1. Introduction Computation of the force of radiation on a given object, through evaluation of the electro- magnetic field distribution according to Maxwells equations, followed by a direct application of the Lorentz law of force, has been described in Ref [1]-[4]. In particular, for an isotropic piecewise-homogeneous dielectric medium, the total force was shown to result from the force of the magnetic field acting on the induced bound current density, JbxB=[(1-1/E)VXHXB and from the force exerted by the electric component of the light field on the induced bound charge density at the interfaces between media of differing relative permittivity E. The contri- bution of the E-field component of the Lorentz force is thus specified(Ref [Im) by the force density PbE=(EoV.EE.(Note: As far as the total force and torque of radiation on a solid object are concerned, Barnett and Loudon Ref [5] have recently shown that an altemative for- mulation of the lorentz law -one that is often used in the radiation pressure literature- leads to exactly the same results. We discuss the relation between these two formulations in the Appen dix, and extend the proof of their equivalence to the case of solid objects immersed in a liquid which is a prime concern of the present paper. In a previous publication Ref [6] we described the numerical implementation of the afore- mentioned approach to the computation of the Lorentz force, based on the Finite-Difference Time-Domain(FDTD) solution of Maxwell's equations (An alternative application of the FDTD method to problems of radiation pressure may be found in Ref [7].)Our application of the FDTD method to the computation of the force exerted by a focused laser beam on a spherical dielectric particle immersed in a liquid showed that the forces experienced by the liquid layer immediately at the particle's surface could impact the overall force experienced by the particle. a detailed discussion of the(conceptual) separation of the bound charges on the surface of the particle from the bound charges induced in the surrounding liquid at the solid-liquid interface is given in Ref. [2]. The analysis indicated that the contribution to the Pbe part of the Lorentz force by the component of the E-field perpendicular to the interface can be computed in different ways, depending on the assumptions made concerning the nature of the electromagnetic and hydrodynamic interactions between the solid particle and its liquid In the present study we apply the FDTD method to analyze the polarization dependence of the interaction between a focused laser beam and a small spherical particle trapped either in the air or in a liquid host medium(water). In the latter case, results from different methods of be compared, with the goal of quantifying the effects that might be possible to differentiate in experiments Ref [8]-[9]. The polarization dependence of optical tweezers has been studied in the past, and the dependence of trap stiffness on polarization direction is well documented Ref [10]-[13]. The goal of the present paper is not a re-evaluation of the existing models, but rather a demonstration of the applicability of our own new model Ref [1]-[4 to the problem of trap stiffness anisotropy. Also, upon comparing our numerical results with experiment data, we gain further insight into the nature of the Lorentz force acting on solid objects liquid environments, and identify a preferred interpretation of the proposed physical model In a nutshell, there exists an ambiguity as to the nature of the effective force at the surface of the sphere, with at least three different models in contention. Carefully examining the trapping orce on a dielectric sphere immersed in water provides enough information to establish one of the three competing models and rule out the other two The paper is organized as follows. Section 2 discusses example cases used to validate our ted stiffness of the trap two orthogonal linear polarizations of a beam illuminating a micro-sphere suspended in air and in water, respectively. Summary and conclusions are presented in section 5 #67575-$15.00USD Received 15 February 2006, revised 7 April 2006, accepted 10 April 2006 (C)2006OSA 17 April 2006/Vol 14, No 8/OPTICS EXPRESS 36611. Introduction Computation of the force of radiation on a given object, through evaluation of the electro￾magnetic field distribution according to Maxwell’s equations, followed by a direct application of the Lorentz law of force, has been described in Ref. [1]-[4]. In particular, for an isotropic, piecewise-homogeneous dielectric medium, the total force was shown to result from the force of the magnetic field acting on the induced bound current density, J b ×B = [(1−1/ε)∇×H]×B, and from the force exerted by the electric component of the light field on the induced bound charge density at the interfaces between media of differing relative permittivity ε. The contri￾bution of the E-field component of the Lorentz force is thus specified (Ref. [1]) by the force density ρbE = (ε0∇ · E)E. (Note: As far as the total force and torque of radiation on a solid object are concerned, Barnett and Loudon Ref. [5] have recently shown that an alternative for￾mulation of the Lorentz law - one that is often used in the radiation pressure literature - leads to exactly the same results. We discuss the relation between these two formulations in the Appen￾dix, and extend the proof of their equivalence to the case of solid objects immersed in a liquid, which is a prime concern of the present paper.) In a previous publication Ref. [6] we described the numerical implementation of the afore￾mentioned approach to the computation of the Lorentz force, based on the Finite-Difference Time-Domain (FDTD) solution of Maxwell’s equations. (An alternative application of the FDTD method to problems of radiation pressure may be found in Ref. [7].) Our application of the FDTD method to the computation of the force exerted by a focused laser beam on a spherical dielectric particle immersed in a liquid showed that the forces experienced by the liquid layer immediately at the particle’s surface could impact the overall force experienced by the particle. A detailed discussion of the (conceptual) separation of the bound charges on the surface of the particle from the bound charges induced in the surrounding liquid at the solid-liquid interface is given in Ref. [2]. The analysis indicated that the contribution to the ρbE part of the Lorentz force by the component of the E-field perpendicular to the interface can be computed in different ways, depending on the assumptions made concerning the nature of the electromagnetic and hydrodynamic interactions between the solid particle and its liquid environment. In the present study we apply the FDTD method to analyze the polarization dependence of the interaction between a focused laser beam and a small spherical particle trapped either in the air or in a liquid host medium (water). In the latter case, results from different methods of computing the contributions to the net force by bound charges at the solid-liquid interface will be compared, with the goal of quantifying the effects that might be possible to differentiate in experiments Ref. [8]-[9]. The polarization dependence of optical tweezers has been studied in the past, and the dependence of trap stiffness on polarization direction is well documented Ref. [10]-[13]. The goal of the present paper is not a re-evaluation of the existing models, but rather a demonstration of the applicability of our own new model Ref. [1]-[4] to the problem of trap stiffness anisotropy. Also, upon comparing our numerical results with experimental data, we gain further insight into the nature of the Lorentz force acting on solid objects in liquid environments, and identify a preferred interpretation of the proposed physical model. In a nutshell, there exists an ambiguity as to the nature of the effective force at the surface of the sphere, with at least three different models in contention. Carefully examining the trapping force on a dielectric sphere immersed in water provides enough information to establish one of the three competing models and rule out the other two. The paper is organized as follows. Section 2 discusses example cases used to validate our numerical computations. In sections 3 and 4 we compare the computed stiffness of the trap for two orthogonal linear polarizations of a beam illuminating a micro-sphere suspended in air and in water, respectively. Summary and conclusions are presented in section 5. #67575 - $15.00 USD Received 15 February 2006; revised 7 April 2006; accepted 10 April 2006 (C) 2006 OSA 17 April 2006 / Vol. 14, No. 8 / OPTICS EXPRESS 3661