed of multiple bright and dark fringes, and the phenomenon of surface plasmon resonance (SPR) was observed for the first time [1] .In 1960, Ferrell proposed the concept of SPP [2] .In 1968, Otto and Kretschmann invented the prism-coupled structure to match the wave vectors of the incident light and the SPP separately [3,4] .And this coupling strategy is still a common way to stimulate SPR so far.
SPR phenomenon is used in optical sensing technology, since the resonance condition is sensitive to changes on the metal surface in the vicinity approximate 100nm.In this paper, we propose to use the setup of the traditional optical tweezers combined with a 50nm thick gold film to excite the SPP propagating in a circular pattern.Changing the relative axial position of the metal surface and the waist position of the focused beam [5] can change the diameter of the exciting ring.Trapping yeast cells has been conducted, and the result shows that the trapping system has a highest stiffness coefficient at a specific relative axial distance.The portion of the non-SPR resonance incident beam is reflected by the metal film, and the scattering force that pushed the particle along the light propagating direction is minimized consequently.It is advantageous to the optical trapping.Since only the propagating surface plasmon polariton of the metal film needed for this SPR tweezers, complex nanofabrication processes can be avoided.This research has potential to be applied in different size particles sorting.

2.Experiment
The SPR tweezers system is based on a traditional optical tweezers configuration using an inverted objective.The incident laser beam is highly focused to excite SPR [6] to capture yeast cells.The schematic diagram is shown in FIG. 1.In the system, a nanometer resolution stage is used to accurately displace the sample cell.A gold thin film (50 nm) is used to support the SPR phenomenon at the interface of gold/water.The 100X objective (NA=1.4)can support the SPP resonance angle, while the 50X objective (NA=0.8)cannot provide this resonance condition.A polarization beam splitter is used to generate a linear polarized incident beam.The trapping beam is a laser at 638nm.The images of the yeast cells are captured by a CMOS camera.In this paper, the thermal equilibrium method is used to calibrate the stiffness coefficient of the optical trap [7] according to the Brownian motion characteristics of the yeast cell.We adjust the relative axial distance between the focused beam and the metal film (Figure 2), then record the captured video.A MATLAB program is used to process the video and record the coordinates of the trapped cell position and the particle radius of each frame.The same relative axial distances are examined both for the SPR tweezers and the traditional optical tweezers.

Conventional optical tweezers
First, a cover glass is used to prepare a sample pool to study the trap effect of the traditional optical tweezers.The focused beams using 100x and 50x objective lenses are tested, respectively.The trap stiffness results are shown in Figures 3 and 4, respectively.Axial relative distance 0 is at the waist spot, a positive axial distance indicates that the focused beam moves into the cover glass, and a negative value indicates that the focused beam moves into the sample pool, i.e., the yeast cells solution.
Figure 3: Relationship between stiffness coefficient and relative axial distance of a traditional optical tweezers based on 100X objective The stiffness coefficient of the traditional optical tweezers varies with the axial position into two regions, the low stiffness region and the high stiffness region.In the low stiffness region, the yeast cells were close to the surface of the cover glass.The optical force exerted by the optical tweezers was not enough to overcome the yeast cell deformation, which affected the stiffness coefficient of the optical tweezers.In the high stiffness region, the stiffness coefficient is basically unchanged, and yeast cells are captured slightly above the focused beam waist, i.e., the gradient force [8] and scattering force [9] balanced and a stable trap achieved.The stiffness coefficient of the traditional optical tweezers based on a 50X objective lens is lower than that of traditional optical tweezers based on a 100X objective lens.

SPR tweezers
A 50nm thick gold film [10] is used to form SPR tweezers, and 100X and 50X objective lenses are used to test the capture effect of SPR tweezers.The experimental results are shown in Figure 5 and Figure 6 respectively.The 100X objective lens can satisfy the large incidence angle to excite SPR.With the increasing of the relative axial distance between the gold film and the objective lens, the overall trend of the stiffness coefficients using x and y polarized incident beam is the same.The trap stiffness dramatically increases to the highest point (x polarized beam is 7.58×10 -7 N/m and y polarized beam is 2.68×10 -7 N/m) and then dramatically decrease, and the relative axial distance corresponding to the maximum trap stiffness is about 5 µm.The 50X objective does not satisfy the incident angle requirement to excite SPP.We observe that the stiffness shows a high stiffness region and a low stiffness region, similar to the traditional optical tweezers.When the relative axial distance is greater than 6 μm, the stiffness coefficient is in a high range.The size of the yeast cell is approximately 6 μm.When decreases the relative axial distance, the gold surface gradually approaches to the waist of the focused beam.As a result, the force exerted by the optical tweezers is not sufficient to resist the deformation of the yeast cells.Compared to the conventional optical tweezers with a 50X objective, due to the presence of the gold film, the stiffness coefficient of SPP optical tweezers is significantly smaller than that of conventional optical tweezers in the high stiffness region.The difference between the stiffness coefficient value and the low stiffness region is not obvious, most of the incident light is reflected by the metal film.It also verifies that the 100X objective SPR tweezers can improve the optical stiffness coefficient.

4.Conclusion:
In this paper, the trapping stiffness of SPR tweezers based on a gold film on yeast cells is studied.The relative axial position between the gold film surface and the focused beam waist are examined specifically.The results demonstrate that there is an optimum relative axial distance for yeast cells trapping.Away from this position, the trap stiffness of the SPR tweezers dramatically decreases.This phenomenon can be used to sort particles with different size.

Figure 1 :
Figure 1: Schematic diagram of the SPR tweezers system

Figure 2 :
Figure 2: Demonstration of the relative axial distance between the focused beam and the metal film or glass substrate (case not shown).

Figure 4 :
Figure 4: Relationship between stiffness coefficient and relative axial distance of a traditional optical tweezers based on 50X objective

Figure 5 :
Figure 5: Relationship between stiffness coefficient and relative axial distance of a SPR tweezers based on 100X objective

Figure 6 :
Figure 6: Relationship between stiffness coefficient and relative axial distance of a SPR tweezers based on 50X objective