The effect of Mie resonances on trapping in optical tweezers Alexander B. Stilgoe, Timo A. Nieminen, Gregor Kn ¨ oner, Norman R. Heckenberg and Halina Rubinsztein-Dunlop Centre for Biophotonics and Laser Science, School of Physical Sciences, The University of Queensland, Brisbane, QLD 4072, Australia stilgoe@physics.uq.edu.au Abstract: We calculate trapping forces, trap stiffness and interference effects for spherical particles in optical tweezers using electromagnetic theory. We show the dependence of these on relative refractive index and particle size. We investigate resonance effects, especially in high refractive index particles where interference effects are expected to be strongest. We also show how these simulations can be used to assist in the optimal design of traps. © 2008 Optical Society of America OCIS codes: (140.7010) Laser trapping, (290.4020) Mie theory, (350.4855) Optical tweezers or optical manipulation. References and links 1. Y. Harada and T. Asakura, “Radiation forces on a dielectric sphere in the Rayleigh scattering regime,” Opt. Commun. 124, 529–541 (1996). 2. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992). 3. L.Lorenz, “Lysbevægelsen i og uden for en af plane Lysbølger belyst Kugle,” Videnskabernes Selskabs Skrifter 6, 2–62 (1890). 4. G. Mie, “Beitr¨ age zur Optik tr ¨ uber Medien, speziell kolloidaler Metall¨ osungen,” Annalen der Physik 25, 377–445 (1908). 5. T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Kn¨ oner, A. M. Bra ´ nczyk, N. R. Heckenberg and H. Rubinsztein- Dunlop, “Optical tweezers computational toolbox,” J. Opt. A 9, 5192–S203 (2007). 6. Ashkin 1986 7. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophysics and Biomolec- ular Structure 23, 248–285 (1994). 8. P. Ch´ ylek and J. Zhan, “Interference structure of the Mie extinction cross section,” J. Opt. Soc. Am. A 6, 1846– 1851 (1989). 1. Introduction While a large part of previous theoretical work on optical tweezers has made use of approxi- mate methods such as Rayleigh scattering [1], suitable for small particles (radius < 0.1λ ), or geometric optics [2], suitable for large particles (radius > 5–10λ ), neither of these are suitable for describing the trapping of particles of sizes on the order of the wavelength. However, an analytical solution to scattering of light by a sphere of arbitrary size—and hence the optical trapping of spherical particles—exists [3, 4], and the computational power needed to extract numerical results from the theory is now readily and cheaply available. We use a computational implementation of Lorenz–Mie theory, in the form of an optical tweezers toolbox [5], to investigate the forces in optical tweezers as a function of the most #99909 - $15.00 USD Received 7 Aug 2008; revised 3 Sep 2008; accepted 3 Sep 2008; published 9 Sep 2008 (C) 2008 OSA 15 September 2008 / Vol. 16, No. 19 / OPTICS EXPRESS 15039