beads having n=1.5, trapped under a 20=1064nm focused beam through a 0.9NA objective 00050.100150.200250.300050.100.150200250300050.100.15020025030 Fig. 5. Plots of the net force components(Fr, F) experienced by a glass micro-sphere(d 460nm, n=1.5) versus the offset from the focal point in the xs-plane. The incidence medium is air, no=532nm, the objective lens NA is 0.9, and the incident beams power is P= 1. oW. Top row: x-polarization, bottom row: y-polarization. The stiffness coefficients Kx, Ky are computed at the center of the small rectangles shown on the left-hand-side of the Fr plots 0=1064m,NA=0.9 -0.2 -0.4 micro-sphere diameter [um] Fig. 6. Computed trap stiffness anisotropy s)=1-(Kx/K, )versus particle diameter d, fo micro-spheres of refractive index n= 1.5 trapped in the air with a no= 1064nm laser beam focused through a 0. 9NA objective lens. The stiffness is computed at x-offset= 50nm, =-oftset Oum, where, for the chosen value of x-offset, the lateral trapping force F is at a maximum. For the offset ranges and particle diameters considered, the radiation force along the =-axis Fs, was found to be negative (i.e, inverted traps are necessary to achieve stable trapping). The #67575-$15.00USD Received 15 February 2006, revised 7 April 2006, accepted 10 April (C)2006OSA 17 April 2006/Vol 14, No 8/OPTICS EXPRESSbeads having n = 1.5, trapped under a λ 0 = 1064nm focused beam through a 0.9NA objective. Fx Fz (Fx,Fz) Fig. 5. Plots of the net force components (Fx,Fz) experienced by a glass micro-sphere (d = 460nm, n = 1.5) versus the offset from the focal point in the xz-plane. The incidence medium is air, λ0 = 532nm, the objective lens NA is 0.9, and the incident beam’s power is P = 1.0W. Top row: x-polarization, bottom row: y-polarization. The stiffness coefficients κx, κy are computed at the center of the small rectangles shown on the left-hand-side of the Fx plots. 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 micro-sphere diameter [μm] -0.4 -0.2 0 0.2 0.4 1 - κx /κy FDTD: n = 1.5, ninc = 1.0, λ0 = 1064nm, NA = 0.9 Cubic spline interpolation Fig. 6. Computed trap stiffness anisotropy sl = 1 − (κx/κy) versus particle diameter d, for micro-spheres of refractive index n = 1.5 trapped in the air with a λ0 = 1064nm laser beam focused through a 0.9NA objective lens. The stiffness is computed at x-offset = 50nm, z-offset ≈ 0μm, where, for the chosen value of x-offset, the lateral trapping force Fx is at a maximum. For the offset ranges and particle diameters considered, the radiation force along the z-axis, Fz, was found to be negative (i.e., inverted traps are necessary to achieve stable trapping). The #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 3666