shows time-snapshots of the field distributions for a linearly-polarized wave(o=0.65um) having a top-hat cross-sectional profile with smooth edges. The beam is incident from the free-space at inc=50 onto a semi-infinite dielectric of index ny=2.0; the dielectric fills the half-space :<0. The case of p-polarization is shown on the left-, that of s-polarization on the ght- hand side For the p-polarized beam, its angle of incidence being close to Brewster's angle BB=63.43, there is little reflectivity at the interface and most of the light is transmitted through to the dielectric medium, whereas for the s-polarized beam a goo fraction of the incident light is being reflected Fig. 4. Time snapshots of the field components for a linearly-polarized wave (o=0.65um) having a top-hat cross-sectional profile with smooth edges, incident at Binc=50% from free- dielectric of refractive index n,=2.0. located in the half-s field H, in the case of p-polarization, the superposed arrows represent the electric-field(En Er).(Right) Electric field Ex in the case of s-polarization, the superposed Computed force densities(Fy F: )inside the dielectric medium are displayed in Fig. 5; the interface region has been excluded to avoid, in the case of p-light, the high force region of the induced surface charges(For s-light the E-field is continuous at the boundary and, therefore no surface charges are induced. In both cases the force fields near the leading edge of the beam show oscillatory behavior, whereas the trailing edge is fairly smooth. Despite oscillations near the edge, the force is seen to be generally expansive for p-light and compressive for s-light, that is, the sign of the integrated lateral force on each side of the center is consistent with the theoretical arguments presented in [1]. In units of pN/m, the integrated force(JFy dy, JF: dy) for p-light is(-2.64, -1. 13)for the left-edge and(2.59, 1.096) for the right-edge. These edge forces are nearly identical in strength(to better than +1.5%) are orthogonal to the propagation direction within the dielectric, and are in fair agreement with the theoretical value of +(2.51, 1.04)PN/m2 obtained from Eq (9)with E=0.64 V/m The corresponding edge forces for the s-light depicted in Fig. 5, right-hand column,are (1.957, 0.821) for the left edge and(1.939,-0815)for the right edge. Again, this compressive force is orthogonal to the propagation direction, and is in reasonable agreement with the theoretical value of+(1.92, 0.8)pN/m2 obtained from Eq (9)with E.=0.56 V/m 5. Cylindrical rod illuminated by Gaussian beam Figure 6 shows time-snapshot plots of Hx, Ey, E: components of a p-polarized, one- dimensional Gaussian beam(no=0.65 um, amplitude FWHM=0.5 um), propagating in free- space along the negative :-direction the beams waist is at ==0.5 um. Given the amplitude profile as H( z=0.5um)=Ho exp[-wvlyo)"], the value of yo at the waist is 0.3um, which corresponds to a divergence half-angle 8=arctan(dIy)=35%. The small diameter of the beam at the waist thus results in its rapid divergence along the propagation direction. The cone angle of the beam, although large enough to exhibit lateral trapping of small dielectric objects, is not sufficient to produce vertical trapping [5], as will be seen below #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 2327shows time-snapshots of the field distributions for a linearly-polarized wave (λo = 0.65µm) having a top-hat cross-sectional profile with smooth edges. The beam is incident from the free-space at θ inc = 50° onto a semi-infinite dielectric of index ns = 2.0; the dielectric fills the half-space z < 0. The case of p-polarization is shown on the left-, that of s-polarization on the right-hand side. For the p-polarized beam, its angle of incidence being close to Brewster’s angle θ B = 63.43°, there is little reflectivity at the interface and most of the light is transmitted through to the dielectric medium, whereas for the s-polarized beam a good fraction of the incident light is being reflected. Fig. 4. Time snapshots of the field components for a linearly-polarized wave (λo = 0.65µm) having a top-hat cross-sectional profile with smooth edges, incident at θ inc = 50° from free￾space onto a semi-infinite dielectric of refractive index ns = 2.0, located in the half-space z < 0. (Left) Magnetic field Hx in the case of p-polarization; the superposed arrows represent the electric-field (Ey, Ez). (Right) Electric field Ex in the case of s-polarization; the superposed arrows represent the magnetic-field (Hy, Hz). Computed force densities (Fy, Fz) inside the dielectric medium are displayed in Fig. 5; the interface region has been excluded to avoid, in the case of p-light, the high force region of the induced surface charges. (For s-light the E-field is continuous at the boundary and, therefore, no surface charges are induced.) In both cases the force fields near the leading edge of the beam show oscillatory behavior, whereas the trailing edge is fairly smooth. Despite oscillations near the edge, the force is seen to be generally expansive for p-light and compressive for s-light, that is, the sign of the integrated lateral force on each side of the center is consistent with the theoretical arguments presented in [1]. In units of pN/m2 , the integrated force ( ∫Fy dy, ∫Fz dy) for p-light is (−2.64, −1.13) for the left-edge and (2.59, 1.096) for the right-edge. These edge forces are nearly identical in strength (to better than ±1.5%), are orthogonal to the propagation direction within the dielectric, and are in fair agreement with the theoretical value of ±(2.51, 1.04) pN/m2 obtained from Eq. (9) with Eo = 0.64 V/m. The corresponding edge forces for the s-light depicted in Fig. 5, right-hand column, are (1.957, 0.821) for the left edge and (−1.939, −0.815) for the right edge. Again, this compressive force is orthogonal to the propagation direction, and is in reasonable agreement with the theoretical value of ±(1.92, 0.8) pN/m2 obtained from Eq. (9) with Eo = 0.56 V/m. 5. Cylindrical rod illuminated by Gaussian beam Figure 6 shows time-snapshot plots of Hx, Ey, Ez components of a p-polarized, one￾dimensional Gaussian beam (λo = 0.65 µm, amplitude FWHM = 0.5 µm), propagating in free￾space along the negative z-direction; the beam’s waist is at z = 0.5 µm. Given the amplitude profile as Hx( y,z = 0.5µm) = Ho exp[−(y/yo) 2 ], the value of yo at the waist is 0.3µm, which corresponds to a divergence half-angle θ = arctan (λo/πyo) ≈ 35°. The small diameter of the beam at the waist thus results in its rapid divergence along the propagation direction. The cone angle of the beam, although large enough to exhibit lateral trapping of small dielectric objects, is not sufficient to produce vertical trapping [5], as will be seen below. (C) 2005 OSA 4 April 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2327 #6863 - $15.00 US Received 14 January 2005; revised 15 March 2005; accepted 15 March 2005