Electrostatic Force and Torque Description of Generalized Spheroidal Particles in Optical Landscapes Ryan W. Going, Brandon L. Conover, Michael J. Escuti North Carolina State Univ, Dept Electrical & Computer Engineering, Raleigh (USA) ABSTRACT Optical trapping, mixing, and sorting of micro- and nano-scale particles of arbitrary shape (e.g., blood cells and nanorods) are but a few of the burgeoning applications of optical interference landscapes. Due to their non-invasive, non-contact manipulation potential, biologists and nanotechnologists alike are showing increased interest in this area and experimental results continue to be promising. A complete and reliable theoretical description of the particles’ response within these fields will allow us to accurately predict their behavior and motion. We develop an electrostatic model of the optical force and torque on anisotropic particles in optical intensity gradients. The complete optical field is defined and a Maxwell stress tensor approach is taken to realize the force and torque induced by the electric field due to the polarizability of the particle. We utilize the properties of real dielectrics and steady state optical fields to extend this approach to the electrodynamic case inherent in optical trapping. We then compare our results against our recently reported form factor approach and use the differences to try to determine the importance of polarizability in optical trapping. Keywords: Optical Trapping, Spheroidal Harmonics, Maxwell Stress Tensor 1. INTRODUCTION Since the gradient force optical trap was demonstrated by Ashkin and associates in 1986, 1 the ability to ma- nipulate dielectric particles with light has made great advancement. Experimental work has promised to make optical traps an industry tool, not simply a magical laboratory demonstration. 2 Biological particle sorting, 3 nano-assembly, 4 and studies of fundamental interactions between cells and molecules show just how far this im- portant technique can travel. In order to fully harness this new technology, however, a fundamental theoretical understanding is first required. While there has been a significant theoretical treatment of trapping simple shapes such as spheres and cylinders 5–7 there has been very little study of particles with other common shapes (spheroids, ellipsoids, wires, etc.) beyond a few studies of optically-induced torque and constrained motion. 8, 9 The study of non-spherical dielectrics is quite important because the majority of particles in practical settings (e.g., blood cells, nanowires) are modeled better as shapes more complex than spheres. For those particles much smaller than the illuminating wavelength (Rayleigh particles), a dipole model may be used to calculate the resultant forces, while for particles much larger (Mie particles), a ray optics model is often used. However, when the particle size is on the order of the illuminating wavelength, neither of these approximations hold true and more complete electromagnetic treatment is required. To this end, continuous form factor models have been developed to provide analytic expressions for the optically-induced force 10 and torque 11 on dielectrics of varying size and shape. While results show promise, a more rigorous treatment encompassing all arbitrary particles and fields is still needed. We calculate the response of a spheroidal dielectric in an arbitrary optical field using the well-known Maxwell stress tensor (MST) method. 12–14 In order to calculate the electric field, we make use of spheroidal harmonics to solve the Laplace equation. We first take an electrostatic approach in solving the MST and then take advantage of the properties of real dielectrics and steady-state optical fields to apply this to the electrodynamic case of optical trapping. This approach lends itself to a complete study of the effects of field polarization as it pertains to optical manipulation. Finally, we compare results of our MST model to those of the form factor models. Correspondence should be addressed to: mjescuti@ncsu.edu, +1 919 513 7363 Optical Trapping and Optical Micromanipulation V, edited by Kishan Dholakia, Gabriel C. Spalding, Proc. of SPIE Vol. 7038, 703826, (2008) · 0277-786X/08/$18 · doi: 10.1117/12.795701 Proc. of SPIE Vol. 7038 703826-1