We propose a plasmonic system consisting of nano-disks (NDs) with graded diameters for the realization of nano-optical conveyor belt. The system contains a couple of NDs with individual elements coded with different resonant wavelengths. By sequentially switching the wavelength and polarization of the excitation source, optically trapped target nano-particle can be transferred from one ND to another. The feasibility of such function is verified based on the three-dimensional finite-difference time-domain technique and the Maxwell stress tensor method. Our design may provide an alternative way to construct nano-optical conveyor belt with which target molecules can be delivered between trapping sites, thus enabling many on-chip optofluidic applications.
© 2014 Optical Society of America
All-optical trapping and manipulation of small objects using far-field techniques have shown powerful application perspectives in biochemical and life sciences [1,2]. As the size of the objects to be trapped enters the nano-scale, high numerical aperture focusing and large incident power are required to create sufficient field gradient force overcoming the Brownian motion. This also renders damage in the target object, e.g., biological samples, because of the intense heat generation . Recently, with the help of surface plasmons (SP), plasmonic nano-optical tweezers (PNOTs) based on metal nano-gap , disk , antenna [5,6], pillars [7,8], strips [9,10], nano-ring , optical lattices [12,13], and coaxial aperture  etc have been proposed and demonstrated to provide strong trapping force with low incident power densities due to the field localization and enhancement. Trapping of nano-objects in a non-diffraction limited regime with ultra-high accuracy has become accessible .
However, the main emphasis of reported efforts is on the exploration of new types of PNOTs [4,5,7–13], and strengthening of the near-field force to achieve trapping with high degree of confinement [3,6,14]. On the other hand, not much has been reported in the literature on nano-particle (NP) manipulation using the plasmonic effect. Wang et al. have developed two schemes to address this issue [8,9]. In the first approach, manipulation of the trapped NP around a gold nano-pillar was achieved by rotating the incident polarization . In the second one, they controlled the particle position by tuning the relative intensity of two input beams that excited counter-propagating surface plasmon polaritons . Nonetheless, all-optical transference of target objects in a predefined pathway still remains challenging. Very recently, a series of C-shaped plasmonic structures with different size or orientation has been proposed and demonstrated to behave as nano-optical conveyor belt, which can achieve the transport of target in a peristaltic fashion by controlling the resonant wavelength or rotating the incident polarization [16,17].
The key concept is to create mobile trapping potential wells in the near-field, thus the trapped particle can be manipulated along with the movement of the potential well. Previously, plasmonic structures with graded property have been proposed to localize the SP at different position for different frequencies, therefore realizing the plasmonic “Rainbow” trapping effect [18–21]. The operation window is considerably broad ranging from visible to THz. The graded plasmonic effect can be implemented by changing one of the geometry parameters.
In this article, we propose the use of plasmonic nano-disks (NDs) having graded diameters [see Fig. 1(a)] as nano-optical conveyor belt for delivering the target in a controllable manner. Simulation studies conducted using the three-dimensional (3D) finite-difference time-domain (FDTD) technique and the Maxwell stress tensor (MST) method demonstrate the feasibility of scaling such manipulation from µm to nm level. The metal is silver and target is gold NP. Our design is capable of controlling the target position continuously via rotating the polarization and switching the wavelength of incident light. Because of its simplicity, the proposed device is easy to be fabricated . While manipulation of target objects in the nano-scale is clearly an important attribute for many domains within the field of bionanotechnology, we anticipate that our design holds promising potential for biochemistry and biophysics applications.
2. Modeling and optical forces calculations
In our modeling study, all NDs have a thickness of 35 nm and are fabricated on silica (n = 1.5). The environment is water (n = 1.33), and the target is a gold nanoparticle (Au-NP) of diameter 30 nm, while practically the fluorescent molecule labeled target should be used for tracking the trajectory of target . The choice of parameters is based on practical considerations. The light source (plane wave) illuminates the device from the top [along -Z axis, Fig. 1(a)] with X-polarized electric field. Perfect matching layers are used as absorption boundary. The relative permittivity of Ag is taken from reported data .
Figure 1(b) shows the normalized extinction characteristics of ND1 (diameter D1 = 150 nm, red line) and ND2 (D2 = 100 nm, blue line), respectively. Their resonant wavelengths are 775 and 622 nm, which are well separated from each other for the purpose of avoiding mutual disturbance between NDs. The respective full width at half maximum (FWHM) are 248 and 148 nm, indicating that decreasing the ND size will lead to higher Q-value and hence stronger resistance towards mutual disturbance. Moreover, it is worth pointing out that wavelengths such as 785 and 633 nm, etc., according to the practical availability of light sources, can also be chosen in the design by varying the size of NDs.
Figures 2(a)-2(b) present the distribution of the optical force Fxz in the XZ plane as experienced by the Au-NP for λ = 775 nm and 622 nm, respectively. It is clear that the optical force is significant around the resonant ND, and all resultant force vectors point towards the edge of the ND. In the non-resonant ND, we also see a trace amount of trapping force due to the cross-talk effect between the two NDs. In addition, field coupling between the target particle and the near-field of NDs is also present in the system. Such field coupling has been included in our MST calculation in order to achieve better accuracy of the final calculated optical force. Our results clearly demonstrate the wavelength-addressable character of the NDs. Consequently, if we sequentially excite the NDs by varying wavelength and polarization direction (to be demonstrated in the next section) of the incident beam, the overall effect of the optical force will always bring the target to a desired edge area of the ND where the optical field is most enhanced (i.e., hot-spot).
3. Optical potentials and rotational forces
Figure 3(a) shows the electric field intensity distribution in an XY plane at 10 nm above the NDs for λ = 775 nm and 622 nm. As one can see, plasmonic resonance of ND1 at λ = 775 nm provides strong field localization along the edge of ND1. Meanwhile, weak field enhancement also occurs around ND2 due to the cross-talk effect. Similar phenomenon is also present for the case of λ = 622. We take the common notation that the location of maximum intensity refers to a position where the trapping potential is strongest. Figures 3(b)-3(c) display the MST calculated force components Fx (blue ‒○‒) and Fz (red ‒□‒) experienced by the Au-NP along the X axis (Y = 0) at a distance of 10 nm above the NDs for λ = 775 nm and 622 nm, respectively. On the one hand, the horizontal force component Fx varies significantly over the resonant ND. The zero crossings of Fx indicate that the Au-NP will be dragged to the edge of resonant ND because of the intense field localization there. On the other hand, the vertical force component Fz remains negative and reaches a maximum at the edges. Therefore, the overall force will finally lead the target being trapped to the edge of ND which is in resonance.
The trapping potential corresponds to the work needed to move a target particle from a location directly above the structure to infinity [3,16]. Figure 3(d) shows the potential results as we integrate Fx along the X axis to a position far away from the edge of NDs where Fx almost vanishes. For the case of λ = 775 nm [red ‒○‒, Fig. 3(d)], ND1 is at resonance, and the trap depth reaches a maximum of ~230 kBT/W/µm2 around its edge. At the same time, the trapping potential is insignificant above the non-resonant ND2. While for the case of λ = 622 nm [blue ‒○‒, Fig. 3(d)], the maximum trapping potential moves to ND2, whose depth reaches a level of ~150 kBT/W/µm2 around the edge. However, a trace potential well due to cross-talk (i.e. spectral overlap) is also present in a region directly above ND1. This potential has a depth of ~60 kBT/W/µm2, and is resulted from field enhancement around ND1, despite being in a non-resonant state. The wider FWHM of ND1 as compared to that of ND2 means that excitation under λ = 622 nm will also give rise to a certain amount of field localization and enhancement around ND1. This trace potential well is not sufficient to influence the delivery of the trapped target from ND1 to ND2. For example, if we use a laser power density of 10 mW/µm2, the non-resonant field enhancement of ND1 only results in a trap depth of 0.6 kBT, which is not sufficient to provide any trapping effect. Consequently, one can readily see that by switching the excitation wavelength from 775 to 622 nm, the trapped target will be released from the left edge of ND1 and then trapped by the potential well at the right edge of ND2, where the trap depth (1.5 kBT) and is larger than the kinetic energy of Brownian motion kBT.
Because of their circular symmetry, the NDs have the ability of moving the target along its edge by changing the polarization angle . Figure 4 shows the overall force vectors Fxy, Fxz, Fyz as a function of incident polarization direction for λ = 775 nm and 622 nm, respectively. As the incident polarization being rotated anticlockwise from a starting direction along the X axis (i.e. at zero degree) to 90°, the force in the Y direction is no longer zero. Consequently, the trapped target particle will be dragged along the edge of the ND in the XY plane in anticlockwise direction. Also the weak polarization dependence of Fxz and Fyz ensures that the potential well is always sufficient to keep the target in a trapped state. Overall, by rotating the polarization one can simply move the potential well along the edge of ND.
The nano-optical transportation of target particle within the system can be realized through the following approach. First, by using λ = 775 nm illumination the nearby target can be trapped to the edge of ND1. Then by slowly rotating the polarization direction the target will move around the edge until it is at a location adjacent to ND2. Second, the target is released by ND1 and then trapped by ND2 by switching the wavelength from λ = 775 nm to 622 nm, and the time needed for switching the trapping force from one ND to another is on the order of 10 femtoseconds, according to the plasmon relaxation time . In this process the target will readily move into the trapping region of ND2. Consequently, manipulation of target particle arbitrarily between ND1 and ND2 can be controlled in the same manner, offering target confinement as well as movement at the nano-scale.
This scheme may have extensive potential applications. First, multifunctional operations are possible as the target (molecule, organism, or NP) could be manipulated to different locations for specific treatments, e.g. to perform a biochemical reaction or detection (e.g., Raman and fluorescence spectroscopy). Second, a long conveyor belt is contemplated as one duplicates the pair of graded NDs periodically in the X direction. Therefore a long working distance is realized without having to introduce any mechanical movement of optical components. Instead, one only needs to perform controlled switching of resonant wavelengths and rotation of the polarization angle.
On the other hand, in a practical implementation one should also take consideration that the photothermal effect resulted from light absorption as the heat will lead to thermal convection and thermophoretic forces which may compete with the optical trapping force [25,26]. The temperature around the plasmonic structure will increase inevitably, which results in a large temperature gradient in the surrounding. For the disk case, the resultant fluid convective velocity hardly exceeds 10 nm/s , which corresponds to a drag force of 2.8 × 10−3 fN on the target particle according to Stokes’ law . This force is not significant as compared to the optical force achieved by the NDs [~70 fN at 1 mW/µm2, see Fig. 3(b)]. Therefore, thermal convection is not expected to contribute significant disturbance to the optical trapping performance of our design. The thermophoresis effect is more complicated as it sometimes opposes the trapping and sometimes not . Generally, low incident power density is used in order to minimize thermal effects. However, one could consider fabricating the NDs on a thermally conducting material such as chemical vapor deposited diamond or aluminum nitride for efficient heat removal from the substrate. Indeed the photothermal problem is a common issue in the field of optical trapping. In addition, it should be mentioned that the incorporation of a heat sink, e.g. Au/Cu configuration [8,17], may modify the resonant wavelength of each ND in the final design. The dimensional parameters of the system will have to be re-calculated accordingly. Another method to avoid such change is the use of transparent substrate with high thermal conductivity such as diamond.
To sum up, we have proposed a nano-optical conveyor belt design based on graded silver NDs. The position of the hot-spots, as well as the target can be changed continuously by switching the incident beam wavelength and rotating the polarization. 3D FDTD technique and MST method are used to verify the feasibility of such function. Our design provides an alternative way for transporting targets within a nano-scale region, and is promising for biochemistry and optofluidic lab-on-a-chip applications.
The authors acknowledge the financial support from CRF grant (CUHK1/CRF/12G) provided by the Research Grants Council (RGC) of Hong Kong Special Administrative Region, China.
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