Ey, EZ, HX n surf ,△FDTD,2D,A=5nm △,△FDID,2D,△=5mm FDTD.3D.△=1020nm Fig. 1. Surface force integrated over the left-half of the cylinder as function of the cylinder's refractive index ncy The incident plane-wave has vacuum wavelength 2o=0.65um, and the incidence mediums refractive index is ninc= 1.0 (solid lines)or ninc = 1. 3(dashed lines). The exact results of the Lorentz-Mie theory(circles)are compared with those of our FDTD-based method(triangles and crosses). In the case of cylinder immersed in water, the charges induced at the solid-liquid interface were lumped together, then subjected to the average E-field at the nterface; in other words, no attempts were made in these calculations to distinguish the force of the light's E-field on the solid surface from that on the adjacent liquid. For each FDtD mulation the grid resolution A is indicated 2. Comparison to exact solutions To validate our numerical procedures, we first consider the problem of computing the surface forces exerted by a plane-wave incident on a dielectric cylinder, with propagation direction be- ing perpendicular to the cylinder axis. We consider in the Y Z-plane of incidence a p-polarized plane-wave(Ey, Es, Hr), for which the electric-field component normal to the cylinder surface El, is discontinuous; see Fig. 1. The free-space wavelength of the incident light is 20=0.65um and the radius of the cylindrical rod is rev=1.Oum. The surface forces computed in our FDTD simulations can be compared with those obtained from the Lorentz-Mie theory of light scat- tering, Ref [14. In computing the Lorentz force of the E-field on the interfacial(bound) harges induced on the cylinder surface we used the average(Ref. [2]) of the E-field nor mal to the surface(the tangential component of the E-field is continuous across the interface) the surface-charge density is assumed to be proportional to the discontinuity of the ei field at the interface. While in the Lorentz-Mie theory El at the surface is readily available, on the FDTD grid the cylinder surface is approximated as a discrete staircase, and the surface force density components(Fyur/Eur) are evaluated along the coordinate axes, Ref (6]. Figure I shows, for two different cases, the surface force integrated over one-half of the cylinder sur- face(180°≤6≤360°), as function of the refractive index norl of the cylinder. The agreement between exact theory and numerical simulation is remarkable. Our numerical discretization er ror is of the order of 1-2% for nay ranging from 1.5 to 3. 4, consistent with the 30-60 points per wavelength discretization and first-order convergence due to staircase approximation of the geometry. For the high index-contrast case of n inc/ncw=1/3.4 the error(Fig. 1, A)was found to be dominated by the inadequate convergence to a time-harmonic state; the error was reduced (Fig. 1, v) when we increased the integration time In the second test problem we used the exact solutions for radiation pressure distribution in a solid dielectric prism illuminated by a Gaussian beam of light at Brewster's incidence, Ref[2] #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 3662ninc ncyl F z surf F y surf Ey,Ez,Hx r cyl Z Y 1.5 2 2.5 3 ncyl -12 -10 -8 -6 -4 -2 [pN/m] Fy surf, theory, ninc=1.0 Fz surf, theory, ninc=1.0 FDTD, 2D, Δ=5nm Fy surf, theory, ninc=1.3 Fz surf, theory, ninc=1.3 FDTD, 2D, Δ=5nm FDTD, 3D, Δ=10-20nm , , Fig. 1. Surface force integrated over the left-half of the cylinder as function of the cylinder’s refractive index ncyl. The incident plane-wave has vacuum wavelength λ0 = 0.65μm, and the incidence medium’s refractive index is ninc = 1.0 (solid lines) or ninc = 1.3 (dashed lines). The exact results of the Lorentz-Mie theory (circles) are compared with those of our FDTD-based method (triangles and crosses). In the case of cylinder immersed in water, the charges induced at the solid-liquid interface were lumped together, then subjected to the average E-field at the interface; in other words, no attempts were made in these calculations to distinguish the force of the light’s E-field on the solid surface from that on the adjacent liquid. For each FDTD simulation the grid resolution Δ is indicated. 2. Comparison to exact solutions To validate our numerical procedures, we first consider the problem of computing the surface forces exerted by a plane-wave incident on a dielectric cylinder, with propagation direction be￾ing perpendicular to the cylinder axis. We consider in the Y Z-plane of incidence a p-polarized plane-wave (Ey,Ez,Hx), for which the electric-field component normal to the cylinder surface, E⊥, is discontinuous; see Fig. 1. The free-space wavelength of the incident light is λ 0 = 0.65μm and the radius of the cylindrical rod is rcyl = 1.0μm. The surface forces computed in our FDTD simulations can be compared with those obtained from the Lorentz-Mie theory of light scat￾tering, Ref. [14]. In computing the Lorentz force of the E-field on the interfacial (bound) charges induced on the cylinder surface we used the average (Ref. [2]) of the E-field nor￾mal to the surface (the tangential component of the E-field is continuous across the interface); the surface-charge density is assumed to be proportional to the discontinuity of the E ⊥ field at the interface. While in the Lorentz-Mie theory E⊥ at the surface is readily available, on the FDTD grid the cylinder surface is approximated as a discrete staircase, and the surface force density components (Fsur f y ,Fsur f z ) are evaluated along the coordinate axes, Ref. [6]. Figure 1 shows, for two different cases, the surface force integrated over one-half of the cylinder sur￾face (180◦ ≤ θ ≤ 360◦), as function of the refractive index ncyl of the cylinder. The agreement between exact theory and numerical simulation is remarkable. Our numerical discretization er￾ror is of the order of 1-2% for ncyl ranging from 1.5 to 3.4, consistent with the 30-60 points per wavelength discretization and first-order convergence due to staircase approximation of the geometry. For the high index-contrast case of ninc/ncyl = 1/3.4 the error (Fig. 1, ) was found to be dominated by the inadequate convergence to a time-harmonic state; the error was reduced (Fig. 1, ) when we increased the integration time. In the second test problem we used the exact solutions for radiation pressure distribution in a solid dielectric prism illuminated by a Gaussian beam of light at Brewster’s incidence, Ref. [2]. #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 3662