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A high-resolution optical trapping and manipulating scheme combining an optical fiber probe and an AFM metallic probe is proposed. This scheme is based on the combination of evanescent illumination and light scattering at the metallic probe apex, which shapes the optical field into a localized, three-dimensional optical trap. Detailed simulations of the electromagnetic fields in composite area and the resulting forces are described the methods of Maxwell stress tensor and three-dimensional FDTD. Calculations show that the scheme is able to overcome the disturbance of other forces to trap a polystyrene particle of up to 10nm in radius with lower laser intensity (~1040W/mm2) than that required by conventional optical tweezers (~105W/mm2). Based on the discussion of high manipulating efficiency dependent on system parameters and the implementing procedure, the scheme allowing for effective manipulation of nano-particles opens a way for research on single nano-particle area.
©2011 Optical Society of America
1. Introduction
After the invention of the laser, many new techniques have been proposed for optical trapping and manipulation of microscopic particles. The optical tweezers developed by Ashkin provides a convenient way to manipulate small particles non-destructively in a liquid environment [1], and has been widely investigated for trapping and observing cells and viruses in biological researches [2]. It has proved useful not only for trapping particles, but also for assembling objects ranging from micro spheres to biological cells [3]. However, due to the optical diffraction limit, most of these manipulations involve particles whose size is between one and several micrometers. For much smaller particles, such as atoms or molecules, the scanning tunneling microscope (STM) provides a powerful tool for manipulation and engineering, while dealing with neutral particles of a few nanometers, new experimental approaches are required.
STM developed in the early 1980s led to the invention of a series of scanning probe techniques with ultra-high resolution, such as atomic force microscope (AFM), near-field scanning optical microscope (NSOM), etc. The NSOM uses the evanescent field confined at the aperture of the optical fiber probe to provide images of surfaces with a resolution beyond the classical diffraction limit. Recently some researchers began to use the evanescent field for transportation and trapping of nano-particles and atoms [4–8]. Novotny proposed a scheme for optical trapping at the nanometer scale based on the highly enhanced electric field close to a laser-illuminated metal tip [9]. In the scheme the trapped particle can be moved only within the focal region of the illuminating light. Furthermore, the trapped particle is generally detected by the scattered light, which is often used to judge the status of a group of nano-particles, not suitable for observation and positioning of one single nano-particle. Tanaka proposed a novel high-resolution trapping scheme and presented a new methodology for calculating the trapping forces acting on a nano-scale particle in the near-field of optical fiber probe [10]. This scheme is yet limited to the theoretical numerical simulation, since the low-pass efficiency of the near-field optical fiber probe and the weakness of the evanescent field lead to the difficult manipulation for near-field optical tweezers. To solve the problem of weak near-field gradients, Chaumet proposed a novel approach to create an optical trap using evanescent wave scattering at the tip of an apertureless near-field probe [11]. In the scheme an apertureless near-field probe is used to create localized optical traps allowing for the selectively capture and manipulation of nano-particles in vacuum or air above a substrate. However, the particle can’t be manipulated vertically in a large region as well as horizontally due to a linearly decrease of the trapping force as the particle is moved away from the substrate.
For effective manipulation and better observation of single neutral nano-particle, an optical manipulation scheme for nano-particles combining an optical fiber probe and an AFM metallic probe is proposed. The possibility of trapping and manipulation of a nano-particle by strongly gradient forces generated by the evanescent field near two near-field probes needs to be discussed. More realistic models about near-field distribution from optical fiber probe have been proposed, such as Multiple-Multipole method and Boundary Integral Equation method [12,13], but these methods are quite complicated and restricted to 2D studies due to time and memory constraints. Here the treatment is based on the conservation law for momentum of electromagnetic field, and the expression using Maxwell stress tensor to compute trapping forces for arbitrary particles placed in near-field is presented. Because this new configuration of optical trap depends entirely on the near-fields near the tips, the near-field distribution is first investigated. Subsequently, the forces acting on a particle in three axis directions and the comparison of other forces versus optical trapping force are calculated. Then the efficiency of the manipulation scheme dependent on the distance between two probes and the incident angle, as well as the incident polarization direction and the wavelength is analyzed. Finally, the implement for near-field trapping is discussed.
2. Modeling of near-field trapping using Maxwell stress tensor and 3D FDTD methods
With the field distribution around the probe determined, the gradient force for a Rayleigh particle can be easily calculated using electromagnetic model [14]. In the model the external field is assumed to be homogeneous across the particle and the particle does not alter the field. These assumptions, however, do not hold for a nano-particle close to the probe tip. To overcome the limitation of dipole approximation, a rigorous treatment of the trapping force is performed by applying the direct calculation of Maxwell stress tensor using three-dimensional finite difference time domain method (3D FDTD). In the case of linear polarized continue light radiation, the emitting electromagnetic fields have six components in three-dimensional directions due to the depolarization after incident wave is scattered by the probe tip and the particle. Given the volume V near the geometry, the external boundary surrounded by the area is S, then the system’s conservation law of total momentum can be written as:
According to Eq. (1), it can be seen that the total force acting on the particle in the electromagnetic field is equal to the surface integral of stress tensor in the area S. While the electromagnetic field distribution near the probes is determined, the trapping force acted on a nano-particle can be expressed by Maxwell stress tensor [15]. For the need of typical analysis, only the distributions of trapping force in three axis directions are considered in the three-dimensional model. When projected intervals of the boundary surrounding the particle in the plane parallel to x=0 plane are [a 1, b 1] in y-axis and [c 1, d 1] in z-axis, projected intervals in the plane parallel to y=0 plane are [a 2, b 2] in x-axis and [c 2, d 2] in z-axis, and projected intervals in the plane parallel to z=0 plane are [a 3, b 3] in x-axis and [c 3, d 3] in y-axis respectively, the optical trapping forces along x-axis, y-axis and z-axis can be expressed as:
Here Δx, Δy and Δz is the grid space step of the discrete three-dimensional space in the FDTD calculation. If the computed force is positive, the direction of the axial force is along the positive direction of the corresponding axis. The trapping potential U of a particle located at r 0 is then given by:
Because the nano-particle is trapped in near-field region, the tapered metal-coated fiber probe used in NSOM and the metallic probe used in AFM have been optimized for the chosen of geometry size and wavelength in previous work [16,17]. Figure 1 shows the configuration of a three-dimensional model for the near-field simulation combining an actual optical fiber probe and a metallic probe under polarized laser irradiation. It is assumed that the optical fiber probe has two regions, i.e., a uniform waveguide region and a tip region. The optical fiber probe at the wavelength of λ=632.8nm is located perpendicular to a conical probe made of copper with the conductivity of l=5.8×107S/m, refractive index of 0.27 and extinction coefficient of 3.2. The finite height of the metallic cone illuminated by the emitting evanescent wave of optical fiber probe is 600nm with the radius of b=275nm, and the distance between the metallic probe and the optical fiber probe is 150nm. The waveguide is filled with homogeneous dielectric material with the refractive index of n 2=1.5. The tip angle of the fiber probe with diameter of φ 1=700nm is θ=90°. The metal cover with thickness of 140nm is assumed to be a perfect conductor. The aperture diameter φ 2=200nm is used in the computation that is carried out in Cartesian coordinates, setting the aperture center of the fiber probe as coordinates origin. Because the match between the polarization direction and probe axis is important for large optical enhancement in the near-field near the metallic probe, the 35mW excitation light polarized along axis y is incident on the optical probe with the coupled power of 400μW by regulating the laser power and with the expression of E=Eysin(2πft)=8.85×105sin(2πft). Direction and polarization of the incident laser are indicated by the K and E vectors. A small dielectric particle with the radius of a=10nm, the density of ρ=2.4×103kg/m3 and the refractive index of n 3=1.8 is assumed to be placed near the probe in a medium with refractive index n 1=1.3.
Fig. 1 The three-dimensional model for the near-field manipulating simulation combining two near-field probes. The calculated fiber probe consists of an Al-coated waveguide that extends infinitely to the left and has a nano-wavelength aperture at the right cutting-off end. The metallic cone probe with finite height is illuminated by the emitting evanescent wave of the optical fiber probe.
3. Results
3.1 Distribution of near-field electric intensity
In view of the interaction between the light and the particle is mainly caused by electric field, it mainly considers the distribution of the electric field intensity before calculating the trapping force acted on the particle. In order to reduce computation due to the limitation of the computer memory, the employed configuration is placed in a volume discretized in mesh cells of 120×178×101 for the FDTD calculation, with space step of Δx=Δy=Δz=10nm, and time step of Δt=Δx/2c, where c is the light speed in vacuum. Figure 2 gives the distributions of total electric field in y=0 and x=0 plane. Seen from Fig. 2(a), in the transmission of light to the optical fiber probe tip, most of light is reflected inward by metal cover and then superimposes on the incident light forming a strong standing wave field along probe axis. Based on the waveguide theory, light transmits in single-mode optical fiber waveguide in HE11 mode, when the light injects into the metal-coated optical probe, it will associate to the problem of transmission in metal waveguide where light is coupled to TE11 mode. As can be seen from the calculation, the internal electric field of optical probe is divided into two parts by the cut-off face. One part of light superimposes on the incident light forming a strong standing wave field, while other part decays exponential and then emits from the aperture yielding field enhancement at the tip of metallic probe. The field enhancement of metallic probe is caused mainly by the localized surface plasma mode excited at the probe tip by the evanescent field. The incident electric field has a component vertical to the surface of the metallic probe so that the localized-mode surface plasma can be subsequently excited. The distribution of electric field shown in Fig. 2(b) reflects that the emitting wave spreads along all directions and decays quickly after emitting from the aperture, thus the clear diffraction of emitting light occurs in x=0 plane. The near-field enhancement effect is apparent at the edge of aperture along y-axis and at the tip of metallic probe. After the electric field reaching the outside of metal cover, the secondary near-field high enhancement appears in the angularity of metal cover near metallic probe because of point effect, while no clear near-field enhancement occurs in the other angularity away from metallic probe. The field distribution asymmetry around metallic probe is induced by the field propagation direction, and field enhancement at the Cu/SiO2 interface also occurs in virtue of point effect. The complicated near-field distribution in x=0 plane will affect the manipulation of nano-particles, so different trapping positions will appear with different parameters. Compared the distributions in two planes, it is found that the light intensity around probe in x=0 plane is stronger than that in y=0 plane depending on the polarization of incident laser. Seen from the simulation of the near-field distribution, the highly confined coupling evanescent fields present strong three-dimensional field gradients after adding the AFM metallic probe, resulting in the trapping capability of near-field optical tweezers increasing. If one particle is placed in the field gradients, it will inevitably be trapped to the extreme points of the near-field when the gradient force is strong enough to overcome the external interference.
Fig. 2 FDTD simulated instantaneous field distributions in (a) y=0 plane, (b) x=0 plane. In the metal-coated fiber probe, few photons travel through the waveguide with a diameter less than a half wavelength because there is no waveguide propagation mode travelling through such a narrow waveguide, while the apertureless metallic probe with a scattering point at the tip does not need any narrow waveguide for photon transmission. A large optical enhancement can be gained comparing the metal-coated fiber probe near the tip where the diameter of the probe is much shorter than the wavelength.
3.2 Analysis of trapping forces in near-field
In above calculation, the interaction of the probe and the nano-particle close to the tip is not counted. For the force calculation, the geometry including the particle is placed in a volume discretized in mesh cells with space step of Δx=Δy=Δz=3nm. A concrete example of the real force on the particle is calculated firstly. In an actual experiment, the particle is mainly in five kinds of force: Brownian motion, gravitational, capillary, van der Waals and trapping forces. In order to get the information of trapping strength, Table 1 compares various forces acted on the nano-particle from the viewpoint of order-of-magnitude. The calculated trapping force is ~1×10−13N, thus the corresponding trapping potential is ~1×10−21J according Eq. (5). From the theorem of equal partition of energy in thermodynamics where T is the temperature in degrees Kelvin and k is the Boltzman constant, each degree of freedom of Brownian motion has kinetic energy Ek~1×10−21J at room temperature [18]. It is of the same order as the trapping force potential. However, it should be noted that the calculation above is only limited to the tip region of fiber probe less than 1μm for the need of reducing computation. According to tip-induced plasma oscillations, much stronger field enhancement will occur at the tip of the metal-coated fiber probe with longer tip height [19]. Hence the magnitude of trapping force generated in the near-field of fiber probe with actual tip height of about 200μm must be much greater than 1×10−13N. The results suggest that the trapped dielectric particle used in the scheme isn’t affected heavily by Brownian motion. If the radius of the particle is equal to 10nm it is found that the force of gravity is 9.8×10−20N. Since the trapping force experienced by the particle is larger (by a factor 107) than the gravitational force, the gravity can be neglected. If there is water on the substrate, according to the expression of capillary force where γ is the surface tension of water, one can get Fc=4.5×10−12N for a particle with radius of 10nm [20]. This force is about the same order as the optical force hence it isn’t easy for trapping particles on this substrate. However, it is beneficial to trap particles on the surface of water to the probe tip when the probe is placed in water. The van der Waals force between two objects can be described as a short range force, derived from the Lennard-Jones potential with the force form where h is the distance between the two objects, A is the Hamaker constant, z corresponds to the separation of lowest energy between two objects, and S is the Derjaguin geometrical factor related to the mutual curvature of the two objects [21]. When computing the van der Waals force between the dielectric particle and the substrate surface one has S=a (a radius of the particle), hence the force is 3.0×10−13N. This force does not hamper the manipulation of the particle as the actual trapping force is much larger than 1×10−13N. In addition, it is necessary to consider the van der Waals force between the tip of AFM probe and the particle when they are in contact. For the case where the radius of the particle and the curvature of the tip apex are equal to 10nm, with S=5nm, A=109.5zJ, one obtain Fw=2.7×10−13N. Hence the two van der Waals forces are of comparable magnitude and cancel each other out when the particle is in contact with both the substrate and the metallic tip. Under the action of van der Waals forces, the trapped particle tends to be released to the substrate when turning off the laser.
Table 1. Comparison of other forces versus optical trapping force.
Based on the discussion on forces above, it is concluded that one can trap a particle smaller than 20nm with an aperture of fiber probe larger than 200nm, for the role of forces other than the trapping force is weaken as the particle size decreasing. However, because the trapping force increases as the square of the intensity of the field while it is only linearly proportional to the particle diameter, the particles trapped by the scheme will be limited in size to above 20nm diameter. Thus one can trap a particle as small as 20nm diameter with an aperture around 200nm. To obtain stable trapping for a 20nm diameter particle, the incident laser intensity could be reduced to only 1040W/mm2, at least two orders of magnitude less than that for classical optical tweezers. This intensity is low enough to allow, for example, real-time investigations of the self-assembly process of delicate biological nanoparticles such as small virus capsids around trapped nanoparticle cores [22].
Because the particle is small, the scattering force is negligible, and since the relative permittivity is real, absorption does not contribute to the real force. Therefore, the trapping force exerted on particle mainly consists of two gradient forces. One is the positive gradient force due to the evanescent incident field located at the tip of optical fiber probe. For a dielectric particle, this gradient force always pushes the particle toward the region of high field intensity, as the evanescent field decays in the direction of z negative, this gradient force behaves as a positive value on the particle. The other one is the gradient force resulting from the interaction between the AFM metallic probe and the particle. This gradient force can be either positive or negative. For near-field illumination, there is a large enhancement of the field near the apex of the metallic probe due to the discontinuity across the air/copper boundary. This enhancement generates a negative gradient which counterbalances the positive contribution due to the incident evanescent field at short distance, resulting in the trapping force in z-axis direction experienced by the particle changes sign when the particle is 50 nm away from the fiber probe shown in Fig. 3 . Figure 3 gives the z-axis trapping forces acting on the dielectric particle at different heights. When the trapping force is positive the particle moves along z-axis direction. In contrast, the particle moves along -z-axis direction when the trapping force is negative. It can be seen that the forces decay rapidly in accord with the variation of the electric field outside of the probe as z becomes smaller. The attractive trapping force near the fiber probe tip descends to zero after z less than half the radius of the aperture, then becomes repulsive due to the gradient force of the metallic probe when the distance between the particle and fiber probe increases. The attractive force caused by the metallic probe is much stronger than that in the near-field trap using an optical fiber probe caused by the dominant gradient force. It is also larger than the trapping force in the model of near-field trap proposed by Chaumet [23], because the enhanced emitting evanescent field from the fiber probe is stronger than that generated by the total internal reflection of prism. Thus for a smaller dielectric particle, the variation of the trapping force in the axial direction can form two deep one-dimensional trap (A and B in Fig. 3) in the near-field region. In the z-axis direction, the particle tends to be trapped to the tip of the fiber probe or stay nearby the metallic probe. Especially, the particle with larger radius intends to be trapped to the tip of metallic probe attributed to the dominant trapping force under the metallic probe, which is similar to the trapping process in Chaumet’s scheme.
Fig. 3 Trapping force acting on the particle in z-axis direction. The small dielectric particle with the radius of a=10nm, the density of ρ=2.4×103kg/m3 and the refractive index of n 3=1.8 is placed near the probe in a medium with refractive index n l=1.3, it tends to be trapped to the tip of the fiber probe or stay nearby the metallic probe.
Considering the trapping forces in x=0 plane and y=0 plane regardless of the trapping force in other axis direction, the simulation results of the trapping force in y-axis direction and in x-axis direction given to the particle with the radius of a=10nm at 10nm and 150nm height above the aperture are plotted in Fig. 4(a) and Fig. 4(b) respectively. In Fig. 4, the particle moves along y-axis (or x-axis) direction when the trapping force is positive. In contrast, the particle moves along -y-axis (or -x-axis) direction when the trapping force is negative. As can be seen in Fig. 4(a), the curve in z=−150nm plane shows that the radial trapping force is expected to be attractive and decrease with the increase of the distance from the metallic probe tip. In this case, the particle is pulled close to the tip of metallic probe along its central axis. The other curve in z=−10nm plane shows that the relationship between the radial trapping force and the axial offset distance is different from that in z=−150nm plane. In z=−10nm plane, due to the complicated field distribution very near the aperture, the force changes sign for four times around the z-axis and the field peak near the aperture edge, then goes down to zero gradually in y-axis direction. Therefore, the trapping forces around the z-axis and two interior edge points of aperture are attractive, that means three trapping positions will appear in z=−10nm plane. The nano-particle will be trapped to one of those trapping position when using proper parameters to reduce the influence of the outer edge point near the metallic probe on the trapping effect. As shown in Fig. 4(b), as the intensity distributions of the electric field along x-axis keep one peak in z-axis direction far away from the aperture, the trapping force along x-axis is always attractive and symmetric to the z-axis. It will change sign near the z-axis and the field peak of the aperture edge, when the nano-particle is placed very near the aperture. Thus the particle is tends to be attracted to the z-axis or the aperture edge in x-axis direction. From Fig. 4(a) and Fig. 4(b), it is found that the physical properties of the trapping forces in x-axis direction and in y-axis direction are almost the same.
Fig. 4 Lateral trapping forces acting on the particle (a) in y-axis direction in x=0 plane and (b) in x-axis direction in y=0 plane at height 10nm and 150 nm above the aperture plane. The physical properties of the trapping forces in x-axis direction and in y-axis direction are shown.
To obtain the force field, the calculation is repeated for different center positions of the particle. Figure 5 shows the distributions of force exerted on the particle with the radius of a=10nm in y=0 plane and x=0 plane in vector form. The initial point of vector represents the center position of the particle, and the length and direction of the vector show the relative strength and direction of the trapping force. For each calculation, the position of the particle is changed near two probes, and gray circles represent the particle placed at the lowest positions. Comparing Fig. 5(a) and Fig. 5(b) with Fig. 2(a) and Fig. 2(b), it is found that the force distribution obtained for a nano-particle is approximately proportional to the distribution of near-field electric intensity. Thus a force direction would be toward maximum field intensity, and the force magnitude is strong in the region where its field gradient is large. When the particle with radius of several nanometers is placed very near the aperture and around two near-field peaks near the edge of the aperture, it will intend to be dragged to the aperture edge directly. While the particle placed at other positions far from the aperture in the near-field region, it will be pulled to the tip of metallic probe, then tends to be attracted to the tip surface of the probe. Furthermore, due to the dominant trapping force under the metallic probe, the particle with larger radius is only trapped to the tip of metallic probe.
Fig. 5 Distributions of force in vector form acting on particle (a) in y=0 plane and (b) in x=0 plane. The origin of each arrow represents the center of the particle and vectors represent the direction and the magnitude of forces. Due to the magnitude of the force varies significantly, only the forces with large magnitude are apparent in the force distribution.
3.3 Dependence of trapping efficiency on system parameters
The analysis of the trapping forces established the possibility to manipulate a nano-particle using the intense gradients near two probes. The particle tends to move to the higher intensity region where it has lower potential energy, but the trapping potential is sensitively dependent on the distance between two probes and the incident angle, as well as the incident polarization direction and the wavelength. It therefore needs to study the influence of different parameters of the system on the efficiency of the trap.
Figure 6(a) and Fig. 6(b) show the influence of the illumination on the capability of the scheme to manipulate a nano-particle. Figure 6(a) represents the z force experienced by the particle when it is located at the apex of the metallic tip, versus the distance between the optical fiber probe and the metallic tip. In Fig. 6(a) one can see that for a fixed angle of incidence, the larger the distance between two probes, the smaller the magnitude of the force experienced by the trapped particle. The highly confined coupling evanescent fields present strong three-dimensional field gradients after adding the AFM metallic probe, resulting in the trapping capability of near-field optical tweezers increasing. However, when the distance between two probes is adjusted, the trapping capability is different in virtue of the variation of perturbation between the optical fiber probe and the metallic tip. The exponential decay curve indicates that the strong trapping force under metallic probe occurs only when it approaches to the optical fiber probe in 0-100nm region. Therefore, it can be concluded that the near-field interaction between two probes is limited to a nanometer region, which means that the action range of the trapping force is about the radius of the aperture. Figure 6(b) shows the evolution of the z component of the force at the apex of the metallic tip as the distance between two probes keeps unchanged, versus the angle of incidence. Notice that for the original incidence perpendicular to the metallic probe axis, the magnitude of the z force decreases when the angle of incidence increases. When θ 1=90°, the evanescent wave is incident from the side with the polarization parallel to the tip axis, whereas θ 1=180° the tip is illuminated from the bottom with the polarization perpendicular to the metallic tip axis. A striking difference is seen for these two different incidences: for θ 1=90°, Fz=3×10−12N, and for θ 1=180°, Fz=3×10−13N. This means that it is easier to manipulate the particle when the angle of incidence is close to 90°. The result is different from that in the manipulation scheme proposed by Chaumet, in which the metallic probe is mainly illuminated from the bottom, and the light-intensity enhancements in near-field regions near a surface illuminated by total internal reflection give rise to enhanced trapping forces capable of trapping nano-particles [23]. At the incident angle of 90°, the intensity enhancement profile has a high contrast and the tip of metallic probe gets the highest enhancement. Accordingly, the interaction between the tip and the particle becomes weaker as the angle increases, and the magnitude of the force decreases due to the less component of the excitation field along the metallic tip axial direction.
Fig. 6 z component of the force experienced by the particle at the apex of the metallic tip as a function of (a) the distance between the optical fiber probe and the metallic tip with incident angle θ 1=115°, giving wavelength λ=632.8nm and polarization direction φ=0°, (b) the angle of incidence with the distance h 1=150nm, giving wavelength λ=632.8nm and polarization direction φ=0°, (c) the polarization direction with the distance h 1=150nm, giving wavelength λ=632.8nm and incident angle θ 1=90°. (d) z component of the force experienced by the particle with different laser wavelengths. Solid line: λ=543.5nm. Dashed line: λ=632.8nm. Dash dot line: λ=1523nm.
In the scheme the manipulating capability is also influenced by the excitation light, Fig. 6(c) and Fig. 6(d) show the influence of the polarization direction and wavelength of the incident laser. Figure 6(c) gives the evolution of the z force at the apex of the metallic tip versus polarization direction, for incident angle θ 1=90°. When the laser is p-polarized (i.e., φ=0°), maximum force can be expected at the tip of metallic probe. With increase in the laser polarization angle, the force decreases gradually. This implies that the match between the polarization direction and metallic probe axis is important for strong optical force in the trapping scheme. Due to the existence of birefringence in single-mode optical fiber with the variation of ambient temperature and stress, the polarization direction of incident laser may change randomly. Thus it is important to weaken the random polarization for high efficiency of the manipulation. Figure 6(d) shows the force acting on the dielectric particle along z-axis direction at three different wavelengths of incidence laser. A maximum force of 3×10−12N is predicted under the metallic tip with a wavelength of 543.5 nm, while the similar simulation with an incident laser beam of 1523nm yields a much lower optical force of 3×10−13N. This can be attributed to the fact that the “antenna-effect” which is prevalent at longer wavelengths is less dominant at visible wavelengths, and additional effects, such as tip-induced plasma oscillations, may affect the field enhancement [19]. With the decrease in the laser wavelength, the force region expands, thus the efficiency of the trap is frequency-dependent, and for higher efficiency, shorter wavelength laser should be preferred.
When employing FDTD to solve complicated geometries with different parameters, particularly the nanoscale probe tips that involve sharp discontinuities, unstable or false solutions may occur as a result of inappropriate choices of meshing elements or time evolution step. The trapping force on the dielectric particle can be also calculated using the Extended Lorenz-Mie Theory (ELMT) [24]. Therefore it can check the correctness of the computer simulation by comparing the FDTD results using Maxwell stress tensor with that using ELMT. Table 2 shows the numerical errors of trapping forces along z-axis acted on the particle for two methods with different parameters. When giving incident angle θ 1=90°, wavelength λ=632.8nm and polarization direction φ=45°, the z component of trapping force experienced by the particle at the apex of the metallic tip is calculated with different distances between two probe tips. It is found that most of results satisfy the ELMT results within an accuracy of 2% from the table. The good quantitative agreement between the results of two methods confirms the validity of the Maxwell stress tensor and 3D FDTD method with the combined system.
Table 2. Trapping force on the particle for different combined distance.
4. Implement for near-field trapping
The scheme is useful not only for trapping nano-particles, but also for assembling objects ranging from biological cells to nano-spheres. The schematic diagram of preliminary system is shown in Fig. 7 . The light reflected from the tapered metalized probe tip is propagated to the optical fiber and directed by the fiber splitter to a power meter for detection. The back-reflected light at the detector consists of a small depolarized component due to the polarization scrambling nature of the fiber. This light is optimized to ensure that the laser beam is efficiently coupled into the small diameter core and then directed all the way to the fiber tip. The combination of the flange attenuator and the polarization rotator permits continuous variation of the laser power and laser polarization suited for nano-manipulation. The fiber probe is attached to a multidimensional positioning stage, and then inserted into a sample on the substrate. Because this all-fiber coupling optical circuit with low-loss can well match the near-field optical probe, the stability of manipulating nano-particles will be greatly enhanced due to the good transmission performance of the optical circuit.
Fig. 7 The schematic diagram of experimental setup using the combination of an optical fiber probe and an AFM metallic probe. The AFM metallic probe attaches to a piezoelectric tube (PZT) controlled by a computer and the fiber probe is fixed on the turntable. The composite probes are inserted synchronously into a sample chamber moved by a nano-positioning stage, which includes three piezoelectric tubes.
The procedure for manipulating a nanometric particle using the combination of an optical fiber probe and an AFM metallic probe is as follows. First the inserted angle of the optical fiber probe is adjusted using the three-dimensional turntable fixed on the positioning stage to determine the direction of evanescent illumination. The constant-force mode is adopted while the AFM metallic probe approaches the fiber probe with piezoelectric device. Such mode avoids the contact of tips and maintains the distance suitable for nano-manipulation in the near-field between the optical fiber probe and the AFM probe. Once the adjustment of two probes has been finished, the AFM probe combined with a fiber probe remains stationary. The composite probes are placed above the substrate and immersed into the solution, when the piezoelectric tube moving the sample chamber in the z-axis direction. The laser power is then adjusted so that gradient forces generated by the localized field, which is shaped in the combination of evanescent illumination from the fiber probe and light scattering at the metallic probe apex, are strong enough to manipulate nanometer particles. A diluted solution ensures that only one particle is trapped each time by the composite probes, and ensures that there is little chance of a pair of particles being trapped in the same position. Therefore, the composite probes can move one trapped particle to a new position near the substrate, where it can be released by turning off the laser, both horizontally and vertically with the movement of the sample chamber using piezoelectric device. The released particle is then directly adsorbed to the substrate due to van der Waals interaction. Next, the composite probes return to the original position above the substrate with the movement of the sample chamber in the reverse direction for another nano-manipulation, so repeatedly. After completing the formation of ordered structure on the substrate that consists of nano-particles, AFM probe scans the surface in tapping mode for the observation of manipulation results.
The enhanced manipulating technique, although very promising, is delicate to implement for manipulating particles with diameters of tens of nanometers in practice until now for three reasons. First, before the particle can be captured, Brownian fluctuations will have a disruptive effect. Second, it is inconvenient to observe the whole process of manipulating nano-particles in real-time. The radiation pressure from the illuminating laser will impart momentum to the nano-particle. Therefore, one would have to capture a moving particle. Finally, due to the complexity in controlling the distance between the fiber probe and AFM probe, the trapping stability may be affected. It requires improved experimental approaches when dealing with those problems.
5. Conclusion
In conclusion, a scheme performing near-field optical trapping by combining an optical fiber probe and an AFM metallic probe has been proposed. The calculation based on Maxwell stress tensor gives the analysis of electromagnetic field in composite area and resulting forces acted on a nano-particle. One can obtain near-field optical trapping with much lower intensity than that required by aperture or apertureless probe-based trapping. Since the fiber probe has a strongly enhanced evanescent field by adding the AFM metallic probe, the near-field scheme is better suited to trap smaller particles, which is theoretically employable down to a particle size of 20 nm. The trapping ability is sensitively dependent on the distance between two probes and the incident angle, as well as the incident polarization direction and the wavelength. In addition, the implement for near-field trapping is discussed. It is convenient to find and position one nano-particle directly during manipulation due to the high resolution of AFM system. It is believed that this trapping scheme will provide a promising basis for the research on properties of subwavelength-sized structures and ultra-sensitive measurements of particles.
Acknowledgments
This research is supported by the National Natural Science Foundation of China (90923041), State Key Laboratory of Robotics and System (Harbin Institute of Technology) (SKLRS-2010-2D-10), and the 111 Project of China (B07018).
References and links
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