Table 1. Definitions of the surface charge and surface force densities for methods l, II and lll. Method 0(E1-E21)oE81-E21)(Ex⊥-E21) E E 2(E1+E21)/2o2(E1+E21)/22(Eg1+E2L) When the prism is immersed in water, the interfacial charges induced on the solid and liquid ides of the interface must be distinguished from each other. The interaction of these charged layers with the local E-field determines their contribution to the net force acting on the prism Following the notation introduced in Ref [2] we enumerate in Table I the three approaches to the computation of the surface force density acting on the solid side of the solid-liquid interface Here(Fur/ fsr are the surface force density components parallel and perpendicular to the solid's surface; O2 is the surface charge density belonging to the solid side, El, E11, E21 are, respectively, the E-field components parallel to the interface, normal to the interface on the iquid side, and normal to the interface on the solid side; and EoEgl=EoE Ell=EoE2E21 is the electric displacement field Di normal to the interface Method Ill isolates the force acting on the solid side of the interface by introducing a small (artificial) gap between the solid and the liquid, then using the gap field Egl(derived from the continuity of the normal component of the displacement field D)to evaluate both the charge density o2 and the average E-field that acts on the solid; this corresponds to Eq (21)in Ref. [2]. While the conceptual introduction of a small gap at the solid-liquid interface is essential for the calculation of o2, it gives rise to a mutual attractive force between the two charged layers thus pushed apart. This force, which is included in the total force experienced by the solid object as calculated by Method lll,is probably inactive in practice and should be excluded. In Method II the contribution of this attractive force between the two charged layers (induced on the solid and liquid sides of the interface)is removed by using(E11+E21)/2 as the effective perpendicular field acting on the surface charge density o2 on the solid side of the interface; see Eq (24)in Ref [2]. In Method n ninc=1.33 F(△=20m)1663483×10-22383095 64 224231.08 Fy( exact)‖16664.05×10-224531 F(△=20mm)-0.0473.13×10-002016 +b=90° Table 2. Radiation force on the prism of Fig. 2, computed with Fig. 2. Dielectric prism the exact method and with the FDTD simulations. A p-polarized (Hr, Ey, E-)Gaussian beam illuminates the prism at Brewster's angle 0B. The net radiation force exerted on the prism is denoted medium of refractive by(Fy, F=-). The value of the mesh parameter A used in each #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 3663Table 1. Definitions of the surface charge and surface force densities for methods I,II and III. Method I II III σ2 ε0(E1⊥ −E2⊥) ε0(Eg⊥ −E2⊥) ε0(Eg⊥ −E2⊥) Fsur f  σ2E σ2E σ2E Fsur f ⊥ σ2(E1⊥ +E2⊥)/2 σ2(E1⊥ +E2⊥)/2 σ2(Eg⊥ +E2⊥)/2 When the prism is immersed in water, the interfacial charges induced on the solid and liquid sides of the interface must be distinguished from each other. The interaction of these charged layers with the local E-field determines their contribution to the net force acting on the prism. Following the notation introduced in Ref. [2] we enumerate in Table 1 the three approaches to the computation of the surface force density acting on the solid side of the solid-liquid interface. Here (Fsur f  ,Fsur f ⊥ ) are the surface force density components parallel and perpendicular to the solid’s surface; σ2 is the surface charge density belonging to the solid side; E,E1⊥,E2⊥ are, respectively, the E-field components parallel to the interface, normal to the interface on the liquid side, and normal to the interface on the solid side; and ε 0Eg⊥ = ε0ε1E1⊥ = ε0ε2E2⊥ is the electric displacement field D⊥ normal to the interface. Method III isolates the force acting on the solid side of the interface by introducing a small (artificial) gap between the solid and the liquid, then using the gap field Eg⊥ (derived from the continuity of the normal component of the displacement field D) to evaluate both the charge density σ 2 and the average E-field that acts on the solid; this corresponds to Eq.(21) in Ref. [2]. While the conceptual introduction of a small gap at the solid-liquid interface is essential for the calculation of σ2, it gives rise to a mutual attractive force between the two charged layers thus pushed apart. This force, which is included in the total force experienced by the solid object as calculated by Method III, is probably inactive in practice and should be excluded. In Method II the contribution of this attractive force between the two charged layers (induced on the solid and liquid sides of the interface) is removed by using (E1⊥ +E2⊥)/2 as the effective perpendicular field acting on the surface charge density σ2 on the solid side of the interface; see Eq.(24) in Ref. [2]. In Method ninc n y z Gaussian beam F y Fz B B B B Fig. 2. Dielectric prism of refractive index n immersed in a host medium of refractive index ninc. Net force ninc = 1 ninc = 1.33 [pN/m] I II III Fy (Δ = 20nm) 16.63 4.83×10−3 22.38 30.95 Fy (Δ = 10nm) 16.64 —— 22.42 31.08 Fy (exact) 16.66 4.05×10−3 22.45 31.09 Fz (Δ = 20nm) -0.047 3.13×10−2 -0.02 -0.16 Fz (Δ = 10nm) -0.026 —— -0.016 -0.001 Fz (exact) 0.0 0.0 0.0 0.0 Table 2. Radiation force on the prism of Fig. 2, computed with the exact method and with the FDTD simulations. A p-polarized (Hx,Ey,Ez) Gaussian beam illuminates the prism at Brewster’s angle θB. The net radiation force exerted on the prism is denoted by (Fy,Fz). The value of the mesh parameter Δ used in each simulation is indicated. #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 3663