Figure 1

Coordinates system: ${\mathrm{O}}_{\mathrm{B}}\text{−}uvw$ is for the incident shaped beam and ${\mathrm{O}}_{\mathrm{P}}\text{−}xyz$ is for the spheroid.Reuse & Permissions

Figure 2

Geometry of Cartesian coordinates of the beam and spheroid. ${\mathrm{O}}_{\mathrm{P}}\text{−}xyz$ is the coordinate system of the spheroid and ${\mathrm{O}}_{\mathrm{P}}\text{−}{u}^{\prime }{v}^{\prime }{w}^{\prime }$ is translated from the beam coordinates ${\mathrm{O}}_{\mathrm{B}}\text{−}uvw$ having the origin ${\mathrm{O}}_{\mathrm{B}}$ located at ($x_0,y_0,z_0$) in ${\mathrm{O}}_{\mathrm{P}}\text{−}xyz$.Reuse & Permissions

Figure 3

Comparison of the longitudinal RPCS $C_{\mathrm{pr},z}$ exerted by a plane wave on the spheroid of axis ratio $a∕b=1.01$ to that on the sphere. The incidence and polarization angles of the plane wave are assumed to be 0°. The particles have the same relative refractive index $\widehat{m}=1.5$. The dashed curve is for the prolate spheroid of semiminor axis length equal to the radius of the projection area $(R=b)$ and the dashed-doted curve is for the oblate spheroid of semimajor axis length equal to the radius of the projection area $(R=a)$. The results are compared with GLMT radiation pressure predictions for the sphere of radius $R$. (1) (a) is for $0.1\mu \mathrm{m}⩽R⩽0.8\mu \mathrm{m}$; (2) (b) is for $0.8\mu \mathrm{m}⩽R⩽1.5\mu \mathrm{m}$; (3) (c) is for $1.5\mu \mathrm{m}⩽R⩽2.0\mu \mathrm{m}$.Reuse & Permissions

Figure 4

Same as Fig. 3 but for the axis ratio $a∕b=1.1$. (1) (a) is for $0.1\mu \mathrm{m}⩽R⩽1.0\mu \mathrm{m}$; (2) (b) is for $1.0\mu \mathrm{m}⩽R⩽1.5\mu \mathrm{m}$; (3) (c) is for $1.5\mu \mathrm{m}⩽R⩽2.0\mu \mathrm{m}$. For clarity and convenient identification, the RPCS curves of the prolate and oblate spheroids have been offset by the factors $2\times {10}^{-12}$ and $-2\times {10}^{-12}$, respectively.Reuse & Permissions

Figure 5

Longitudinal RPCS versus the axis ratio for a red blood cell (RBC) of radii 3.00, 3.32, 3.64, and $3.96\mu \mathrm{m}$, located on the beam axis with the location characterized by $\omega ∕R=1.1$. The RBC of refractive index 1.380 is in the buffer of refractive index 1.335, and is deformed from the spherical shape to the spheroidal one under the action of two counter-propagating laser beams in the ${\mathrm{TEM}}_{00}$ mode. The volume of the particle remains constant during the deformation. The circular Gaussian beam has a waist radius ${\omega }_0=0.5\lambda$. Note that $C_{\mathrm{pr},z}$ plotted in Fig. 5 represents the RPCS of beam $A$, which propagates in the direction of the positive $z$ axis. The incidence and polarization angles of the beams are ${\Theta }_{\mathrm{bd}}={\Phi }_{\mathrm{bd}}=0$. Beam $B$, which has the same axis as beam $A$ but opposite propagation direction, has RPCS of the same value as beam $A$ but with opposite sign.Reuse & Permissions

Figure 6

RPCS versus the incidence angle ${\Theta }_{\mathrm{bd}}$. The polarization angle ${\Phi }_{\mathrm{bd}}$ is assumed to be 0. The circular Gaussian beam of the waist radius ${\omega }_0=2\lambda$ is assumed to illuminate a prolate spheroid of axis ratio $a∕b=2.0$, with semiminor axis length $b=0.5\mu \mathrm{m}$ and relative refractive index $\widehat{m}=1.5$. Note that $C_{\mathrm{pr},y}$ is equal to zero and hence is curve is not plotted. (1) In (a) is plotted the RPCS curve versus ${\Theta }_{\mathrm{bd}}$, including the longitudinal component of RPCS $C_{\mathrm{pr},z}$, the transverse the $C_{\mathrm{pr},x}$, as well as the resultant one; (2) in (b) is plotted the direction of the resultant RPF (${\mathrm{O}}_{\mathrm{P}\text{−}xy}$ plane) exerted on the spheroid. Note that $\theta$ is formed by the direction of the resultant RPF and the positive $z$ axis, while ${\Theta }_{\mathrm{bd}}$ is formed by the beam propagation direction and the positive $z$ axis.Reuse & Permissions

Figure 7

RPCS versus the polarization angle ${\Phi }_{\mathrm{bd}}$ for five incidence angles ${\Theta }_{\mathrm{bd}}=0°$, 22.5°, 45°, 67.5°, and 90°. The beam and the spheroid are the same as in Fig. 6. In (a), (b), and (c) are plotted the curves of $C_{\mathrm{pr},z}$, $C_{\mathrm{pr},x}$, and $C_{\mathrm{pr},y}$ versus ${\Phi }_{\mathrm{bd}}$, respectively. For ${\Theta }_{\mathrm{bd}}=0°$, $C_{\mathrm{pr},x}$, and $C_{\mathrm{pr},y}$ are zero and therefore their curves are not explicitly found in the figures.Reuse & Permissions

Figure 8

Longitudinal RPCS versus the location of Rayleigh particle along the $z$ axis. The circular Gaussian beam has a waist radius ${\omega }_0=\lambda$. The spheroids have the relative refractive index $\widehat{m}=1.5$ but different axis ratios $a∕b=1.1$ and 1.2, respectively. The projection radius of the particles is assumed to be $R=0.01\mu \mathrm{m}$ so that we have $R=b$ for the prolate spheroid and $R=a$ for the oblate one. The incidence and polarization angles of the beams are ${\Theta }_{\mathrm{bd}}={\Phi }_{\mathrm{bd}}=0$.Reuse & Permissions

Figure 9

Longitudinal RPCS versus particle location along the $z$ axis. The circular Gaussian beam has a waist radius ${\omega }_0=2\lambda$. The spheroids have the same relative refractive index $\widehat{m}=1.5$ but the different axis ratios $a∕b=1.05$ and 1.10, respectively. The projection radius of the particles is assumed to be $R=1.0\mu \mathrm{m}$ so that we have $R=b$ for the prolate spheroid and $R=a$ for the oblate one. The incidence and polarization angles of the beams are ${\Theta }_{\mathrm{bd}}={\Phi }_{\mathrm{bd}}=0$.Reuse & Permissions

Figure 10

Transverse RPCS $C_{\mathrm{pr},x}$ versus the beam center location along the positive $x$ axis. The circular Gaussian beam of a waist radius ${\omega }_0=2\lambda$ is assumed to be incident on spheroids of the same relative refractive index $\widehat{m}=1.5$ but with different axis ratios $a∕b=1.00$, 1.01, and 1.10, respectively. The beam center locates on the $x$ axis so that $y_0=z_0=0\mu \mathrm{m}$. The incidence and polarization angles of the beam are ${\Theta }_{\mathrm{bd}}={\Phi }_{\mathrm{bd}}=0$. The projection radius of the particle is $R=1.0\mu \mathrm{m}$. (1)(a) is for the longitudinal RPCS $C_{\mathrm{pr},z}$ versus $x_0$; and (2)(b) is for the transverse RPCS $C_{\mathrm{pr},x}$ versus $x_0$. Attention should be paid to the fact that, in the current case, another transverse RPCS, $C_{\mathrm{pr},y}$, is zero and its curve is not plotted.Reuse & Permissions

Figure 11

Same as Fig. 10 but for the transverse RPCS $C_{\mathrm{pr},y}$ versus the beam center location along the positive $y$ axis. The beam center ${\mathrm{O}}_{\mathrm{B}}$ locates on the positive $y$ axis so that $x_0=z_0=0\mu \mathrm{m}$. (1) (a) is for the longitudinal RPCS $C_{\mathrm{pr},z}$ versus $y_0$; and (2) (b) is for the transverse RPCS $C_{\mathrm{pr},y}$ versus $y_0$. Attention should be paid to the fact that, in the current case, another transverse RPCS, $C_{\mathrm{pr},x}$, is zero and its curve is not plotted.Reuse & Permissions

Figure 12

Longitudinal RPCS versus $z_0$ for a prolate spheroid of axis ratio $a∕b=1.5$ and semiminor axis length $b=1.0\mu \mathrm{m}$ illuminated by an astigmatic elliptical Gaussian beam of waist radii along $u$ and $v$ directions being $\lambda$ and $10\lambda$, respectively (${\omega }_{0u}=\lambda$ and ${\omega }_{0v}=10\lambda )$. The locations of the waist radii ${\omega }_{0u}$ and ${\omega }_{0v}$ are $-0.5\mu \mathrm{m}$ and $0.5\mu \mathrm{m}$, respectively ($w_u=-0.5\mu \mathrm{m}$ and $w_v=0.5\mu \mathrm{m}$). The incidence and polarization angles of the beam are ${\Theta }_{\mathrm{bd}}={\Phi }_{\mathrm{bd}}=0$. The five curves correspond to spheroids of different refractive indices $\widehat{m}=1.5$, $1.5+0.001i$, $1.5+0.01i$, $1.5+0.1i$, and $1.5+i$.Reuse & Permissions