Computing the force of radiation on an immersed solid particle requires that the bound charges on the surface of the particle be distinguished from the charges induced on the surrounding liquid. This issue has been discussed in detail in [8], where we have also argued that the perpendicular component of the E-field at the particle's surface -used in computing the E-field contribution to the Lorentz force- may be obtained in several different ways. In the present simulations we used the average E-field across the boundary (i.e, at the sphere surface)in computing the Lorentz force on the interfacial charges accumulated on the sphere For the case of focusing a circularly-polarized beam at (x,y, =)=(0, 0, 0.7um)onto a particle centered at(0.25um, 0, 0), Fig. 8 shows color-coded force-component distributions in various cross-sectional planes through the center of the sphere. The superposed arrows show the projection of the force-density vector in the corresponding plane, e.g., plots on the yz- plane show the(Fy Fs) vector field. Contributions to force-density come from both(bound) surface charges and( bound) electric currents within the volume of the sphere. When the force density exceeds the range of color coding, the corresponding region is depicted as white. This happens in the area where the beam enters the sphere, seen in the xz and y= cross-sectional planes of Fig.8 near the top of each frame. Reflection, refraction, and diffraction create complex interference patterns within the spherical particle, as evidenced by the richly textured force density profiles throughout the volume of the sphere. The surrounding liquid also experiences the effects of radiation pressure, as the bound currents within the liquid body el the Lorentz force of the B-field, while the bound charges on the liquid side of the interface sense the Lorentz force of the E-field, in the same way that the particle itself experiences such forces. The force imparted to the liquid is strongest in the vicinity of the region where the beam enters the particle, but weak forces are felt(by the liquid) also in those regions where the light leaves the solid particle and re-emerges into the liquid environment y LemI Fig 9. Cross-sectional profiles of the integrated force-density components along the direction erpendicular to each cross-section. Left) Distribution of F:(x, y, s)de in the central xy-plane Middle)Distribution of F,(x, y, =)dy in the central x-plane.(Right)Distribution of F(x,y,a)dx in the central y=-plane. The range of integration includes the charges on the surface of the sphere, but excludes any forces that might be exerted on the surrounding liquid For the system of Fig 8, profiles of the integrated force density in the normal direction to each cross-section are shown in Fig 9; the distribution of JF- (x, y, =)d= in the central xy-plane appears on the left, that of F,(x,y, =)dy in the central xz-plane in the middle, and the profile of JF(x, y, =)dx in the central yz-plane on the right-hand side. The range of integration includes the(bound) charges on the surface of the particle, but excludes any forces that might be exerted by the entering/exiting light on the surrounding liquid. The presence of a strong near the top of the frame in the xz and yz cross-sections depicted in Flg. 9 ng the color scale) force on the surface charges is indicated by the white regions (i.e, exceed In the above case of focusing a circularly-polarized beam at(x,y, ==(0,0, 0.7um) onto a glass bead centered at(0.25um, 0, 0), the net force on the bead, obtained by tting the #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 2332Computing the force of radiation on an immersed solid particle requires that the bound charges on the surface of the particle be distinguished from the charges induced on the surrounding liquid. This issue has been discussed in detail in [8], where we have also argued that the perpendicular component of the E-field at the particle’s surface – used in computing the E-field contribution to the Lorentz force – may be obtained in several different ways. In the present simulations we used the average E-field across the boundary (i.e., at the sphere surface) in computing the Lorentz force on the interfacial charges accumulated on the sphere. For the case of focusing a circularly-polarized beam at (x, y, z) = (0, 0, 0.7µm) onto a particle centered at (0.25µm, 0, 0), Fig. 8 shows color-coded force-component distributions in various cross-sectional planes through the center of the sphere. The superposed arrows show the projection of the force-density vector in the corresponding plane, e.g., plots on the yz￾plane show the (Fy, Fz) vector field. Contributions to force-density come from both (bound) surface charges and (bound) electric currents within the volume of the sphere. When the force density exceeds the range of color coding, the corresponding region is depicted as white. This happens in the area where the beam enters the sphere, seen in the xz and yz cross-sectional planes of Fig. 8 near the top of each frame. Reflection, refraction, and diffraction create complex interference patterns within the spherical particle, as evidenced by the richly textured force density profiles throughout the volume of the sphere. The surrounding liquid also experiences the effects of radiation pressure, as the bound currents within the liquid body feel the Lorentz force of the B-field, while the bound charges on the liquid side of the interface sense the Lorentz force of the E-field, in the same way that the particle itself experiences such forces. The force imparted to the liquid is strongest in the vicinity of the region where the beam enters the particle, but weak forces are felt (by the liquid) also in those regions where the light leaves the solid particle and re-emerges into the liquid environment. Fig. 9. Cross-sectional profiles of the integrated force-density components along the direction perpendicular to each cross-section. (Left) Distribution of ∫Fz (x, y, z) dz in the central xy-plane. (Middle) Distribution of ∫Fy (x, y, z) dy in the central xz-plane. (Right) Distribution of ∫Fx (x, y, z) dx in the central yz-plane. The range of integration includes the charges on the surface of the sphere, but excludes any forces that might be exerted on the surrounding liquid. For the system of Fig. 8, profiles of the integrated force density in the normal direction to each cross-section are shown in Fig. 9; the distribution of ∫Fz (x, y, z) dz in the central xy-plane appears on the left, that of ∫Fy (x, y, z) dy in the central xz-plane in the middle, and the profile of ∫Fx (x, y, z) dx in the central yz-plane on the right-hand side. The range of integration includes the (bound) charges on the surface of the particle, but excludes any forces that might be exerted by the entering/exiting light on the surrounding liquid. The presence of a strong force on the surface charges is indicated by the white regions (i.e., exceeding the color scale) near the top of the frame in the xz and yz cross-sections depicted in Fig. 9. In the above case of focusing a circularly-polarized beam at (x, y, z) = (0, 0, 0.7µm) onto a glass bead centered at (0.25µm, 0, 0), the net force on the bead, obtained by integrating the (C) 2005 OSA 4 April 2005 / Vol. 13, No. 7 / OPTICS EXPRESS 2332 #6863 - $15.00 US Received 14 January 2005; revised 15 March 2005; accepted 15 March 2005