Radiation pressure and the distribution of electromagnetic force in dielectric media Armis R. Zakharian, Masud Mansuripur, and Jerome v Moloney Optical Sciences Center, The University of Arizona, Tucson, Arizona 85721 Abstract: Using the Finite-Difference-Time-Domain(FDTD)method, we compute the electromagnetic field distribution in and around dielectric media of various shapes and optical properties. With the aid of the constitutive relations, we proceed to compute harge current densities, then employ the Lorentz law of force to determine the distribution of force density within the regions of interest. For a few simple cases where analytical solutions exist, these solutions are found to be in complete agreement with our numerical results. We also analyze the distribution of fields and forces in more complex systems, and discuss the relevance of our findings to experimental observations. In particular, we demonstrate the single-beam trapping of a dielectric micro-sphere immersed in a liquid under conditions that are typical of optical tweezers C 2005 Optical Society of America OCIS codes:(2602110)Electromagnetic theory; (140.7010) Trapping. References L. M. Mansuripur, Radiation pressure and the linear momentum of the electromagnetic field, " Opt. Express 12 5375-5401(2004),http://www.opticsexpressorg/abstract.cfm?uri=opex-12-22-5375 2. D. A. White, "Numerical modeling of optical gradient traps using the vector finite element method, "J Compt. Phys.159,13-37(2000) 3. A. Mazolli, P. A M. Neto, and H M. Nussenzveig, " Theory of trapping forces in optical tweezers, Proc.Roy.Soc.Lond.A459,3021-3041(2003) 4. C. Rockstuhl and H P Herzig, "Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders, " J Op Appl.Op.6,921-31(2004) Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime, Biophys.J.61,569-582(1992) 6. A. Rohrbach and E. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations, "AppL. Opt. 41, 2494(2002) 7. J D. Jackson, Classical Electrodynamics, edition (Wiley, New York, 1975) 8. M. Mansuripur, A. R. Zakharian, and J. V. Moloney, "Radiation pressure on a dielectric wedge, Opt. Express 13,2064-2074(2005),http://www.opticsexpress.orgabstract.cfm?uri=opex-13-6-2064 9. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles, "Opt. Lett. 11, 288-290(1986 10. A. Ashkin and J. M. Dziedzic, "Optical trapping and manipulation of viruses and bacteria, Science 235, 1517- 1 Introduction In a previous paper [1] we showed that the direct application of the Lorentz law of force in conjunction with Maxwells equations can yield a complete picture of the electromagnetic force in metallic as well as dielectric media. In the case of the dielectrics, bound charges and bound currents were found to be responsible, respectively, for the electric and magnetic components of the Lorentz force. When a dielectric medium is homogeneous and isotropic, or can be divided into two or more such regions- each with its own uniform dielectric constant E- the bound charges appear only at the surface(s)and/or the interface(s)between adjacent dielectrics. The bound currents, however, induced by the local E-field in proportion to the time-rate of change of the polarization P=&(E-D)E, are distributed throughout the medium The E-field of the light exerts a force on the induced charge density, while the local H-field #6863·$1500US Received 14 January 2005; revised 15 March 2005; accepted 15 March 2005 (C)2005OSA 4 April 2005/VoL 13, No. 7/OPTICS EXPRESS 2321Radiation pressure and the distribution of electromagnetic force in dielectric media Armis R. Zakharian, Masud Mansuripur, and Jerome V. Moloney Optical Sciences Center, The University of Arizona, Tucson, Arizona 85721 armis@email.arizona.edu Abstract: Using the Finite-Difference-Time-Domain (FDTD) method, we compute the electromagnetic field distribution in and around dielectric media of various shapes and optical properties. With the aid of the constitutive relations, we proceed to compute the bound charge and bound current densities, then employ the Lorentz law of force to determine the distribution of force density within the regions of interest. For a few simple cases where analytical solutions exist, these solutions are found to be in complete agreement with our numerical results. We also analyze the distribution of fields and forces in more complex systems, and discuss the relevance of our findings to experimental observations. In particular, we demonstrate the single-beam trapping of a dielectric micro-sphere immersed in a liquid under conditions that are typical of optical tweezers. © 2005 Optical Society of America OCIS codes: (260.2110) Electromagnetic theory; (140.7010) Trapping. References 1. M. Mansuripur, “Radiation pressure and the linear momentum of the electromagnetic field,” Opt. Express 12, 5375-5401 (2004), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5375 2. D. A. White, “Numerical modeling of optical gradient traps using the vector finite element method,” J. Compt. Phys. 159, 13-37 (2000). 3. A. Mazolli, P. A. M. Neto, and H. M. Nussenzveig, “Theory of trapping forces in optical tweezers,” Proc. Roy. Soc. Lond. A 459, 3021-3041 (2003). 4. C. Rockstuhl and H. P. Herzig, “Rigorous diffraction theory applied to the analysis of the optical force on elliptical nano- and micro-cylinders,” J. Opt. A: Pure Appl. Opt. 6, 921-31 (2004). 5. 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). 6. A. Rohrbach and E. Stelzer, “Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations,” Appl. Opt. 41, 2494 (2002). 7. J. D. Jackson, Classical Electrodynamics, 2nd edition (Wiley, New York, 1975). 8. M. Mansuripur, A. R. Zakharian, and J. V. Moloney, “Radiation pressure on a dielectric wedge,” Opt. Express 13, 2064-2074 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-6-2064 9. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11, 288-290 (1986). 10. A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517- 1520 (1987). 1. Introduction In a previous paper [1] we showed that the direct application of the Lorentz law of force in conjunction with Maxwell’s equations can yield a complete picture of the electromagnetic force in metallic as well as dielectric media. In the case of the dielectrics, bound charges and bound currents were found to be responsible, respectively, for the electric and magnetic components of the Lorentz force. When a dielectric medium is homogeneous and isotropic, or can be divided into two or more such regions – each with its own uniform dielectric constant ε – the bound charges appear only at the surface(s) and/or the interface(s) between adjacent dielectrics. The bound currents, however, induced by the local E-field in proportion to the time-rate of change of the polarization P = εo(ε − 1)E, are distributed throughout the medium. The E-field of the light exerts a force on the induced charge density, while the local H-field (C) 2005 OSA 4 April 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2321 #6863 - $15.00 US Received 14 January 2005; revised 15 March 2005; accepted 15 March 2005