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Photonic Tractor Beams: a Review Review Article Photonic tractor beams: a review Weiqiang Ding,a,* Tongtong Zhu,a,b Lei-Ming Zhou,b and Cheng-Wei Qiub,* aHarbin Institute of Technology, Department of Physics, Harbin, China bNational University of Singapore, Department of Electrical and Computer Engineering, Singapore Abstract. Usually, an unfocused light beam, such as a paraxial Gaussian beam, can exert a force on an object along the direction of light propagation, which is known as light pressure. Recently, however, it was found that an unfocused light beam can also exert an optical pulling force (OPF) on an object toward the source direction; the beam is accordingly named an optical tractor beam. In recent years, this intriguing force has attracted much attention and a huge amount of progress has been made both in theory and experiment. We briefly review recent progress achieved on this topic. We classify the mechanisms to achieve an OPF into four different kinds according to the dominant factors. The first one is tailoring the incident beam. The second one is engineering the object’s optical parameters. The third one is designing the structured material background, in which the light–matter interaction occurs, and the fourth one is utilizing the indirect photophoretic force, which is related to the thermal effect of light absorption. For all the methods, we analyze the basic principles and review the recent achievements. Finally, we also give a brief conclusion and an outlook on the future development of this field. Keywords: optical pulling force; optical tractor beam; optical manipulation; Bessel beam; nanophotonic structures; photophoresis; photophoretic force. Received Oct. 12, 2018; accepted for publication Feb. 27, 2019; published online Mar. 27, 2019. © The Authors. Published by SPIE and CLP under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI. [DOI: 10.1117/1.AP.1.2.024001] 1 Introduction an unfocused beam, the intensity gradient force vanishes and 1 1–3 the object is expected to be pushed away. However, about Since the pioneering works by Ashkin, optical manipulation 10 years ago, researchers found that the object may experience utilizing the mechanical effect of light has developed exten- an optical pulling force (OPF) toward the source direction when sively in various contexts. Optical tweezers and other related illuminated by an unfocused beam, such as a diffraction-free manipulation technologies have become indispensable in 27,28 – (nondiffraction) Bessel beam, which is named an optical various disciplines, including biology,4 7 chemistry,8 quantum science and technology,9–11 and nanotechnology.12–14 One re- tractor beam (OTB). Although it seems counterintuitive, OPF markable trend amid this progress is that optical manipulation has been theoretically proved and experimentally demonstrated has been extended, from the initial single freedom of trapping within recent years, as will be reviewed in this paper. The pulling force by a single beam was first noticed by using the conservative optical force, to multiple freedoms using 29,30 both conservative and nonconservative forces,15 including push- Marston in acoustics, who found that the axial radiation force ing,16 pulling,17 lateral shifting, rotating,18–21 and spinning.22 of a Bessel acoustic beam on a sphere could be inverted (from Among all the newly developed manipulation freedoms, pushing to pulling) for some carefully designed objects, which optical pulling is one of the most interesting and has attracted suppressed the scattering to the back hemisphere. Since the much attention,23–26 due to the potential applications and in- acoustic and optical waves share many common features, triguing physics behind it. Usually, when illuminated by a it is not surprising to find pulling force in optics using similar tightly focused beam, the intensity gradient resorting force can methods. Shortly after Marston, optical pulling phenomena overcome the scattering force, and the object can be trapped were predicted by Lee et al.24 in an optical solenoid beam, which near the focus spot.2 On the other hand, when illuminated by is a diffractionless beam with in-plane intensity peak spirals around the optical axis. In the same year, the concept of OTB 26 *Address all correspondence to Weiqiang Ding, E-mail: [email protected]; Cheng- was confirmed by Sukhov and Dogariu. Following, another 27 Wei Qiu, E-mail: [email protected] two theoretical works published independently by Chen et al. Advanced Photonics 024001-1 Mar∕Apr 2019 • Vol. 1(2) Ding et al.: Photonic tractor beams: a review Fig. 1 (a) Definition of the OPF used in this paper. The source and object are centered at A and B, respectively, and the center-to-center vector AB (dashed blue) defines the pulling or pushing force axis. When the angle θ between the optical force F (the black thick arrow) and the axis AB is larger than π∕2, the force is a pulling one. The special case of θ ¼ π is the most desirable in practice. When θ is less than π∕2, the force is a pushing one and the special case of θ ¼ 0 is widely investigated in practice. (b)–(e) Four different mechanisms for achieving the OPF, where the special case of θ ¼ π is shown for clarity and S shows the energy flow. OPF (b) using structured light beams, (c) using objects with exotic optical parameters, (d) using structured background media, and (e) using the photophoresis effect. and Novitsky et al.28 gave a clear analysis of the criteria and impinge on and are scattered by the object using various me- method to obtain an OPF. Since then, the OTB began to attract chanics. In order to make this review clear and easy to follow, more and more attention due to the interesting phenomena and we classify the mechanisms of OPF into four kinds based on physics involved and possible applications in optical manipula- the predominant factor in the pulling process, as shown in tion technology. What is more, the concept of OTB and pulling Figs. 1(b)–1(d). The first one is using structured beams, the sec- force has been extended to other forms of wave, including ond is using objects with exotic structures and parameters, the the water wave31 and quantum matter wave,32 which are beyond third one is using a structured background that supports special the scope of this paper. modes, and the last one is using the photophoretic force that Here we would like to make a clear and consistent definition results from light absorption. Certainly, this classification of the OPF. Usually, pulling means that the object moves against method is not rigorous and not unique, because in some cases (or the force is reverse to) the direction of light propagation. more than one effect is involved simultaneously. However, the “direction of light propagation” is ambiguous in Before discussing OPF, we would like to address the theo- some cases since the directions of wavevector and Poynting retical and numerical methods used to investigate the OPF. vector may be different, especially in structured optical beams Basically, the calculation methods of OPF are exactly the same and nanostructures related to OPF. Due to this reason, in this as those used in optical trapping.15 For objects much smaller paper, OPF is defined relative to the relative position of the optical than the wavelength of the trapping light, dipole approximation source and object, as shown in Fig. 1(a).Supposethesourceis could be used to obtain analytical formulas for the optical located at A and the object is at B, then the center-to-center vector forces,33 from which the OPF can be identified. In this case, AB (the blue dashed arrow) defines the axis of the force. The the outstanding angular scattering features of magnetic or larger pulling force means that the angle θ between the optical force dielectric particles determine the direction of the optical force, F (the thick red arrow) and the axis AB is larger than π∕2,as and the Kerker scattering conditions are useful in exploring the shown in Fig. 1(a). In this case, the projection of optical force OPF.34–36 For objects much larger than the wavelength, the ray on AB is directed from B to A. On the contrary, the pushing force tracing method could be used to calculate the optical forces.37,38 means that the force projection is from A to B, or θ < π∕2. Since For the objects with moderate size comparable to the wave- the relative position of the source and object can be determined length, an integration of Maxwell’s stress tensor on a closed explicitly, this definition is reasonable and acceptable. surface surrounding the object is necessary to calculate the In this work, we aim to make a brief review on the progress- optical force,39 and some numerical simulation methods, such ing topic of OPF. From the viewpoint of linear momentum as the finite-difference time-domain method or finite-element conservation, in order to get an OPF, the effective forward methods, are typically used to obtain the electromagnetic fields momentum of the incident light should be enhanced when scat- around the object. Since those methods can be found easily in tered by the object. Due to this reason, many works in this topic the literature, we will skip these detailed methods, and readers are about tailoring the momentums of light beams when they may refer to the references when necessary. Advanced Photonics 024001-2 Mar∕Apr 2019 • Vol. 1(2) Ding et al.: Photonic tractor beams: a review 2 Optical Pulling Force Achieved by region in propagation.
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