4. Single-beam optical trap in water In computing the optical trap properties in a liquid host medium(refractive index n inc=1.33), a collimated laser beam having 2o=532nm(or 1064nm)was focused through an NA N 1.4 immersion objective designed for diffraction-limited focusing within an immersion liquid of refractive index noil=1. 47; see Figs. 7, 8. In our first set of simulations corresponding to no 532nm, the spherical particle has d=460nm, n=1.5, and the total power of the incident beam is P=1. ow. For Methods 1, Il, and Ill of computing the surface-force discussed in section 2 Figs, 9-1I show the net force components(Fx, Fs)exerted on the micro-sphere illuminated by x-or y-polarized light. For most of the offset range considered in Fig. 9, the Fx force component computed with method I for x-polarized light is opposite in direction to the Fr computed for y-polarized light, indicating the impossibility of lateral trapping with x-polarization. Such a marked difference in the behavior of Fr for different polarization states exhibited by method ontradicts the experimental observations which show trapping(with similar strengths)for both polarization states. We conclude, therefore, that Method I is unphysical and must be abandoned The root of the problem with Method I can be traced to the lumping together of the solid and liquid charges at the interface, which weakens the negative contribution of Fx, thus allowing the positive contribution by the magnetic part of the Lorentz force(acting on the micro-sphere volume)to push the particle away from the focal point. In contrast, for y-polarized light, the contribution of the magnetic Lorentz force to Fr is negative, thus enabling lateral trapping I x um] y [um Fig8 Computed distributions of the electric field intensity EP(units: [2/m)in the xs- and yz-planes near the focus of a 2 o=532nm beam in water. The focused spot is obtained by sending an x-polarized plane-wave through an oil-immersion N 1. 4NA objective. The oil water are separated by a thin glass slide, index-matched to the immersion oil, Fig. 7. The force distributions computed with Method /l(Fig. 10)and Method Ill (Fig. I1) show qualitatively similar behavior for the two polarization states, and indicate trapping along botha and z-directions. Fr is strongest at lateral offset values on the order of one micro-sphere radius While both methods /I and ll result in trapping of the micro-bead, the ratio of the maximum lateral restoring forces Fx(sampled inside the dashed rectangles in Figs. 10 and 11)for x-and polarized beams is found to be 0.92 for method ll and 1.2 for method Ill. Thus, although Figs 10 and Il exhibit qualitatively similar behavior, their quantitative estimates of the restoring forces are sufficiently different to enable one to distinguish Method l from Method Ill based #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 36684. Single-beam optical trap in water In computing the optical trap properties in a liquid host medium (refractive index n inc = 1.33), a collimated laser beam having λ0 = 532nm (or 1064nm) was focused through an NA ≈ 1.4 immersion objective designed for diffraction-limited focusing within an immersion liquid of refractive index noil = 1.47; see Figs. 7, 8. In our first set of simulations corresponding to λ 0 = 532nm, the spherical particle has d = 460nm, n = 1.5, and the total power of the incident beam is P = 1.0W. For Methods I, II, and III of computing the surface-force discussed in section 2, Figs. 9-11 show the net force components (Fx,Fz) exerted on the micro-sphere illuminated by x- or y-polarized light. For most of the offset range considered in Fig. 9, the Fx force component computed with method I for x-polarized light is opposite in direction to the Fx computed for y-polarized light, indicating the impossibility of lateral trapping with x-polarization. Such a marked difference in the behavior of Fx for different polarization states exhibited by method I, contradicts the experimental observations which show trapping (with similar strengths) for both polarization states. We conclude, therefore, that Method I is unphysical and must be abandoned. [The root of the problem with Method I can be traced to the lumping together of the solid and liquid charges at the interface, which weakens the negative contribution of F sur f x , thus allowing the positive contribution by the magnetic part of the Lorentz force (acting on the micro-sphere volume) to push the particle away from the focal point. In contrast, for y-polarized light, the contribution of the magnetic Lorentz force to Fx is negative, thus enabling lateral trapping.] Fig. 8. Computed distributions of the electric field intensity |E| 2 (units: [V2/m2]) in the xz￾and yz-planes near the focus of a λ0 = 532nm beam in water. The focused spot is obtained by sending an x-polarized plane-wave through an oil-immersion ≈ 1.4NA objective. The oil and water are separated by a thin glass slide, index-matched to the immersion oil, Fig. 7. The force distributions computed with Method II (Fig. 10) and Method III (Fig. 11) show qualitatively similar behavior for the two polarization states, and indicate trapping along both x￾and z-directions. Fx is strongest at lateral offset values on the order of one micro-sphere radius. While both methods II and III result in trapping of the micro-bead, the ratio of the maximum lateral restoring forces Fx (sampled inside the dashed rectangles in Figs. 10 and 11) for x- and y￾polarized beams is found to be 0.92 for method II and 1.2 for method III. Thus, although Figs. 10 and 11 exhibit qualitatively similar behavior, their quantitative estimates of the restoring forces are sufficiently different to enable one to distinguish Method II from Method III based #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 3668