force-density through the spherical volume, is IF(x, y, =dx dy d==(-040, +0.018, +0. 34)pN The direction of the total force clearly indicates trapping of the particle by the focused beam as Fx tends to pull the particle to the left while F: tries to lift it up, toward the center of the focused spot. (Similar calculations were carried out for different positions of the bead relative to the focused spot, and trapping was demonstrated in all cases; see Fig. 10.) It must be inted out that the y-component of the net force, although small, is not negligible, thus ating the transfer of a certain amount of angular momentum from the circularly polarized to the illuminated particle(this point will be discussed in more detail below 0.25,0 ocused spot z-coordinate [um] focused spot Z-coordinate [um focused spot z-coordinate [um] focused spot Z-coordinate [um splacement A of the focal point from the sphere center(A>0 when the beam is focused above the sphere center). Fa and F: are in units of pico Newtons. Each colored curve represents fixed lateral displacement Ax of the center of the particle from the optical axis of the objective lens. The beam is focused in the liquid through a 1. 25NA immersion lens. The polarization state of the 0.5 mw plane wave (o=0.65um)entering the objective's pupil is: circular( top row), linear along the Y-axis(middle row), linear along the y-axis(bottom row) #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 2333force-density through the spherical volume, is ∫∫∫F(x, y,z) dx dy dz= (−0.40,+0.018, +0.34) pN. The direction of the total force clearly indicates trapping of the particle by the focused beam, as Fx tends to pull the particle to the left while Fz tries to lift it up, toward the center of the focused spot. (Similar calculations were carried out for different positions of the bead relative to the focused spot, and trapping was demonstrated in all cases; see Fig. 10.) It must be pointed out that the y-component of the net force, although small, is not negligible, thus indicating the transfer of a certain amount of angular momentum from the circularly polarized beam to the illuminated particle (this point will be discussed in more detail below). Fig. 10. Computed force components Fx (left column) and Fz (right column) versus the vertical displacement ∆z of the focal point from the sphere center (∆z > 0 when the beam is focused above the sphere center). Fx and Fz are in units of pico Newtons. Each colored curve represents a fixed lateral displacement ∆x of the center of the particle from the optical axis of the objective lens. The beam is focused in the liquid through a 1.25NA immersion lens. The polarization state of the 0.5 mW plane wave (λo = 0.65µm) entering the objective’s pupil is: circular (top row), linear along the x-axis (middle row), linear along the y-axis (bottom row). (C) 2005 OSA 4 April 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2333 #6863 - $15.00 US Received 14 January 2005; revised 15 March 2005; accepted 15 March 2005