IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 14, NO. 1, JANUARY/FEBRUARY 2008 151 A Novel Approach to Fiber-Optic Tweezers: Numerical Analysis of the Trapping Efficiency Paolo Minzioni, Francesca Bragheri, Carlo Liberale, Enzo Di Fabrizio, and Ilaria Cristiani, Member, IEEE Abstract—We present a novel all-fiber optical tweezer (OT) for biological applications. The tweezer is based on a new approach relying on total internal reflection in an annular core fiber or into a fiber bundle. The proposed device, whose trapping efficacy has been recently demonstrated experimentally, is extremely promis- ing, also because optical manipulation and analysis functions can be easily added to the tweezer basic structure, leading to the real- ization of a powerful biotool. In this paper, a detailed numerical analysis of the structure properties and of its efficiency is carried out in the Mie regime. Moreover, by defining a new parameter to evaluate the trapping efficiency, we perform a comparison be- tween the proposed tweezer structure and a standard OT based on a strongly focused Gaussian beam. Index Terms—Optical fiber cable, optical fiber devices, optical trapping, optical tweezer (OT). I. INTRODUCTION O PTICAL tweezers (OTs) have found many fundamental applications in biology, physics, and force spectroscopy. Important achievements in biomedical sciences have been ob- tained through the mechanical manipulation without physical contact of biological specimens and by the combination of an OT with optical diagnostic techniques (like two-photon fluores- cence, Raman scattering, and coherent anti-Stokes Raman spec- troscopy) providing a unique tool for optical bioanalysis [1]–[7]. State-of-the-art OT schemes utilize a freely propagating laser beam that is tightly focused inside the medium, where the par- ticles under investigation are immersed, by means of a micro- scope having a high numerical aperture (NA) objective. Despite the relevant results achieved in many fields, the bulky structure of standard OT still limits their utilization in several environ- ments. In addition, the use of standard OTs in turbid media or in thick samples presents significant challenges, being difficult to achieve the tight focusing necessary for optical trapping. The realization of an OT based on a single optical fiber would turn this device into a miniaturized and handy diagnostic tool, suitable for many relevant applications, like in vivo biologi- cal operations, where standard OTs cannot be successfully ex- ploited. Some OT structures, based on a single microlensed Manuscript received September 5, 2007; revised October 18, 2007. This work was supported in part by the Consorzio Nazionale Interuniversitario per le Scienze fisiche della Materia (CNISM) under Grant INNESCO. P. Minzioni, F. Bragheri, and I. Cristiani are with the Consorzio Nazionale Interuniversitario per le Scienze fisiche della Materia (CNISM) and the University of Pavia, I-27100 Pavia, Italy (e-mail: paolo.minzioni@unipv.it; francesca.bragheri@unipv.it; ilaria.cristiani@unipv.it). C. Liberale and E. Di Fabrizio are with the Dipartimento di Medicina Speri- mentale e Clinica, Universit` a degli Studi Magna Graecia di Catanzaro, I-88100 Catanzaro, Italy (e-mail: carlo.liberale@unicz.it; difabrizio@tasc.infm.it). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/JSTQE.2007.912910 optical fiber, are reported in the literature, but they allow obtain- ing only 2-D trapping [8], [9]. 3-D trapping at a large distance from the fiber-end has been demonstrated with a specially de- signed fiber OT by counterbalancing the optical forces with the electrostatic interaction between the fiber and the object to be trapped [10]. Purely optical 3-D trapping by means of a single- fiber OT has been achieved through highly tapered fibers: in this case, the trapping point gets very close to the fiber tip, making the tweezer quite unpractical for real applications [11]. Recently, we have proposed [12], and experimentally demon- strated [13], a new fiber-optic-tweezer that was designed by successfully combining two concepts: the use of nonstandard fibers in which light propagates through an annular core and the achievement of light focusing with high NA by using total internal reflection (TIR) (instead of refraction) at the interface between fibers and surrounding medium. In the following, we will indicate such a tweezer as TIR-based optical fiber tweezer (TOFT). In this paper, we evaluate the TOFT performance through nu- merical simulations of the optical forces exerted by such a device in the Mie regime. In Section II, the TOFT working principle is explained. A brief description of the fabricated tweezers and of the obtained experimental results is also reported. Section III is devoted to optical forces calculations. To evaluate the trapping effectiveness, we introduce a new parameter that depends on strength, direction, and spatial distribution of the optical forces. The TOFT performance is compared to that of a standard OT (microscope based) where trapping is obtained by means of a strongly focused Gaussian beam. II. NEW APPROACH TO FIBER OPTIC TWEEZERS A. Working Principle The TOFT basic working principle is sketched in Fig. 1 with reference to a fiber with an annular core [Fig. 1(b)]. For sake of simplicity, the beam emitted by the core is here treated as a ray, neglecting the effect of diffraction. By properly drilling the fiber-end at an angle θ, as shown in Fig. 1(a), the light beam carried in the core [gray annulus in Fig. 1(b)] experiences TIR at the fiber/medium interface. The beam is first deflected through the fiber cladding, and then out of the fiber, converging in a point positioned along the probe axis, thus producing the equivalent effect of a focused beam. By simple trigonometric considerations, and by using Snell law, it is possible to express the angle of convergence φ through the following relation (n F and n M being the refractive indexes 1077-260X/$25.00 © 2008 IEEE