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Trapping of Resonant Metallic Nanoparticles with Engineered Vectorial Optical Field

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Trapping of Resonant Metallic Nanoparticles with Engineered Vectorial Optical Field Nanophotonics 2014; 3(6): 351–361 Research article Guanghao Rui and Qiwen Zhan* Trapping of resonant metallic nanoparticles with engineered vectorial optical field Abstract: Optical trapping and manipulation using optical trapping have evolved from simple manipulation focused laser beams has emerged as a powerful tool in the to the application of calibrated forces on, and the meas- biological and physical sciences. However, scaling this urement of nanometer-level displacement of optically technique to metallic nanoparticles remains challeng- trapped objects. Because of their unique features, optical ing due to the strong scattering force and optical heating tweezers have revolutionized the experimental study of effect. In this work, we propose a novel strategy to opti- small particles and become an important tool for research cally trap metallic nanoparticles even under the resonant in the fields of biology, physical chemistry and soft matter condition using engineered optical field. The distribution physics [2]. of the optical forces can be tailored through optimizing Nowadays, optical trapping has been successfully the spatial distribution of a vectorial optical illumina- implemented in two main size regimes: the sub-nanometer tion to favour the stable trapping of a variety of metallic (e.g., cooling of atoms, ions and molecules) and microm- nanoparticles under various conditions. It is shown that eter scale (such as cells). However, it has been difficult to this optical tweezers has the ability of generating negative apply these techniques to the nanoscale between ∼1 nm scattering force and supporting stable three-dimensional and 100 nm because of the challenges in scaling up the trapping for gold nanoparticles at resonance while avoid- techniques optimized for atom cooling, or scaling down ing trap destabilization due to optical overheating. The those used for micro-particle trapping [3]. New approaches technique presented in this work offers a versatile solu- were thus developed to stably trap and manipulate nano- tion for trapping metallic nanoparticles and may open up structures. Over the past few years, these techniques have new avenues for optical manipulation. been successfully applied to a variety of objects, such as metallic nanoparticles, [4, 5] carbon nanotubes [6, 7] and Keywords: radial polarization; optical trapping; resonant quantum dots [8, 9]. metallic nanoparticle. Some of the unique size-dependent properties of metallic nanoparticles make them highly attractive in many areas from biology to electronics. For example, sur- DOI 10.1515/nanoph-2014-0006 Received March 11, 2014; accepted August 4, 2014; previously pub- face-enhanced Raman spectroscopy (SERS) takes advan- lished online August 25, 2014 tage of the local field enhancement offered by optically resonant metallic nanoparticles to amplify the Raman signal and allows in principle for label-free detection of 1 Introduction proteins, pollutants, and other molecules [10]. Due to the noncontact and “holding” nature, optical trapping is well In 1986, Ashkin and colleagues reported the first obser- suited to be combined with SERS, potentially enabling vation of stable three-dimensional (3D) optical trapping, ultrasensitive molecular recognition in liquids. However, or optical tweezers, created using radiation pressure from trapping resonant metallic nanoparticle is challenging a single laser beam [1]. Since then, the capabilities of due to two main reasons. Firstly, at the electronic reso- nance condition, the induced polarization is resonantly *Corresponding author: Qiwen Zhan, Electro-Optics Program, enhanced, and so is the induced scattering force. It is University of Dayton, 300 College Park, Dayton, OH 45469, USA, difficult to trap resonant particles with a single focused e-mail: [email protected] laser beam because the resonantly enhanced scattering Guanghao Rui: Electro-Optics Program, University of Dayton, 300 force strongly pushes particles away from the focal spot. College Park, Dayton, OH 45469, USA Secondly, resonant illuminations of metallic nanopar- Edited by Andrea Alu ticles give rise to strong heating effects because of the © 2014 Science Wise Publishing & De Gruyter 352 G. Rui and Q. Zhan: Trapping of resonant metallic nanoparticles with engineered vectorial optical field light absorption [11]. The high temperature of the trapped beam [17, 18], a recently reported technique to generate a nanoparticles caused by this heating effect may destroy scattering force that points against the optical power flow. the trapping and release the nanoparticles. Several The main difference is the tractor beam pulls the particles approaches were developed to increase the trapping effi- all the way towards to the light source with no equilibrium ciency of metallic nanoparticles [5, 12, 13]. For example, point, while the particles conveyed by the engineered vecto- radially polarized beam was proposed to replace the con- rial optical beam introduced in this work gets stably trapped ventional linear polarization as the illumination in optical at an equilibrium position. The optical forces exerted on a tweezers [14]. Highly focused radial polarization provides gold nanoparticle are numerically calculated as examples stronger gradient force to pull the particles towards the and the associated optical heating effect is also studied by center of the focus. The feasibility and advantage of using a finite element method (FEM) modeling. The results dem- radial polarization to trap metallic nanoparticles have onstrate that this novel optical trapping strategy has the been both theoretically and experimentally demonstrated capability to trap resonant metallic nanoparticles and the when the trapping wavelength is far from the plasmon optical force can be engineered to suit for different needs by resonance [15]. However, as the trapping laser wavelength modifying the vectorial optical field illumination. approaches the resonance of the nanoparticle, the scat- tering force become comparable to or even larger than the gradient force owing to the unique vector field distribu- tion of the highly focused radial polarization [16], thus the 2 Results benefit of using radial polarization appears to be reduced. In this manuscript, a novel strategy is proposed to form 2.1 Configuration of the optical tweezers a stable 3D trapping of metallic nanoparticles even under resonant conditions through careful and purposeful engi- The proposed optical tweezers is schematically illustrated neering a vectorial optical field as the illumination. The in Figure 1. The optical tweezers is constructed around a required optical illumination is created by sculpting the high NA aplanatic objective lens that focuses the illumi- amplitude and phase of a radially polarized optical field. nation as tightly as possible. The main idea of the trap- When strongly focused by a high numerical aperture (NA) ping method is to build a vectorial optical field that is objective lens, this specially engineered vectorial optical beneficial for the formation of a stable 3D confinement for field offers both the non-propagating feature of the radial metallic nanoparticles. Since stable trapping requires the polarization and the optical pulling feature of the tractor axial gradient force to dominate over the scattering force, Radial polarization incident Objective lens Diffractive optical element Figure 1 Diagram of the proposed optical tweezers setup. An incident radially polarized beam with increasing intensity towards the edge is highly focused by an objective lens. Q(r, ϕ) is an observation point in the focal plane. A diffractive optical element (DOE) is inserted at the entrance pupil plane of the objective lens. The boundary between the inner and outer zones of the DOE is indicated by θ0. G. Rui and Q. Zhan: Trapping of resonant metallic nanoparticles with engineered vectorial optical field 353 θ a potential viable approach is to minimize the scattering E (,rz φθ, )2= AUmax ()MP()θθ()sincθθos Jk(sreinθθ),ikz cosθd r ∫0 1 θ effect through the generation of negative scattering force. max 2cikz osθ E (,rz φθ, )2=iA UM() ()θθPJ()sin(θθkr sin)edθ, Usually the scattering force is considered to deteriorate z ∫0 0 θ 1 max ikz cosθ the optical trapping. However, under certain conditions Hφ(,rz φθ, )2= AU()MP()θθ()sin(θθJkresin) dθ, Z ∫0 1 the direction of the scattering force can be reversed to be 0 against the power flow, which pulls particles towards the (1) light source. For example, this type of backward scatter- where Z is the intrinsic impedance of the ambient ing force has been reported for some Bessel beams gen- 0 medium, J (r) is the nth order Bessel function of the first erated with a cone of plane waves converging at very n kind, U(θ) is the amplitude distribution of the illumina- high angles [17]. It is known that the axial component of tion, M(θ) is the phase modulation provided by the DOE, highly focused radial polarization is proportional to the P(θ) is the pupil apodization function of the objective zero-order Bessel function. Thus the radial polarization is lens, θ is the maximal angle determined by the NA of chosen as the building block of the trapping optical field max the objective lens, and k is the wavenumber of the incident in the proposed method for the purpose of creating a nega- light in the medium. The constant A is given by A = πfl /λ, tive scattering force. The NA of the objective lens is chosen 0 where f is the focal length, λ is the wavelength of incident such that the maximum converging angle from the edge of wave in the ambient environment, and l is associated the lens is 89° in order to increase the negative scattering 0 with the laser beam power. The aplanatic objective lens force as much as possible. Since the negative scattering obeys the sine condition such that the spatial coordinates force is mainly attributed to the optical field that comes in the entrance pupil and the angular direction after the from large converging angle, a non-uniform amplitude lens is related through r = f·sin(θ) and its apodization func- distribution of the illumination will be used such that tion is given by [20]: the intensity increases gradually from the center to the edge.
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