A simple method to trap and manipulate metallic micro/nano-particles on the surface of photorefractive crystals is proposed. After inducing inhomogeneous charge density and space-charge fields in photorefractive crystals by non-uniform illumination, both uncharged and charged metallic particles can be trapped on the illuminated surface due to dielectrophoretic force and electrophoretic force, respectively. A transition from dielectrophoresis to electrophoresis is observed when manipulating nano-silver particles with high surface space-charge field. Our results show that this method is simple and effective to form surface microstructures of metallic particles.
©2009 Optical Society of America
Manipulation of micro- and nanometer particles such as dielectric spheres, viruses, bacteria, living cells, organelles, small metallic particles, and even strands of DNA, plays a more and more important role in biology, physics, chemistry and material science. These tools are used to perform important functions such as the sorting, addressing, transporting, and trapping of cells and particles in these fields. The number of potential applications of nanoscopic metallic particles is growing rapidly because of their unique electronic structures, extremely large specific surface areas and unique optical property. Therefore, many researchers pay more attention to manipulate metallic nanoparticles to form different kinds of microstructures and nanostructures (such as metal islands [1,2], metal wires  and metal gratings ) by physical or chemic methods. Metal island films could couple incident light into the waveguide modes of the detector, resulting in increased absorption and enhanced the sensitivity of very thin semiconductor photodetector . Silver nanowires were of special importance and could significantly enhance the Raman scattering signal of molecules adsorbed on the surface , because silver possessed the highest electrical conductivity among metals. Eureniusl et al.  demonstrated patterning with subwavelength periodicity through interference between incoming light and light coupled into the waveguided modes of a thin membrane. The grating structure was formed by single-laser-pulse irradiation of disordered, evaporated gold (or silver) films of discrete island on a 40-nm-thick, square membrane.
Micro- and nanometer particles can be trapped optically [5–8] or electrokinetically [9–13]. In general, optical trapping and manipulation are derived from optical tweezers, which were first introduced and realized in experiment by Ashkin in the early 1970s . Conventional optical tweezers rely on the field gradients near the focus of a laser beam which give rise to a trapping force towards the focus. Optical tweezer can trap objects as small as 5 nm and can exert forces exceeding 100 pN with resolutions as fine as 100 aN . Optical manipulation techniques apply to particles as diverse as atoms, large molecules, small dielectric spheres in the size range of tens of nanometers to tens of micrometers. Electrokinetic trapping includes two mechanisms: dielectrophoresis and electrophoresis. While uncharged particles are driven by electric forces via dielectrophoresis from nonuniform electric fields, charged particles can be manipulated via electrophoresis and thus by uniform as well as nonuniform electric fields [14–16].
Optical trapping provides highly accurate manipulation, but requires high light illumination intensities and the number of particles that can be manipulated in parallel is limited. Electrokinetic methods can drive large and a mess of particles, but demand external voltage supplies. There is another choice, namely combining optical with electrokinetic methods using photorefractive crystals [17,18]. Spatially inhomogenous illumination excites and redistributes the charge carriers in photorefractive crystals to form space-charge fields which modulate the refractive index via the electro-optic effect [19,20]. The light-induced space-charge fields not only affect the refractive index but also provide near-surface lateral forces to manipulate small particles. Sarkisov et al. demonstrated the principle of trapping of micron-size dielectric particles by near-surface electric forces on lithium niobate (LN) crystals . Polystyrene spheres of 2.6μm diameter in colloidal water suspension were successfully deposited on the surface and formed periodical distributions of the particles. Recently, Eggert et al. continued these studies: dielectric particles, e.g. chalk particles in air and silicon carbide particles in paraffin oil were trapped on the surface of photorefractive crystals . The grating period of the dielectric particles was half of the one of the space-charge field.
This method is attractive since it neither requires high light intensity nor external voltage supply. The space-charge fields of photorefractive crystals can manipulate the uncharged particles via dielectrophoresis and charged particles via electrophoresis in the same way as the external electric field does. Dielectrophoresis [9–12] is defined as the motion imparted on uncharged particles by polarization and by action of the so-called electric field gradient. The direction of motion of the particle is independent of the direction of the electric field. The magnitude of the dielectrophoretic force depends on the size and shape of the particles, on the conductivity and permittivities of the particles and their suspending medium, and on the magnitude and gradient of the applied electric field. Electrophoresis  is the motion of charged particles relative to the surrounding liquid under the influence of an electric field. Particles dispersed in solution almost always carry an electric surface charge, hence an electrostatic Coulomb force is exerted on the dispersed particles from an external electric field. Negatively charged particles move towards the positive electrode and vice versa. The electrophoretic force is proportional to the product of the charge of the particles and the magnitude of the applied electric field.
When a particle is placed in an electrical field, it experiences a lateral force given by 
The first term embodies all electrophoretic phenomena while other terms contain all dielectrophoretic phenomena. The first term describes the Coulomb interaction between the net charge q of the particles and the electric field E. This term vanishes in the absence of a net charge on the particle or in an alternating field, whose time average is zero. The rest terms in Eq. (1) arise from the interaction of the dielectric polarization components induced in the particle by the spatially inhomogeneous electric field including the dipole (), the quadrupole () and higher order phenomena.
The dielectrophoretic force on a polarizable particle in a non-uniform field can be written as 
In this paper, we investigate the trapping of metallic micro and nanoparticles and the formation of metallic microstructures by light-induced space-charge fields on the surface of LN crystals. Our results show that uncharged metallic particles can be manipulated via the dielectrophoretic effect, and charged ones via the electrophoretic effect. Moreover, a transformation from dielectrophoresis to electrophoresis is observed when manipulating nano-silver particles with strong space-charge fields.
2. Experimental results and discussion
Two LN crystals (y-cut) were used in our experiments both with the dimensions of x × y × z(c) = 10.0 × 1.0 × 21.0 mm3. Sample I and Sample II were doped with 0.025 wt.% iron and with 0.05 wt.% iron, respectively. Two extraordinary polarized coherent beams from an Argon ion laser (wavelength λ = 488 nm) overlapped to form a light pattern with a sinusoidal intensity distribution in the sample. The light modulation depth m was approximately 1. A Mach-Zehnder interferometer was employed in our optical system to obtain the inhomogeneous light pattern, the periods of the light patterns were several hundreds of micrometers. The grating vector of the light pattern was parallel to the c-axis of the crystal. Charge carriers redistributed under the illumination and built up space-charge fields with the same fringe spacing. Metallic or non-metallic nanoparticles were dispersed into silicon oil by ultrasonic dispersion to form a colloidal solution. The colloid was dripped onto the surface of the modulated crystal, which was inclined so that the colloidal drop could pass through the illuminated area. A Zeiss microscope was used to observe the distribution of particles on the surface of the crystal.
Charged particles can be trapped by electrophoretic force from the space-charge fields. Firstly, aluminum particles with an average diameter of 1.52 μm, which were positively charged, were dispersed into silicone oil by ultrasonic dispersion. Holographic gratings with a period of 250 μm were recorded in Sample I without application of an external voltage. Then a drop of silicone oil with the suspended particles was brought onto the illuminated region of the inclined sample. Most of the particles were trapped onto the surface of the sample, the distribution of the particles result is shown in Fig. 1 . The period of the particle distribution was the same as that of the interference pattern.
In a second experiment, we used negatively charged non-metallic particles as well as aluminum particles to form particles lines. The non-metallic particles chosen here were carbon particles, the ones of a carbon powder for HP laser printers, which could easily be negatively charged. The diameter of those carbon particles was about 8~16 μm. The period of the light pattern, i.e. the space-charge field, was 400 μm. We dropped both the silicone oil with suspended toner particles and the silicone oil with suspended aluminum particles on the recorded grating region. Clear particle lines were established after several seconds on the inclined Sample I as shown in Fig. 2 . The black large particles were toner particles, and the gray small particles were aluminum powder. Carbon and aluminum particles were trapped in different locations, i.e. the carbon particles lines and the aluminum particles lines appeared alternately. Carbon and aluminum particle gratings had the same period as the light pattern. The distance between adjacent carbon and aluminum particle lines was about 200 μm, which was the half of the period of the recorded holographic grating.
We also tried to trap particles on the surface of Sample I in air. After recording the grating, we sprinkled carbon particles on the surface of the crystal. The carbon particles immediately positioned onto periodic lines with the same period as the light pattern. However, the particle lines were less clear than the ones formed by suspension in silicone oil.
Uncharged metallic particles, silver particles in our experiment, were trapped by dielectrophoretic forces, too. The mean diameter of the silver particles was 50 nm. The silver particles were also dispersed in silicone oil by ultrasonic dispersion. The period of the interference pattern was about 540 μm. The suspension of silver particles in silicone oil was dropped onto the illuminated region of Sample I, particle lines established after several seconds. Based on Eq. (2), one expected uniform particle grating with fringe spacing of 270 μm induced by a sinusoidal space-charge field, which was half of the period of the light pattern. However, a nonuniform particle grating was observed in Fig. 3 , the pitches between two adjacent particle strips were 252 μm and 288 μm alternately. The average period of the nonuniform particle grating was 270 μm, which was consistent with the analysis on dielectrophoresis. The nonuniform distribution was due to the high light modulation (m≈1), which caused the space-charge field with an asymmetric ramp function distribution instead of a sine-shape distribution . There was a low concentration line in the middle of every particle strip, which might result from particle-particle interaction by repulsive forces  and the existence of the position of zero dielectrophoretic force.
In order to understand the dynamic behavior of silver particles under the space-charge field, we first assume that the light modulation depth is much smaller than 1 and thus the space-charge field has a distribution of the sinusoidal shape as shown in Fig. 4 , where is the amplitude of the space-charge field with order of magnitude 107 V/m, k is the grating wave vector (, where Λ is the period of the light pattern).
According to the Eq. (2), the maximum dielectrophoretic forces, whose direction is parallel to the surface, take place at the region of high electric field gradients. The arrowheads in Fig. 4 indicate the different direction of the dielectrophoretic force at different regions. The dielectrophoretic forces will drive the polarized particles along the direction of the arrowheads moving to the positions where the dielectrophoretic force is zero, i.e. the high electric field locations (the dotted lines shown in Fig. 4). Thus the metallic particles, which dispersed in the insulation oil, deposit near the location of high electric field. But in Fig. 3, less or no metallic particles exist at center of the high electric field area, which is due to the existence of the zero dielectrophoretic force. There are two high concentration regions in one period, which means that the period of particles lines formed by dielectrophoretic force is half as that formed by electrophoretic force comparing with the same period of light pattern.
However, it is well-known that though the optical intensity is sinusoidal, the space-charge fields and photorefractive gratings in photorefractive crystals are not exactly sinusoidal. The amplitude and phase of the space-charge fields and index gratings depend on the modulation depth of intensity m . Kukhtarev’s theory [19,20] on holographic gratings was carried out under linear approximation with a small modulation depth of the light intensity (), whereas under the large m, the increasing contribution of the high order harmonic implies a localization of the space-charge field pattern, leading to both space-charge field and the ionized donor concentration with sharp-peaked profiles [24–27]. In case of LN:Fe crystals, the dominating mechanism is photovoltaic effect, the saturation voltage of space-charge field can be in excess of 107 V/m . Strong photovoltaic effect can introduce a clear asymmetry in the profile of space-charge fields and the gratings fringes .
Therefore, under the large light modulation, the electric fields have a complicated and asymmetric ramp function distribution instead of a sine-shape distribution, which leading to the asymmetric distribution of the dielectrophoretic force, which can explain the experimental results in Fig. 3.
The transition from a dominating dielectrophoretic effect to a prevailing electrophoresis effect had been observed experimentally with Sample II. Because the iron concentration of Sample II was twice larger than that of Sample I, stronger space-charge fields could be induced in Sample II [20,28]. After recording a photorefractive grating with a period of 600 μm into Sample II, silicone oil with suspended uncharged silver particles was dropped on the illuminated region. The surface was inspected immediately by microscopy. The pictures in Fig. 5 show the change of the distribution of the silver particles with time. The time interval between two adjacent pictures was about 30 seconds.
Because the silver particles were electroneutral in the beginning, the silver particles were trapped by dielectrophoretic force to form non-uniform particle gratings as shown in Fig. 5(a). There were two particle strips in one period of the light pattern, which was the characteristic of the dielectrophoretic effect. The dielectrophoretic forces led particles to the area with positive bound charges and with negative bound charges. High concentration strips were formed at negatively charged regions, while low concentration strips were formed at positively charged regions. The silver particles at regions with positive charges were soon charged, the particle-particle and particle-crystal repulsive forces would drive the charged silver particles away from the initial location by electrostatic Coulomb force. Then particle strips at positively charged area became lighter and lighter and disappeared in the end while those at negatively charged area became darker and darker as illustrated in Fig. 5. The appearance of the lower concentration line in the middle of the particles strip was due to the existence of the zero point of the dielectrophoretic force as explained above.
In summary, we offer a simple and effective method to form surface metal microstructures. Metallic particles had successfully been manipulated and trapped by the strong surface space-charge fields of LN crystals via dielectrophoresis and electrophoresis. Metal particle gratings were formed with periods between several micrometers and several hundreds of micrometers.
Our further study will focus on the fabrication of surface metallic particle patterns with sub-micrometer scale structures. Therefore, we should consider the possible minimal periods of interference pattern and of space-charge field in advance. It is well-known that holographic interference patterns inside a medium have a minimum grating period by use of a pair of counter-propagating beams, where n is the refractive index of the recording medium. For LN crystals, the principal extraordinary refractive index n e is about 2.25 (@λ = 488 nm) , then the minimum grating period in such crystals is about 108 nm. Shen et al. had proposed and demonstrated a novel scheme for recording a second-harmonic index grating to achieve grating period beyond diffraction limit in photorefractive crystals . By using a double-exposure process in a Mach-Zehnder interferometer with a dual input port, they recorded a second harmonic index grating with a period of . Theoretically, the space-charge field with minimum grating periods of about 54 nm might be achieved in LN crystals by employing this technique. Therefore, in principle we might form metallic particles gratings with the period of several tens nanometer with this method. However, there are some other limiting factors to prevent the fabrication of surface particle pattern with sub-micrometer structure, such as inter-particle interactions and the agglomeration of particles. The inter-particle interactions among charged particles prohibit the formation of high concentration of particles, and thus affect the fringe visibility. In order to form smooth and continuous particles lines, it is better to use particles with diameter less than one fifth of the fringe spacing. The agglomeration effect will increase the diameter of particles, so we should and might use proper dispersing agent to avoid agglomeration.
Moreover, grating is the foundational microstructure, we can also obtain arbitrary surface microstructure of metallic particles by extended methods. Space-charge fields can be in principle induced by inhomogenous illumination using imaging method with an amplitude or phase mask. Thus optional particle-decorated surface structures in the micrometer range may be fabricated.
Supported by Tianjin Natural Science Foundation (07JCYBJC16600), National Science Foundation of China (10874093, 10604033, 10804055), National Basic Research Program of China (2007CB307002), the Key International S&T Cooperation Project (2005DFA10170), the 111 Project (B07013).
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