Fz IpNI (Fx, Fz) E 000050.100150200250300.0010015020025030 Fx IpN] FZ PN (Fx. Fz) 00000.100.150200250300.00.100.150200253005D.10015020025030 offset lrm Fig 9. Plots of the net force components (Fr, F), computed with Method 1, for a glass micro- bead (d= 460nm, n=1.5)versus the offset from the focal point. The host medium is water (ninc = 1.33), 20= 532nm, the objective lens NA is a 1.4, and the incident beams power P=1.0W. Top row: x-polarization, bottom row: y-polarization. The non-trapping behavior of Method used in these calculations on experimentally determined values of stiffness anisotropy Figure 12 shows the dependence of the trap stiffness anisotropy s/=l-(K/Ky)on bead diameter d, computed with Method ll for polystyrene micro-beads(n=1.57) trapped in water (nine 133)under a 1o=1064nm laser beam focused through an oil-immersion 1. 4NA obJective lens(with a glass slide used to separate oil from water, as shown in Fig. 7). For d < 850nm, the lateral trap stiffness is found to be smaller for the particle offsets along the larization direction, that is, sI>0. For larger particles (850<d< 1400nm)the trap stiffness in the x-direction becomes greater for x-polarization than that for y-polarization, i.e., S/<0.The trap stiffness anisotropy reaches a minimum before returning to positive values for d> 1400nmm uperimposed on Fig. 12 are two sets of experimental data. The green triangles correspond to measurements carried out with a system similar to that depicted in Fig. 7, operating at 20=1064nm. In practice, this system suffered from chromatic(and possibly spherical)aberra tions; defects that are not taken into account in our computer simulations. The agreement with theoretical calculations is good for the d= 1260nm particle, but not so good for d= 1510nm and d=1900nm particles. The second set of experimental data(solid blue circles in Fig. 12) from Table Il of Rohrbach Ref. 9]. These were obtained with a 1. 2NA water immersion objective, corrected for all aberrations and, therefore, presumably operating in the diffrac tion limit. All other experimental parameters were the same as those used in our simulations Considering the loss of marginal rays at the oil/water interface, apodization due to Fresnel reflection losses, and the relatively small beam diameter at the entrance pupil of the simu lated lens, our focused spot should be fairly close to that used in Rohrbach's experiments #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 3669Fz Fx Fz Fx (Fx,Fz) (Fx,Fz) Fig. 9. Plots of the net force components (Fx,Fz), computed with Method I, for a glass micro￾bead (d = 460nm, n = 1.5) versus the offset from the focal point. The host medium is water (ninc = 1.33), λ0 = 532nm, the objective lens NA is ≈ 1.4, and the incident beam’s power is P = 1.0W. Top row: x-polarization, bottom row: y-polarization. The non-trapping behavior of x-polarized beam, which is contrary to experimental observations, indicates the invalidity of Method I used in these calculations. on experimentally determined values of stiffness anisotropy. Figure 12 shows the dependence of the trap stiffness anisotropy sl = 1 − (κx/κy) on bead diameter d, computed with Method II for polystyrene micro-beads (n = 1.57) trapped in water (ninc = 1.33) under a λ0 = 1064nm laser beam focused through an oil-immersion ≈ 1.4NA objective lens (with a glass slide used to separate oil from water, as shown in Fig. 7). For d < 850nm, the lateral trap stiffness is found to be smaller for the particle offsets along the polarization direction, that is, sl > 0. For larger particles (850 < d < 1400nm) the trap stiffness in the x-direction becomes greater for x-polarization than that for y-polarization, i.e.,s l < 0. The trap stiffness anisotropy reaches a minimum before returning to positive values for d > 1400nm. Superimposed on Fig. 12 are two sets of experimental data. The green triangles correspond to measurements carried out with a system similar to that depicted in Fig. 7, operating at λ0 = 1064nm. In practice, this system suffered from chromatic (and possibly spherical) aberra￾tions; defects that are not taken into account in our computer simulations. The agreement with theoretical calculations is good for the d = 1260nm particle, but not so good for d = 1510nm and d = 1900nm particles. The second set of experimental data (solid blue circles in Fig. 12) is from Table II of Rohrbach Ref. [9]. These were obtained with a 1.2NA water immersion objective, corrected for all aberrations and, therefore, presumably operating in the diffrac￾tion limit. All other experimental parameters were the same as those used in our simulations. (Considering the loss of marginal rays at the oil/water interface, apodization due to Fresnel reflection losses, and the relatively small beam diameter at the entrance pupil of the simu￾lated lens, our focused spot should be fairly close to that used in Rohrbach’s experiments.) #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 3669