Abstract

We present the photonic spin Hall effect on an ellipsoidal Rayleigh particle, which amounts to a polarization-dependent shift in scattering far-field. Based on the dipole model, we demonstrate that such shift is unavoidable when the light incidence is inclined with respect to the main axis of the ellipsoidal Rayleigh particle. The result has general validity and can be applied to metal and dielectric materials. In addition, the photonic spin Hall effect also manifests itself in the optical force and torque exerted on the particle, which is promising for precision metrology, spin-optics devices and optical driven micro-machines. Due to wide existence of the Rayleigh particles in nature, we believe that our findings might provide a useful toolset for investigating polarization-dependent scattering of particles.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

There is a growing interest in phenomena related to photonic spin Hall effect which originates from optical spin-orbit interaction [1]. Optical spin-orbit interaction plays a key role in understanding many fundamental optical processes that can be specifically divided into two types: spin with internal orbital angular momentum (OAM) interaction and spin with external OAM interaction. The second type is named as photonic spin Hall effect due to the transverse spin-dependent redistribution of the light intensity [213]. Such effect results from the coupling between the spin and the trajectory of the optical field [14]. To date, various methods have been presented to realize photonic spin Hall effect via reflection or refraction at optical interfaces [3,6,7,1520], inhomogeneous anisotropic media [2,2127], tilted observation planes [14,2832] and so on. The transverse spin-dependent shift in photonic spin Hall effect is promising for the manipulation of light [33]. Photonic spin Hall effect provides a powerful engine for precision metrology and spin-optics devices. Various relevant works have been reported in recent years [3439]. Based on detecting the spin-dependent displacements, a new method has been proposed to measure the thickness of nanometal film and identify the graphene layers [3436]. The wavelength-scale image error in optical localization has been presented to estimate the position of emitters by spin-orbit coupling of light [37]. The optical edge detecting technology based on spin-to-orbit interactions in image processing have been demonstrated by using air-glass interface reflection and high-efficiency dielectric metasurface [38,39].

In the last decade, the scattering of light by nanoparticles has been the subject of intense research activity [4043]. Spherical silicon nanoparticles with strongly anisotropic scattering in visible spectral range have been experimentally demonstrated [40]. It has been shown that the far-field directivity of single silicon spheres is greatly dependent on the nanoparticle size and the incident wavelength. It has been reported that the spin-based resonance effect and the polarization-sensitive focusing can be observed by using dielectric nanoparticle clusters [41]. The physical origin of the phenomena is attributed to the geometric phase arising from the interaction between light and dielectric nanoparticle clusters. The relationship of the Rayleigh scattering properties of a single Au nanoparticle with its size, shape, and local dielectric environment has been reported in [42] and they also investigated the refractive index sensitivity of nanospheres, oval-shaped nanoparticles and nanorods. Recently, photonic spin Hall effect by a dipole scatterer [43] has been demonstrated, which indicates that the spin-split scattering is highly dependent on the position of the dipole scatterer relative to the beam center.

Rayleigh particles are particles with radii smaller than the tenth of light wavelength. For visible light, the size of the Rayleigh particles is about tens of nanometers. A deep understanding of the optical properties of the nanometer-sized Rayleigh particles has both fundamental and practical significance. The deformation of the particle shape could cause anisotropic polarizability, which might give rise to polarization-dependent scattering field. The interaction between light and the particle brings about the transfers of linear momentum and angular momentum, which will induce the polarization-dependent optical force and torque exerted on the particle. In this paper, we focus on the photonic spin Hall effect on an ellipsoidal Rayleigh particle. To the best of our knowledge, such effect in scattering far-field of a Rayleigh particle has not yet been reported. Based on the dipole model, we will give a general description of the relationship between the scattering far-field and the spin state of the incident light in theory and simulation. It is shown that a polarization-dependent light splitting occurs when a beam of light obliquely incidents on an ellipsoidal Rayleigh particle. The influence of the ellipsoid radius and the incident angle of light, on the direction of the centroid (or barycenter) [28] of scattering far-field are presented. Considering the interaction between light and the ellipsoidal Rayleigh particle, we also show the optical force and torque phenomena related to the photonic spin hall effect which is promising for related technologies of optical driven micro-machines.

2. Theory

The scheme of the problem we considered is shown in Fig. 1(a), in which circularly polarized light obliquely incidents on an ellipsoidal Rayleigh particle. We assume that the axis of the incident beam in the $y$-$z$ plane is tilted by an angle $\beta$ with respect to the $z$ axis (see Fig. 1(a)). We investigate the centroid (or barycenter) of the scattering far-field for an ellipsoidal Rayleigh particle. First, the obliquely input circularly polarized light field can be written as

$$\textbf{E}_{\textrm{inc}} = \textrm{E}_{0}(-\sigma i \hat{\textbf{x}} +\textrm{cos}\beta \hat{\textbf{y}} + \textrm{sin}\beta \hat{\textbf{z}})\textrm{exp}[i k_0(-\textrm{sin}\beta y + \textrm{cos}\beta z)],$$
$$\textbf{H}_\textrm{inc} ={-}\textrm{H}_{0}(\hat{\textbf{x}} +\sigma i \textrm{cos}\beta \hat{\textbf{y}} + \sigma i \textrm{sin}\beta \hat{\textbf{z}})\textrm{exp}[i k_0(-\textrm{sin}\beta y + \textrm{cos}\beta z)],$$
where $\sigma$ denotes the helicity of the beam, $k_0$ is the wave number in vacuum, ${\textrm{E}_0}$ and ${\textrm{H}_0}$ are the amplitudes of incident electric and magnetic fields. In the following, the helicity is chosen as $\sigma$ $\equiv$ 0, +1, and -1 indicating the linear, right-circular, and left-circular polarizations, respectively. In the following analysis, we adopt the dipole model in which the ellipsoidal Rayleigh particle has electric and magnetic dipole responses. Following the dipole model, the scattering far-field can be described by the equations [44]
$$\textbf{E}_\textrm{sc} = {\frac{k_0^2} {4 \pi \epsilon_0}} {\frac{e^{i k_0 r}} {r}}{[(\hat{\textbf{n}}\times{\textbf{p}})\times{\hat{\textbf{n}}}-{\frac{1} {c}}\hat{\textbf{n}}\times{\textbf{m}}]},$$
$$\textbf{H}_\textrm{sc} = {\frac{1} {\eta_0}} {(\hat{\textbf{n}}\times{\textbf{E}_\textrm{sc}})},$$
where $\hat {\textbf {n}}$ is the unit direction vector, $r$ is the distance away from the scatterer, $\eta _0$ is the impedance of free space, $\textbf {p}$ and $\textbf {m}$ are the electric and magnetic dipole moments. For an ellipsoidal Rayleigh particle, we consider $\overline {\alpha }_\textrm{em}$ = $\overline {\alpha }_\textrm{me}$ = 0 for this achiral geometry so the electric and magnetic dipole moments can be expressed as
$$\textbf{p} = \overline{\alpha}_\textrm{ee}\cdot{\textbf{E}_\textrm{inc}},$$
$$\textbf{m} = \overline{\alpha}_\textrm{mm}\cdot{\textbf{H}_\textrm{inc}},$$
where $\overline {\alpha }_\textrm{ee}$ and $\overline {\alpha }_\textrm{mm}$ denote 3 $\times$ 3 polarizability tensors which can be written as
$$\overline{\alpha}_\textrm{ee} = \left(\begin{array}{ccc} \alpha_\textrm{ee1}^{xx}+i \alpha_\textrm{ee2}^{xx} & 0 & 0 \\ 0 & \alpha_\textrm{ee1}^{yy}+i \alpha_\textrm{ee2}^{yy} & 0 \\ 0 & 0 & \alpha_\textrm{ee1}^{zz}+i \alpha_\textrm{ee2}^{zz}\end{array} \right),$$
$$\overline{\alpha}_\textrm{mm} = \left(\begin{array}{ccc} \alpha_\textrm{mm1}^{xx}+i \alpha_\textrm{mm2}^{xx} & 0 & 0 \\ 0 & \alpha_\textrm{mm1}^{yy}+i \alpha_\textrm{mm2}^{yy} & 0 \\ 0 & 0 & \alpha_\textrm{mm1}^{zz}+i \alpha_\textrm{mm2}^{zz}\end{array} \right).$$
It is worth noticing that in the case of lossless or loss ellipsoidal Rayleigh particle, the quantities contained in $\overline {\alpha }_\textrm{ee}$ and $\overline {\alpha }_\textrm{mm}$ are complex due to the radiation loss correction to polarizabilities [4547]. The time-averaged intensity of the scattering field for a monochromatic electromagnetic beam in vacuum is defined as
$$\langle\textbf{S}\rangle = {\frac{1} {2}}{\textrm{Re}} ({\textbf{E}_\textrm{sc}}\times{\textbf{H}_\textrm{sc}^*}).$$
The centroid of scattering far-field can be described by azimuthal angle ($\varphi$) and elevation angle ($\theta$) in a spherical coordinate system. In the spherical coordinate system, the cosine functions of the azimuthal angle and elevation angle can be calculated as [48]
$$\langle{\textrm{cos}\varphi}\rangle = \frac{\iint{\textrm{cos}\varphi} S_r r^2 {\textrm{sin}\theta} d\theta d\varphi} {\iint S_r r^2 {\textrm{sin}\theta} d\theta d\varphi},$$
$$\langle{\textrm{cos}\theta}\rangle = \frac{\iint{\textrm{cos}\theta} S_r r^2 {\textrm{sin}\theta} d\theta d\varphi} {\iint S_r r^2 {\textrm{sin}\theta} d\theta d\varphi},$$
where $S_r$ is the radial component of the time-averaged intensity of the beam. By applying Eqs. (1)–(11), we can obtain
$$\langle{\textrm{cos}\varphi}\rangle \propto \sigma \textrm{sin}{2\beta} \frac{\eta_0 \textrm{W}_3} {\eta_0^2 \textrm{W}_1 + (1/{c^2}) \textrm{W}_2},$$
$$\langle{\textrm{cos}\theta}\rangle \propto \textrm{cos}{\beta} \frac{\eta_0 \textrm{W}_4} {\eta_0^2 \textrm{W}_1 + (1/{c^2}) \textrm{W}_2},$$
with
$$\textrm{W}_1 = ({\alpha_\textrm{ee1}^{xx}{^2}} + {\alpha_\textrm{ee2}^{xx}{^2}}) + ({\alpha_\textrm{ee1}^{yy}{^2}} + {\alpha_\textrm{ee2}^{yy}{^2}}) \textrm{cos}^2\beta + ({\alpha_\textrm{ee1}^{zz}{^2}} + {\alpha_\textrm{ee2}^{zz}{^2}}) \textrm{sin}^2\beta,$$
$$\textrm{W}_2 = ({\alpha_\textrm{mm1}^{xx}{^2}} + {\alpha_\textrm{mm2}^{xx}{^2}}) + ({\alpha_\textrm{mm1}^{yy}{^2}} + {\alpha_\textrm{mm2}^{yy}{^2}}) \textrm{cos}^2\beta + ({\alpha_\textrm{mm1}^{zz}{^2}} + {\alpha_\textrm{mm2}^{zz}{^2}}) \textrm{sin}^2\beta,$$
$$\textrm{W}_3 = ({\alpha_\textrm{mm2}^{zz}} {\alpha_\textrm{ee1}^{yy}} - {\alpha_\textrm{mm1}^{zz}} {\alpha_\textrm{ee2}^{yy}}) - ({\alpha_\textrm{mm2}^{yy}} {\alpha_\textrm{ee1}^{zz}} - {\alpha_\textrm{mm1}^{yy}} {\alpha_\textrm{ee2}^{zz}}),$$
$$\textrm{W}_4 = ({\alpha_\textrm{mm1}^{yy}} {\alpha_\textrm{ee1}^{xx}} + {\alpha_\textrm{mm2}^{yy}} {\alpha_\textrm{ee2}^{xx}}) + ({\alpha_\textrm{mm1}^{xx}} {\alpha_\textrm{ee1}^{yy}} + {\alpha_\textrm{mm2}^{xx}} {\alpha_\textrm{ee2}^{yy}}).$$
From Eqs. (12) and (13), we can see that the helicity of the incident light has no influence on the elevation angle $\theta$ but it strongly affect the azimuthal angle $\varphi$ . The azimuthal angles $\varphi$ for the incident left ( $\sigma$ = -1) and right ( $\sigma$ = +1) circularly polarized lights are symmetric about the plane of incidence. Such symmetric transverse shift for light with opposite handedness is called photonic spin Hall effects [14, 28-30]. As shown in Eq. (12), such photonic spin Hall effect is unavoidable if the incidence is inclined ($\beta \neq 0^\circ , 90^\circ , 180^\circ$) and the value of $\textrm {W}_3$ is not zero. The later condition can be satisfied if the shape of the particle is anisotropic in $y$ and $z$ directions. It is also worth noting that the elevation angle $\theta$ is not rarely equal to the incident angle $\beta$ unless $\beta$ is $90^\circ$, which is indicated in Eq. (13).

 figure: Fig. 1.

Fig. 1. The three-dimensional schematic of the system and polarization dependence of light scattering. (a) The blue and red rotatory arrows represent the incident left and right circularly polarized lights, respectively. The incident directions are all in the $y$-$z$ plane. $\beta$ is the angle between the incident light and the $z$-axis. The blue and red lines represent the scattering directions of left and right circularly polarized lights, respectively. (b) The far-field scattering diagram of a metallic (Au) ellipsoidal Rayleigh particle in ${Oxy}$ plane simulated in COMSOL Multiphysics software for different incident polarized lights. The radii of the particle in the $x$, $y$ and $z$ directions are 10 nm, 3 nm and 30 nm, respectively. The wavelength of the incident light is 650 nm and the incident angle $\beta$ is $45^\circ$. $\sigma \equiv 0$, +1, and -1 indicate the linear, right-circular and left-circular polarizations, respectively.

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3. Results and discussions

To confirm the theoretical analysis, we use the commercial software COMSOL Multiphysics to do some simulations. Figure 1(b) shows the far-field scattering diagram of a metallic (Au) ellipsoidal Rayleigh particle. The radii of the particle in the $x$, $y$ and $z$ directions are 10 nm, 3 nm and 30 nm, respectively. The wavelength of the incident light is 650 nm and the incident angle is $45^\circ$. The relative permittivity of gold at optical frequencies is modeled using Drude formula $\epsilon = 1-\omega _p^2/(\omega ^2 + i \omega _{\tau } \omega )$ with $\omega _p = 1.37 \times 10^{16} rad/s$ and $\omega _{\tau } = 1.215 \times 10^{14} rad/s$ . The angular distributions of the far-field scattering in ${Oxy}$ plane are symmetric about the plane of incidence for the left and right circularly polarized lights. As shown in Fig. 1(b), a clear polarization-dependent split can be seen in the scattering field.

As implied in Eq. (12), the transverse shift of the scattering far-field originates from the anisotropic polarizability in $y$ and $z$ directions. Here, we use $a_x$, $a_y$ and $a_z$ to denote the radii of the particle in $x$, $y$ and $z$ directions and try to change the ratio $a_y/a_z$ and $a_x/a_z$ to check its influence on the transverse shift. First, we set $a_x$ = 10 nm, $a_z$ = 30 nm and change $a_y$ from 5 nm (=1/6$a_z$) to 30 nm (=$a_z$), the cosine values of azimuthal angles and elevation angles for the centroids of scattering far-field are calculated and shown in Figs. 2(a) and 2(b). We also set $a_y$ = 10 nm, $a_z$ = 30 nm and change $a_x$ from 5 nm (=1/6$a_z$) to 30 nm (=$a_z$), the cosine values of azimuthal angles and elevation angles for the centroids of scattering far-field are calculated and shown in Figs. 2(c) and 2(d). The incident angle $\beta$ is fixed at $45^\circ$. It is clearly seen that the azimuthal angles for the incident left and right circularly polarized lights are opposite to each other but they are zero for the linearly polarized light in Figs. 2(a) and 2(c). Figures 2(b) and 2(d) show the elevation angles for the incident left and right circularly polarized lights are same, which is due to the elevation angle independent of the helicity of the incident light according to the Eq. (13). Therefore, the centroids of the scattering far-field for the incident left and right circularly polarized lights are always symmetric about the plane of incidence. The above results reveal the fact that a polarization-dependent split occurs when a beam of light obliquely incidents on an ellipsoidal Rayleigh particle, which are consistent with our theory. It is worth remarking that when the radii of the particle in the $y$ and $z$ directions are equal (both are 30 nm), the cosine values of the azimuthal angles for the linearly, left and right circularly polarized lights are all equal to zero, which indicates the polarization-dependent split disappears. The relevant works show the spin Hall effect of light in Mie spherical particles [4951], which all focus on the transverse shift in perceived location of the source. It implies the phenomenon valid for the ellipsoidal particles and the broken symmetry of the ellipsoidal particles might be more conducive to the spin Hall effect. In this paper, we investigate the centroid (or barycenter) of the scattering far-field for an ellipsoidal Rayleigh particle to manifest the spin Hall effect. In addition, the polarization-dependent shift disappears for an isotropic and homogeneous spherical particle.

 figure: Fig. 2.

Fig. 2. The simulated cosine values of azimuthal angles and elevation angles for the centroids of scattering far-field. The material of the ellipsoidal Rayleigh particle is metallic (Au). The wavelength of the incident light is 650 nm. The incident angle is $45^\circ$. (a) and (b) The changes in the cosine values of azimuthal angles and elevation angles for the centroids of scattering far-field with the radius of the particle in $y$ direction ($a_y$) through simulation. The radii of the particle in the $x$ and $z$ directions are 10 nm and 30 nm, respectively. (c) and (d) The changes in the cosine values of azimuthal angles and elevation angles for the centroids of scattering far-field with the radius of the particle in $x$ direction ($a_x$) through simulation. The radii of the particle in the $y$ and $z$ directions are 10 nm and 30 nm, respectively.

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The dependences of the cosine values of azimuthal angles for the centroids of scattering far-field on the incident angle are shown in Fig. 3, where $a_x$ = 10 nm, $a_y$ = 20 nm and $a_z$ = 30 nm. It is easy to observe that the cosine values of the azimuthal angles for the left and right circularly polarized lights are odd functions with the incident angle. When the incident angle is $0^\circ$ and $\pm 90^\circ$, the cosine values of the azimuthal angles for the linearly, left and right circularly polarized lights are all equal to zero, which indicates the polarization-dependent split disappears. The relationship between the cosine value of azimuthal angle and the incident angle can be described by Eq. (12). This equation can be written in a more simplified form as

$$\langle{\textrm{cos}\varphi}\rangle = \sigma \textrm{sin}{2\beta} \frac{C_1} {C_2 + C_3 \textrm{cos}^2 \beta},$$
where $C_1$, $C_2$ and $C_3$ are parameters which are mainly determined by the polarizability properties of the particle. Using Eq. (15), we obtain the fitting curves as shown in Fig. 3. The curves and the simulated data coincide well. The fitted values of parameters $C_1$, $C_2$ and $C_3$ are -0.000445, 4.4415, and -3.2810, respectively.

 figure: Fig. 3.

Fig. 3. The dependences of the cosine values of azimuthal angles for the centroids of scattering far-field on the incident angle. The radii of the particle in the $x$, $y$ and $z$ directions are 10 nm, 20 nm and 30 nm, respectively.

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4. Optical force

The interaction between light and the ellipsoidal Rayleigh particle brings about the transfer of linear momentum, which will induce optical force exerted on the illuminated object. The photonic spin Hall effect in the scattering field suggests that the directions of the forces on the particle may also shift away from the regular directions. The time-averaged optical force $\langle {\textbf {F}}\rangle$ on the ellipsoidal Rayleigh particle can be calculated by integrating the Maxwell stress tensor over a surface $S$ enclosing the ellipsoidal Rayleigh particle, which is expressed as

$$\langle{\textbf{F}}\rangle = \oint_S \hat{\textbf{n}}\cdot\langle{\overline{\textbf{T}}}\rangle dS,$$
where $\hat {\textbf {n}}$ denotes the unit outward normal vector at surface $S$ and ${\overline {\textbf {T}}}$ is the time-averaged Maxwell stress tensor can be written as
$$\langle{\overline{\textbf{T}}}\rangle = {\frac{1} {2}} \textrm{Re} [\epsilon \textbf{E} \textbf{E}^* + \mu \textbf{H} \textbf{H}^* - {\frac{1} {2}}(\epsilon \textbf{E}\cdot\textbf{E}^* + \mu \textbf{H}\cdot\textbf{H}^*)\overline{\textbf{I}}],$$
with $\overline {\textbf {I}}$ is the unit tensor, $\epsilon$ and $\mu$ denoting the permittivity and permeability of the medium surrounding the particle. Figures 4(a)–4(f) show the simulated optical forces exerted on the metallic (Au) ellipsoidal Rayleigh particle. The wavelength of the incident light is 650 nm. Within the $a_y$ interval between 5 nm and 30 nm, the changes in the $x$, $y$ and $z$ components of optical forces with $a_y$ are shown in Figs. 4(a)–4(c) where $a_x$ = 10 nm, $a_z$ = 30 nm and the incident angle is $45^\circ$. Figures 4(d)–4(f) illustrate the changes in the $x$, $y$ and $z$ components of optical force with the incident angle where $a_x$ = 10 nm, $a_y$ = 20 nm and $a_z$ = 30 nm. It is easy to identify that the $x$ and $y$ components of optical force are odd functions with the incident angle but the $z$ component of optical force is an even function with the incident angle in Figs. 4(d)–4(f). It is seen that the $x$ components of optical forces for the incident left and right circularly polarized lights are always opposite to each other while the handedness of the incident light does not affect the $y$ and $z$ components of optical forces. This result implies that the direction of the optical force is shifted away from the propagation direction of the incident light. The $x$ components of the optical forces for the incident left and right circularly polarized lights are equal to zero when $a_y$ is equal to $a_z$. Because the polarization-dependent split disappears when the radii of the particle in the $y$ and $z$ directions are equal. The simulations are in good agreement with the analytical results. This phenomenon of the optical force is a direct result of the photonic spin Hall effect. It indicates the lateral optical force exerted on the ellipsoidal Rayleigh particle can be generated by the circularly polarized light and the direction of the force can be readily modulated by the handedness of the incident light. It may provide a potential pathway to optical manipulation of Rayleigh particles.

 figure: Fig. 4.

Fig. 4. The simulated optical forces exerted on the metallic (Au) ellipsoidal Rayleigh particle. The wavelength of the incident light is 650 nm. (a) - (c) The changes in the $x$, $y$ and $z$ components of optical forces with the radius of the particle in $y$ direction ($a_y$). The radii of the particle in the $x$ and $z$ directions are 10 nm and 30 nm, respectively. The incident angle is $45^\circ$. (d) - (f) The changes in the $x$, $y$ and $z$ components of optical forces with the incident angle. The radii of the particle in the $x$, $y$ and $z$ directions are 10 nm, 20 nm and 30 nm, respectively.

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5. Optical torque

The time-averaged optical torque $\langle {\mathbf {\Gamma }}\rangle$ on the ellipsoidal Rayleigh particle can be expressed as

$$\langle{\mathbf{\Gamma}}\rangle = \oint_S \hat{\textbf{n}}\cdot(\langle{\overline{\textbf{T}}}\times{\textbf{r}}\rangle) dS,$$
where $\textbf {r}$ is the position vector originating from the center of mass. Utilizing the changing of the $a_y$ and incident angle, we obtain the changing of optical torques exerted on the metallic (Au) ellipsoidal Rayleigh particle, as shown in Figs. 5(a)–5(f). Figures 5(a)–5(c) depict the $x$, $y$ and $z$ components of optical torque varying with $a_y$ where $a_x$ = 10 nm and $a_z$ = 30 nm. The incident angle is fixed at $45^\circ$. In Figs. 5(d)–5(f), we see that the $x$ and $y$ components of optical torque are odd functions with the incident angle and the $z$ component of optical torque is even function with the incident angle. The $y$ ($z$) components of optical torques for the incident left and right circularly polarized lights are the opposite of each other, which originates from the transfers of the angular momenta from the incident photonic spins. The incident left and right circularly polarized lights have opposite angular momentum along the propagation direction which is in the $y$-$z$ plane in our case. The transfer of the angular momentum between the light and the ellipsoidal Rayleigh particle takes place in $y$-$z$ plane and can be projected to the $y$ and $z$ directions, respectively. As a result, the $y$ ($z$) components of the torques for the incident left and right circularly polarized lights are opposite to each other. The nonzero angular momentum of electromagnetic wave interacts with the ellipsoidal Rayleigh particle, which generates the optical torque exerted on the particle due to the conservation of angular momentum in the whole system. If there is a transfer of the angular momentum between the light and the ordinary particle, the change rule of the optical torque of the ellipsoidal particle is also applicable to the ordinary particle. The results can be clearly understood by the relationship between optical angular momentum and optical torque.

 figure: Fig. 5.

Fig. 5. The simulated optical torques exerted on the metallic (Au) ellipsoidal Rayleigh particle. The wavelength of the incident light is 650 nm. (a) - (c) The changes in the $x$, $y$ and $z$ components of optical torques with the radius of the particle in $y$ direction ($a_y$). The radii of the particle in the $x$ and $z$ directions are 10 nm and 30 nm, respectively. The incident angle is $45^\circ$. (d) - (f) The changes in the $x$, $y$ and $z$ components of optical torques with the incident angle. The radii of the particle in the $x$, $y$ and $z$ directions are 10 nm, 20 nm and 30 nm, respectively.

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6. Conclusion

In conclusion, we have explored the photonic spin Hall effect on an ellipsoidal Rayleigh particle in scattering far-field. The results show that a spin split scattering far-field behavior of a beam of light obliquely incident on an ellipsoidal Rayleigh particle. It should be emphasized that the radii of the ellipsoidal Rayleigh particle are different in the plane of incidence. Moreover, we present an analysis about the optical force and torque on a metallic (Au) ellipsoidal Rayleigh particle to get insight into the more application potential of the photonic spin Hall effect. These results will assist in the investigation of optical manipulation which can be used to design precision metrology, spin-optics devices and optical driven micro-machines.

Funding

National Natural Science Foundation of China (11874132, 61307072, 61308017, 61377016, 61405056, 61575055); National Basic Research Program of China (973 Program) (2013CBA01702).

References

1. D. O’Connor, P. Ginzburg, F. J. Rodríguezfortuño, G. A. Wurtz, and A. V. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5(1), 5327 (2014). [CrossRef]  

2. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant pancharatnam-berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002). [CrossRef]  

3. K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006). [CrossRef]  

4. K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007). [CrossRef]  

5. A. Aiello and J. P. Woerdman, “Role of beam propagation in goos-hanchen and imbert-fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008). [CrossRef]  

6. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008). [CrossRef]  

7. H. Onur and K. Paul, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008). [CrossRef]  

8. E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009). [CrossRef]  

9. K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010). [CrossRef]  

10. O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010). [CrossRef]  

11. K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011). [CrossRef]  

12. K. Y. Bliokh and A. Aiello, “Goos-hänchen and imbert-fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013). [CrossRef]  

13. K. Y. Bliokh, G. Yuri, K. Vladimir, and H. Erez, “Coriolis effect in optics: unified geometric phase and spin-hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008). [CrossRef]  

14. J. Korger, A. Aiello, V. Chille, P. Banzer, and G. Leuchs, “Observation of the geometric spin hall effect of light,” Phys. Rev. Lett. 112(11), 113902 (2014). [CrossRef]  

15. M. Onoda, S. Murakami, and A. N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004). [CrossRef]  

16. F. Nori, “Geometrical optics: the dynamics of spinning light,” Nat. Photonics 2(12), 717–718 (2008). [CrossRef]  

17. H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin hall effect of light near the brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011). [CrossRef]  

18. L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012). [CrossRef]  

19. J. B. Götte and M. R. Dennis, “Limits to superweak amplification of beam shifts,” Opt. Lett. 38(13), 2295–2297 (2013). [CrossRef]  

20. X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012). [CrossRef]  

21. Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam-berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26(18), 1424–1426 (2001). [CrossRef]  

22. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006). [CrossRef]  

23. E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014). [CrossRef]  

24. N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011). [CrossRef]  

25. N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013). [CrossRef]  

26. G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013). [CrossRef]  

27. X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015). [CrossRef]  

28. A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009). [CrossRef]  

29. J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011). [CrossRef]  

30. L.-J. Kong, S.-X. Qian, Z.-C. Ren, X.-L. Wang, and H.-T. Wang, “Effects of orbital angular momentum on the geometric spin hall effect of light,” Phys. Rev. A 85(3), 035804 (2012). [CrossRef]  

31. M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014). [CrossRef]  

32. M. Neugebauer, S. Grosche, S. Rothau, G. Leuchs, and P. Banzer, “Lateral spin transport in paraxial beams of light,” Opt. Lett. 41(15), 3499–3502 (2016). [CrossRef]  

33. X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017). [CrossRef]  

34. X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012). [CrossRef]  

35. X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012). [CrossRef]  

36. X. Zhou, L. Sheng, and X. Ling, “Photonic spin hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018). [CrossRef]  

37. G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019). [CrossRef]  

38. T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019). [CrossRef]  

39. J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019). [CrossRef]  

40. Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4(1), 1527 (2013). [CrossRef]  

41. Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103(14), 141101 (2013). [CrossRef]  

42. P. L. Truong, X. Ma, and S. J. Sim, “Resonant rayleigh light scattering of single au nanoparticles with different sizes and shapes,” Nanoscale 6(4), 2307–2315 (2014). [CrossRef]  

43. M. Neugebauer, S. Nechayev, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement enhanced spin hall effect of light for particle displacement sensing,” Nano Lett. 19(1), 422–425 (2019). [CrossRef]  

44. J. D. Jackson, Classical Electrodynamics (Wiley, 2001).

45. J. E. Sipe and J. V. Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974). [CrossRef]  

46. P. A. Belov, S. I. Maslovski, K. R. Simovski, and S. A. Tretyakov, “A condition imposed on the electromagnetic polarizability of a bianisotropic lossless scatterer,” Tech. Phys. Lett. 29(9), 718–720 (2003). [CrossRef]  

47. D. V. Zhirihin, S. V. Li, D. Y. Sokolov, A. P. Slobozhanyuk, M. A. Gorlach, and A. B. Khanikaev, “Photonic spin hall effect mediated by bianisotropy,” Opt. Lett. 44(7), 1694–1697 (2019). [CrossRef]  

48. S. Yushanov, J. S. Crompton, and K. C. Koppenhoefer, “Mie scattering of electromagnetic waves,” https://cn.comsol.com/paper/download/181101/crompton_paper.pdf.

49. A. Banerjee, J. Soni, N. Ghosh, S. D. Gupta, and S. Mansha, “Giant Goos–Hänchen shift in scattering: the role of interfering localized plasmon modes,” Opt. Lett. 39(14), 4100–4103 (2014). [CrossRef]  

50. D. Gao, R. Shi, A. E. Miroshnichenko, and L. Gao, “Enhanced spin hall effect of light in spheres with dual symmetry,” Laser Photonics Rev. 12(11), 1800130 (2018). [CrossRef]  

51. R. Shi, D. L. Gao, H. Hu, Y. Q. Wang, and L. Gao, “Enhanced broadband spin hall effects by core-shell nanoparticles,” Opt. Express 27(4), 4808–4817 (2019). [CrossRef]  

References

  • View by:

  1. D. O’Connor, P. Ginzburg, F. J. Rodríguezfortuño, G. A. Wurtz, and A. V. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5(1), 5327 (2014).
    [Crossref]
  2. Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant pancharatnam-berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
    [Crossref]
  3. K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
    [Crossref]
  4. K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
    [Crossref]
  5. A. Aiello and J. P. Woerdman, “Role of beam propagation in goos-hanchen and imbert-fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
    [Crossref]
  6. K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
    [Crossref]
  7. H. Onur and K. Paul, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
    [Crossref]
  8. E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
    [Crossref]
  9. K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
    [Crossref]
  10. O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
    [Crossref]
  11. K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
    [Crossref]
  12. K. Y. Bliokh and A. Aiello, “Goos-hänchen and imbert-fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
    [Crossref]
  13. K. Y. Bliokh, G. Yuri, K. Vladimir, and H. Erez, “Coriolis effect in optics: unified geometric phase and spin-hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
    [Crossref]
  14. J. Korger, A. Aiello, V. Chille, P. Banzer, and G. Leuchs, “Observation of the geometric spin hall effect of light,” Phys. Rev. Lett. 112(11), 113902 (2014).
    [Crossref]
  15. M. Onoda, S. Murakami, and A. N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
    [Crossref]
  16. F. Nori, “Geometrical optics: the dynamics of spinning light,” Nat. Photonics 2(12), 717–718 (2008).
    [Crossref]
  17. H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin hall effect of light near the brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
    [Crossref]
  18. L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
    [Crossref]
  19. J. B. Götte and M. R. Dennis, “Limits to superweak amplification of beam shifts,” Opt. Lett. 38(13), 2295–2297 (2013).
    [Crossref]
  20. X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
    [Crossref]
  21. Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam-berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26(18), 1424–1426 (2001).
    [Crossref]
  22. L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
    [Crossref]
  23. E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014).
    [Crossref]
  24. N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
    [Crossref]
  25. N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
    [Crossref]
  26. G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
    [Crossref]
  27. X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
    [Crossref]
  28. A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
    [Crossref]
  29. J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011).
    [Crossref]
  30. L.-J. Kong, S.-X. Qian, Z.-C. Ren, X.-L. Wang, and H.-T. Wang, “Effects of orbital angular momentum on the geometric spin hall effect of light,” Phys. Rev. A 85(3), 035804 (2012).
    [Crossref]
  31. M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
    [Crossref]
  32. M. Neugebauer, S. Grosche, S. Rothau, G. Leuchs, and P. Banzer, “Lateral spin transport in paraxial beams of light,” Opt. Lett. 41(15), 3499–3502 (2016).
    [Crossref]
  33. X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
    [Crossref]
  34. X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
    [Crossref]
  35. X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
    [Crossref]
  36. X. Zhou, L. Sheng, and X. Ling, “Photonic spin hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
    [Crossref]
  37. G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019).
    [Crossref]
  38. T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
    [Crossref]
  39. J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
    [Crossref]
  40. Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4(1), 1527 (2013).
    [Crossref]
  41. Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103(14), 141101 (2013).
    [Crossref]
  42. P. L. Truong, X. Ma, and S. J. Sim, “Resonant rayleigh light scattering of single au nanoparticles with different sizes and shapes,” Nanoscale 6(4), 2307–2315 (2014).
    [Crossref]
  43. M. Neugebauer, S. Nechayev, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement enhanced spin hall effect of light for particle displacement sensing,” Nano Lett. 19(1), 422–425 (2019).
    [Crossref]
  44. J. D. Jackson, Classical Electrodynamics (Wiley, 2001).
  45. J. E. Sipe and J. V. Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974).
    [Crossref]
  46. P. A. Belov, S. I. Maslovski, K. R. Simovski, and S. A. Tretyakov, “A condition imposed on the electromagnetic polarizability of a bianisotropic lossless scatterer,” Tech. Phys. Lett. 29(9), 718–720 (2003).
    [Crossref]
  47. D. V. Zhirihin, S. V. Li, D. Y. Sokolov, A. P. Slobozhanyuk, M. A. Gorlach, and A. B. Khanikaev, “Photonic spin hall effect mediated by bianisotropy,” Opt. Lett. 44(7), 1694–1697 (2019).
    [Crossref]
  48. S. Yushanov, J. S. Crompton, and K. C. Koppenhoefer, “Mie scattering of electromagnetic waves,” https://cn.comsol.com/paper/download/181101/crompton_paper.pdf .
  49. A. Banerjee, J. Soni, N. Ghosh, S. D. Gupta, and S. Mansha, “Giant Goos–Hänchen shift in scattering: the role of interfering localized plasmon modes,” Opt. Lett. 39(14), 4100–4103 (2014).
    [Crossref]
  50. D. Gao, R. Shi, A. E. Miroshnichenko, and L. Gao, “Enhanced spin hall effect of light in spheres with dual symmetry,” Laser Photonics Rev. 12(11), 1800130 (2018).
    [Crossref]
  51. R. Shi, D. L. Gao, H. Hu, Y. Q. Wang, and L. Gao, “Enhanced broadband spin hall effects by core-shell nanoparticles,” Opt. Express 27(4), 4808–4817 (2019).
    [Crossref]

2019 (6)

G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019).
[Crossref]

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

M. Neugebauer, S. Nechayev, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement enhanced spin hall effect of light for particle displacement sensing,” Nano Lett. 19(1), 422–425 (2019).
[Crossref]

D. V. Zhirihin, S. V. Li, D. Y. Sokolov, A. P. Slobozhanyuk, M. A. Gorlach, and A. B. Khanikaev, “Photonic spin hall effect mediated by bianisotropy,” Opt. Lett. 44(7), 1694–1697 (2019).
[Crossref]

R. Shi, D. L. Gao, H. Hu, Y. Q. Wang, and L. Gao, “Enhanced broadband spin hall effects by core-shell nanoparticles,” Opt. Express 27(4), 4808–4817 (2019).
[Crossref]

2018 (2)

D. Gao, R. Shi, A. E. Miroshnichenko, and L. Gao, “Enhanced spin hall effect of light in spheres with dual symmetry,” Laser Photonics Rev. 12(11), 1800130 (2018).
[Crossref]

X. Zhou, L. Sheng, and X. Ling, “Photonic spin hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref]

2017 (1)

X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

2016 (1)

2015 (1)

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

2014 (6)

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014).
[Crossref]

D. O’Connor, P. Ginzburg, F. J. Rodríguezfortuño, G. A. Wurtz, and A. V. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5(1), 5327 (2014).
[Crossref]

J. Korger, A. Aiello, V. Chille, P. Banzer, and G. Leuchs, “Observation of the geometric spin hall effect of light,” Phys. Rev. Lett. 112(11), 113902 (2014).
[Crossref]

P. L. Truong, X. Ma, and S. J. Sim, “Resonant rayleigh light scattering of single au nanoparticles with different sizes and shapes,” Nanoscale 6(4), 2307–2315 (2014).
[Crossref]

A. Banerjee, J. Soni, N. Ghosh, S. D. Gupta, and S. Mansha, “Giant Goos–Hänchen shift in scattering: the role of interfering localized plasmon modes,” Opt. Lett. 39(14), 4100–4103 (2014).
[Crossref]

2013 (6)

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4(1), 1527 (2013).
[Crossref]

Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103(14), 141101 (2013).
[Crossref]

K. Y. Bliokh and A. Aiello, “Goos-hänchen and imbert-fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref]

J. B. Götte and M. R. Dennis, “Limits to superweak amplification of beam shifts,” Opt. Lett. 38(13), 2295–2297 (2013).
[Crossref]

2012 (5)

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
[Crossref]

L.-J. Kong, S.-X. Qian, Z.-C. Ren, X.-L. Wang, and H.-T. Wang, “Effects of orbital angular momentum on the geometric spin hall effect of light,” Phys. Rev. A 85(3), 035804 (2012).
[Crossref]

2011 (4)

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011).
[Crossref]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin hall effect of light near the brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
[Crossref]

2010 (2)

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
[Crossref]

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref]

2009 (2)

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref]

2008 (5)

K. Y. Bliokh, G. Yuri, K. Vladimir, and H. Erez, “Coriolis effect in optics: unified geometric phase and spin-hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref]

F. Nori, “Geometrical optics: the dynamics of spinning light,” Nat. Photonics 2(12), 717–718 (2008).
[Crossref]

A. Aiello and J. P. Woerdman, “Role of beam propagation in goos-hanchen and imbert-fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[Crossref]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

H. Onur and K. Paul, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

2007 (1)

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

2006 (2)

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

2004 (1)

M. Onoda, S. Murakami, and A. N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

2003 (1)

P. A. Belov, S. I. Maslovski, K. R. Simovski, and S. A. Tretyakov, “A condition imposed on the electromagnetic polarizability of a bianisotropic lossless scatterer,” Tech. Phys. Lett. 29(9), 718–720 (2003).
[Crossref]

2002 (1)

2001 (1)

1974 (1)

J. E. Sipe and J. V. Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974).
[Crossref]

Aiello, A.

J. Korger, A. Aiello, V. Chille, P. Banzer, and G. Leuchs, “Observation of the geometric spin hall effect of light,” Phys. Rev. Lett. 112(11), 113902 (2014).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

K. Y. Bliokh and A. Aiello, “Goos-hänchen and imbert-fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011).
[Crossref]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref]

A. Aiello and J. P. Woerdman, “Role of beam propagation in goos-hanchen and imbert-fedorov shifts,” Opt. Lett. 33(13), 1437–1439 (2008).
[Crossref]

Alonso, M. A.

K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
[Crossref]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
[Crossref]

Araneda, G.

G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019).
[Crossref]

Banerjee, A.

Banzer, P.

M. Neugebauer, S. Nechayev, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement enhanced spin hall effect of light for particle displacement sensing,” Nano Lett. 19(1), 422–425 (2019).
[Crossref]

M. Neugebauer, S. Grosche, S. Rothau, G. Leuchs, and P. Banzer, “Lateral spin transport in paraxial beams of light,” Opt. Lett. 41(15), 3499–3502 (2016).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

J. Korger, A. Aiello, V. Chille, P. Banzer, and G. Leuchs, “Observation of the geometric spin hall effect of light,” Phys. Rev. Lett. 112(11), 113902 (2014).
[Crossref]

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011).
[Crossref]

Bauer, T.

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

Belov, P. A.

P. A. Belov, S. I. Maslovski, K. R. Simovski, and S. A. Tretyakov, “A condition imposed on the electromagnetic polarizability of a bianisotropic lossless scatterer,” Tech. Phys. Lett. 29(9), 718–720 (2003).
[Crossref]

Biener, G.

Blatt, R.

G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019).
[Crossref]

Bliokh, K. Y.

K. Y. Bliokh and A. Aiello, “Goos-hänchen and imbert-fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
[Crossref]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
[Crossref]

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

K. Y. Bliokh, G. Yuri, K. Vladimir, and H. Erez, “Coriolis effect in optics: unified geometric phase and spin-hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

Bliokh, Y. P.

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

Bomzon, Z.

Boyd, R. W.

E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014).
[Crossref]

Brasselet, E.

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[Crossref]

Bretner, I.

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

Cheah, K. W.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref]

Chen, C.-F.

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

Chen, J.

L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Chen, S.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref]

Chille, V.

J. Korger, A. Aiello, V. Chille, P. Banzer, and G. Leuchs, “Observation of the geometric spin hall effect of light,” Phys. Rev. Lett. 112(11), 113902 (2014).
[Crossref]

Colombe, Y.

G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019).
[Crossref]

Crompton, J. S.

S. Yushanov, J. S. Crompton, and K. C. Koppenhoefer, “Mie scattering of electromagnetic waves,” https://cn.comsol.com/paper/download/181101/crompton_paper.pdf .

Dainty, C.

K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
[Crossref]

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref]

Dennis, M. R.

Erez, H.

K. Y. Bliokh, G. Yuri, K. Vladimir, and H. Erez, “Coriolis effect in optics: unified geometric phase and spin-hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref]

Fan, D.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin hall effect of light near the brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
[Crossref]

Fu, Y. H.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4(1), 1527 (2013).
[Crossref]

Gabriel, C.

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011).
[Crossref]

Gao, D.

D. Gao, R. Shi, A. E. Miroshnichenko, and L. Gao, “Enhanced spin hall effect of light in spheres with dual symmetry,” Laser Photonics Rev. 12(11), 1800130 (2018).
[Crossref]

Gao, D. L.

Gao, L.

R. Shi, D. L. Gao, H. Hu, Y. Q. Wang, and L. Gao, “Enhanced broadband spin hall effects by core-shell nanoparticles,” Opt. Express 27(4), 4808–4817 (2019).
[Crossref]

D. Gao, R. Shi, A. E. Miroshnichenko, and L. Gao, “Enhanced spin hall effect of light in spheres with dual symmetry,” Laser Photonics Rev. 12(11), 1800130 (2018).
[Crossref]

Ghosh, N.

Ginzburg, P.

D. O’Connor, P. Ginzburg, F. J. Rodríguezfortuño, G. A. Wurtz, and A. V. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5(1), 5327 (2014).
[Crossref]

Gong, Q.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

Gorlach, M. A.

Gorodetski, Y.

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

Götte, J. B.

Grosche, S.

Gu, B.

L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Gupta, S. D.

Hasman, E.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant pancharatnam-berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
[Crossref]

Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam-berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26(18), 1424–1426 (2001).
[Crossref]

Higginbottom, D. B.

G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019).
[Crossref]

Hu, H.

Huang, J.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

Huang, K.

X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 2001).

Juodkazis, S.

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[Crossref]

Kang, M.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref]

Karimi, E.

E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014).
[Crossref]

Khanikaev, A. B.

Kleiner, V.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Space-variant pancharatnam-berry phase optical elements with computer-generated subwavelength gratings,” Opt. Lett. 27(13), 1141–1143 (2002).
[Crossref]

Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam-berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26(18), 1424–1426 (2001).
[Crossref]

Kolb, T.

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011).
[Crossref]

Kong, L.-J.

L.-J. Kong, S.-X. Qian, Z.-C. Ren, X.-L. Wang, and H.-T. Wang, “Effects of orbital angular momentum on the geometric spin hall effect of light,” Phys. Rev. A 85(3), 035804 (2012).
[Crossref]

L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Koppenhoefer, K. C.

S. Yushanov, J. S. Crompton, and K. C. Koppenhoefer, “Mie scattering of electromagnetic waves,” https://cn.comsol.com/paper/download/181101/crompton_paper.pdf .

Korger, J.

J. Korger, A. Aiello, V. Chille, P. Banzer, and G. Leuchs, “Observation of the geometric spin hall effect of light,” Phys. Rev. Lett. 112(11), 113902 (2014).
[Crossref]

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011).
[Crossref]

Kranendonk, J. V.

J. E. Sipe and J. V. Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974).
[Crossref]

Kuznetsov, A. I.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4(1), 1527 (2013).
[Crossref]

Lara, D.

K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
[Crossref]

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref]

Leon, I. D.

E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014).
[Crossref]

Leuchs, G.

M. Neugebauer, S. Nechayev, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement enhanced spin hall effect of light for particle displacement sensing,” Nano Lett. 19(1), 422–425 (2019).
[Crossref]

M. Neugebauer, S. Grosche, S. Rothau, G. Leuchs, and P. Banzer, “Lateral spin transport in paraxial beams of light,” Opt. Lett. 41(15), 3499–3502 (2016).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

J. Korger, A. Aiello, V. Chille, P. Banzer, and G. Leuchs, “Observation of the geometric spin hall effect of light,” Phys. Rev. Lett. 112(11), 113902 (2014).
[Crossref]

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref]

Li, G.

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref]

Li, J.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref]

Li, S. V.

Li, S.-M.

L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Li, Y.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Lindlein, N.

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref]

Ling, X.

X. Zhou, L. Sheng, and X. Ling, “Photonic spin hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

Ling, X.-H.

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

Liu, Y.

X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103(14), 141101 (2013).
[Crossref]

Liu, Z.

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

Lou, Y.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

Luk’yanchuk, B.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4(1), 1527 (2013).
[Crossref]

Luo, H.

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
[Crossref]

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin hall effect of light near the brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
[Crossref]

Luo, H.-L.

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

Ma, X.

P. L. Truong, X. Ma, and S. J. Sim, “Resonant rayleigh light scattering of single au nanoparticles with different sizes and shapes,” Nanoscale 6(4), 2307–2315 (2014).
[Crossref]

Maguid, E.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

Mansha, S.

Manzo, C.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

Marquardt, C.

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref]

Marrucci, L.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

Maslovski, S. I.

P. A. Belov, S. I. Maslovski, K. R. Simovski, and S. A. Tretyakov, “A condition imposed on the electromagnetic polarizability of a bianisotropic lossless scatterer,” Tech. Phys. Lett. 29(9), 718–720 (2003).
[Crossref]

Miroshnichenko, A. E.

D. Gao, R. Shi, A. E. Miroshnichenko, and L. Gao, “Enhanced spin hall effect of light in spheres with dual symmetry,” Laser Photonics Rev. 12(11), 1800130 (2018).
[Crossref]

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4(1), 1527 (2013).
[Crossref]

Misawa, H.

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[Crossref]

Murakami, S.

M. Onoda, S. Murakami, and A. N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

Murazawa, N.

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[Crossref]

Nagaosa, A. N.

M. Onoda, S. Murakami, and A. N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

Nechayev, S.

M. Neugebauer, S. Nechayev, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement enhanced spin hall effect of light for particle displacement sensing,” Nano Lett. 19(1), 422–425 (2019).
[Crossref]

Neugebauer, M.

M. Neugebauer, S. Nechayev, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement enhanced spin hall effect of light for particle displacement sensing,” Nano Lett. 19(1), 422–425 (2019).
[Crossref]

M. Neugebauer, S. Grosche, S. Rothau, G. Leuchs, and P. Banzer, “Lateral spin transport in paraxial beams of light,” Opt. Lett. 41(15), 3499–3502 (2016).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

Niv, A.

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

Nori, F.

F. Nori, “Geometrical optics: the dynamics of spinning light,” Nat. Photonics 2(12), 717–718 (2008).
[Crossref]

O’Connor, D.

D. O’Connor, P. Ginzburg, F. J. Rodríguezfortuño, G. A. Wurtz, and A. V. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5(1), 5327 (2014).
[Crossref]

Onoda, M.

M. Onoda, S. Murakami, and A. N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

Onur, H.

H. Onur and K. Paul, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

Orlov, S.

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

Ostrovskaya, E. A.

K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
[Crossref]

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
[Crossref]

Ozeri, D.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

Paparo, D.

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

Paul, K.

H. Onur and K. Paul, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

Pun, E. Y.-B.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref]

Qassim, H.

E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014).
[Crossref]

Qian, H.

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

Qian, S.-X.

L.-J. Kong, S.-X. Qian, Z.-C. Ren, X.-L. Wang, and H.-T. Wang, “Effects of orbital angular momentum on the geometric spin hall effect of light,” Phys. Rev. A 85(3), 035804 (2012).
[Crossref]

Qiu, C. W.

X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

Qiu, M.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

Rauschenbeute, A.

G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019).
[Crossref]

Ren, Z.-C.

L.-J. Kong, S.-X. Qian, Z.-C. Ren, X.-L. Wang, and H.-T. Wang, “Effects of orbital angular momentum on the geometric spin hall effect of light,” Phys. Rev. A 85(3), 035804 (2012).
[Crossref]

Rodríguezfortuño, F. J.

D. O’Connor, P. Ginzburg, F. J. Rodríguezfortuño, G. A. Wurtz, and A. V. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5(1), 5327 (2014).
[Crossref]

Rodríguez-Herrera, O. G.

K. Y. Bliokh, E. A. Ostrovskaya, M. A. Alonso, O. G. Rodríguez-Herrera, D. Lara, and C. Dainty, “Spin-to-orbital angular momentum conversion in focusing, scattering, and imaging systems,” Opt. Express 19(27), 26132–26149 (2011).
[Crossref]

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref]

Rothau, S.

Ruan, Z.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

Schulz, S. A.

E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014).
[Crossref]

Sheng, L.

X. Zhou, L. Sheng, and X. Ling, “Photonic spin hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref]

Shi, R.

R. Shi, D. L. Gao, H. Hu, Y. Q. Wang, and L. Gao, “Enhanced broadband spin hall effects by core-shell nanoparticles,” Opt. Express 27(4), 4808–4817 (2019).
[Crossref]

D. Gao, R. Shi, A. E. Miroshnichenko, and L. Gao, “Enhanced spin hall effect of light in spheres with dual symmetry,” Laser Photonics Rev. 12(11), 1800130 (2018).
[Crossref]

Shitrit, N.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

Shu, W.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin hall effect of light near the brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
[Crossref]

Sim, S. J.

P. L. Truong, X. Ma, and S. J. Sim, “Resonant rayleigh light scattering of single au nanoparticles with different sizes and shapes,” Nanoscale 6(4), 2307–2315 (2014).
[Crossref]

Simovski, K. R.

P. A. Belov, S. I. Maslovski, K. R. Simovski, and S. A. Tretyakov, “A condition imposed on the electromagnetic polarizability of a bianisotropic lossless scatterer,” Tech. Phys. Lett. 29(9), 718–720 (2003).
[Crossref]

Sipe, J. E.

J. E. Sipe and J. V. Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974).
[Crossref]

Slobozhanyuk, A. P.

Sokolov, D. Y.

Soni, J.

Tang, M.

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

Tretyakov, S. A.

P. A. Belov, S. I. Maslovski, K. R. Simovski, and S. A. Tretyakov, “A condition imposed on the electromagnetic polarizability of a bianisotropic lossless scatterer,” Tech. Phys. Lett. 29(9), 718–720 (2003).
[Crossref]

Truong, P. L.

P. L. Truong, X. Ma, and S. J. Sim, “Resonant rayleigh light scattering of single au nanoparticles with different sizes and shapes,” Nanoscale 6(4), 2307–2315 (2014).
[Crossref]

Upham, J.

E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014).
[Crossref]

Veksler, D.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

Vladimir, K.

K. Y. Bliokh, G. Yuri, K. Vladimir, and H. Erez, “Coriolis effect in optics: unified geometric phase and spin-hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref]

Volz, J.

G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019).
[Crossref]

Vorndran, M.

M. Neugebauer, S. Nechayev, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement enhanced spin hall effect of light for particle displacement sensing,” Nano Lett. 19(1), 422–425 (2019).
[Crossref]

Walser, S.

G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019).
[Crossref]

Wang, H.-T.

L.-J. Kong, S.-X. Qian, Z.-C. Ren, X.-L. Wang, and H.-T. Wang, “Effects of orbital angular momentum on the geometric spin hall effect of light,” Phys. Rev. A 85(3), 035804 (2012).
[Crossref]

L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Wang, X.-L.

L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

L.-J. Kong, S.-X. Qian, Z.-C. Ren, X.-L. Wang, and H.-T. Wang, “Effects of orbital angular momentum on the geometric spin hall effect of light,” Phys. Rev. A 85(3), 035804 (2012).
[Crossref]

Wang, Y. Q.

Wen, S.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
[Crossref]

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin hall effect of light near the brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
[Crossref]

Wen, S.-C.

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

Woerdman, J. P.

Wu, Q.

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

Wurtz, G. A.

D. O’Connor, P. Ginzburg, F. J. Rodríguezfortuño, G. A. Wurtz, and A. V. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5(1), 5327 (2014).
[Crossref]

Xiao, Z.

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
[Crossref]

Yi, X.

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

Yu, Y. F.

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4(1), 1527 (2013).
[Crossref]

Yulevich, I.

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

Yuri, G.

K. Y. Bliokh, G. Yuri, K. Vladimir, and H. Erez, “Coriolis effect in optics: unified geometric phase and spin-hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref]

Yushanov, S.

S. Yushanov, J. S. Crompton, and K. C. Koppenhoefer, “Mie scattering of electromagnetic waves,” https://cn.comsol.com/paper/download/181101/crompton_paper.pdf .

Zayats, A. V.

D. O’Connor, P. Ginzburg, F. J. Rodríguezfortuño, G. A. Wurtz, and A. V. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5(1), 5327 (2014).
[Crossref]

Zhang, J.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

Zhang, S.

G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref]

Zhang, X.

Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103(14), 141101 (2013).
[Crossref]

Zhao, J.

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

Zhirihin, D. V.

Zhou, J.

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

Zhou, X.

X. Zhou, L. Sheng, and X. Ling, “Photonic spin hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin hall effect of light near the brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
[Crossref]

Zhou, Y.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

Zhu, S.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

Zhu, T.

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

Appl. Phys. B: Lasers Opt. (1)

J. Korger, A. Aiello, C. Gabriel, P. Banzer, T. Kolb, C. Marquardt, and G. Leuchs, “Geometric spin hall effect of light at polarizing interfaces,” Appl. Phys. B: Lasers Opt. 102(3), 427–432 (2011).
[Crossref]

Appl. Phys. Lett. (3)

X. Zhou, X. Ling, H. Luo, and S. Wen, “Identifying graphene layers via spin hall effect of light,” Appl. Phys. Lett. 101(25), 251602 (2012).
[Crossref]

L.-J. Kong, X.-L. Wang, S.-M. Li, Y. Li, J. Chen, B. Gu, and H.-T. Wang, “Spin hall effect of reflected light from an air-glass interface around the brewster’s angle,” Appl. Phys. Lett. 100(7), 071109 (2012).
[Crossref]

Y. Liu and X. Zhang, “Metasurfaces for manipulating surface plasmons,” Appl. Phys. Lett. 103(14), 141101 (2013).
[Crossref]

Chin. Phys. Lett. (1)

X.-H. Ling, H.-L. Luo, M. Tang, and S.-C. Wen, “Enhanced and tunable spin hall effect of light upon reflection of one-dimensional photonic crystal with a defect layer,” Chin. Phys. Lett. 29(7), 074209 (2012).
[Crossref]

J. Opt. (1)

K. Y. Bliokh and A. Aiello, “Goos-hänchen and imbert-fedorov beam shifts: an overview,” J. Opt. 15(1), 014001 (2013).
[Crossref]

Laser Photonics Rev. (1)

D. Gao, R. Shi, A. E. Miroshnichenko, and L. Gao, “Enhanced spin hall effect of light in spheres with dual symmetry,” Laser Photonics Rev. 12(11), 1800130 (2018).
[Crossref]

Light: Sci. Appl. (2)

E. Karimi, S. A. Schulz, I. D. Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light: Sci. Appl. 3(5), e167 (2014).
[Crossref]

X. Ling, X. Zhou, X. Yi, W. Shu, Y. Liu, S. Chen, H. Luo, S. Wen, and D. Fan, “Giant photonic spin hall effect in momentum space in a structured metamaterial with spatially varying birefringence,” Light: Sci. Appl. 4(5), e290 (2015).
[Crossref]

Nano Lett. (3)

N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin hall effects in plasmonic chains,” Nano Lett. 11(5), 2038–2042 (2011).
[Crossref]

G. Li, M. Kang, S. Chen, S. Zhang, E. Y.-B. Pun, K. W. Cheah, and J. Li, “Spin-enabled plasmonic metasurfaces for manipulating orbital angular momentum of light,” Nano Lett. 13(9), 4148–4151 (2013).
[Crossref]

M. Neugebauer, S. Nechayev, M. Vorndran, G. Leuchs, and P. Banzer, “Weak measurement enhanced spin hall effect of light for particle displacement sensing,” Nano Lett. 19(1), 422–425 (2019).
[Crossref]

Nanoscale (1)

P. L. Truong, X. Ma, and S. J. Sim, “Resonant rayleigh light scattering of single au nanoparticles with different sizes and shapes,” Nanoscale 6(4), 2307–2315 (2014).
[Crossref]

Nat. Commun. (2)

Y. H. Fu, A. I. Kuznetsov, A. E. Miroshnichenko, Y. F. Yu, and B. Luk’yanchuk, “Directional visible light scattering by silicon nanoparticles,” Nat. Commun. 4(1), 1527 (2013).
[Crossref]

D. O’Connor, P. Ginzburg, F. J. Rodríguezfortuño, G. A. Wurtz, and A. V. Zayats, “Spin-orbit coupling in surface plasmon scattering by nanostructures,” Nat. Commun. 5(1), 5327 (2014).
[Crossref]

Nat. Photonics (2)

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2(12), 748–753 (2008).
[Crossref]

F. Nori, “Geometrical optics: the dynamics of spinning light,” Nat. Photonics 2(12), 717–718 (2008).
[Crossref]

Nat. Phys. (1)

G. Araneda, S. Walser, Y. Colombe, D. B. Higginbottom, J. Volz, R. Blatt, and A. Rauschenbeute, “Wavelength-scale errors in optical localization due to spin-orbit coupling of light,” Nat. Phys. 15(1), 17–21 (2019).
[Crossref]

Opt. Express (2)

Opt. Lett. (7)

Phys. Rev. A (6)

L.-J. Kong, S.-X. Qian, Z.-C. Ren, X.-L. Wang, and H.-T. Wang, “Effects of orbital angular momentum on the geometric spin hall effect of light,” Phys. Rev. A 85(3), 035804 (2012).
[Crossref]

M. Neugebauer, P. Banzer, T. Bauer, S. Orlov, N. Lindlein, A. Aiello, and G. Leuchs, “Geometric spin hall effect of light in tightly focused polarization-tailored light beams,” Phys. Rev. A 89(1), 013840 (2014).
[Crossref]

X. Zhou, Z. Xiao, H. Luo, and S. Wen, “Experimental observation of the spin hall effect of light on a nanometal film via weak measurements,” Phys. Rev. A 85(4), 043809 (2012).
[Crossref]

K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momenta and spin-orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82(6), 063825 (2010).
[Crossref]

H. Luo, X. Zhou, W. Shu, S. Wen, and D. Fan, “Enhanced and switchable spin hall effect of light near the brewster angle on reflection,” Phys. Rev. A 84(4), 043806 (2011).
[Crossref]

J. E. Sipe and J. V. Kranendonk, “Macroscopic electromagnetic theory of resonant dielectrics,” Phys. Rev. A 9(5), 1806–1822 (1974).
[Crossref]

Phys. Rev. Appl. (1)

T. Zhu, Y. Lou, Y. Zhou, J. Zhang, J. Huang, Y. Li, H. Luo, S. Wen, S. Zhu, Q. Gong, M. Qiu, and Z. Ruan, “Generalized spatial differentiation from the spin hall effect of light and its application in image processing of edge detection,” Phys. Rev. Appl. 11(3), 034043 (2019).
[Crossref]

Phys. Rev. E (1)

K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75(6), 066609 (2007).
[Crossref]

Phys. Rev. Lett. (8)

K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96(7), 073903 (2006).
[Crossref]

O. G. Rodríguez-Herrera, D. Lara, K. Y. Bliokh, E. A. Ostrovskaya, and C. Dainty, “Optical nanoprobing via spin-orbit interaction of light,” Phys. Rev. Lett. 104(25), 253601 (2010).
[Crossref]

E. Brasselet, N. Murazawa, H. Misawa, and S. Juodkazis, “Optical vortices from liquid crystal droplets,” Phys. Rev. Lett. 103(10), 103903 (2009).
[Crossref]

K. Y. Bliokh, G. Yuri, K. Vladimir, and H. Erez, “Coriolis effect in optics: unified geometric phase and spin-hall effect,” Phys. Rev. Lett. 101(3), 030404 (2008).
[Crossref]

J. Korger, A. Aiello, V. Chille, P. Banzer, and G. Leuchs, “Observation of the geometric spin hall effect of light,” Phys. Rev. Lett. 112(11), 113902 (2014).
[Crossref]

M. Onoda, S. Murakami, and A. N. Nagaosa, “Hall effect of light,” Phys. Rev. Lett. 93(8), 083901 (2004).
[Crossref]

L. Marrucci, C. Manzo, and D. Paparo, “Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media,” Phys. Rev. Lett. 96(16), 163905 (2006).
[Crossref]

A. Aiello, N. Lindlein, C. Marquardt, and G. Leuchs, “Transverse angular momentum and geometric spin hall effect of light,” Phys. Rev. Lett. 103(10), 100401 (2009).
[Crossref]

Proc. Natl. Acad. Sci. U. S. A. (1)

J. Zhou, H. Qian, C.-F. Chen, J. Zhao, G. Li, Q. Wu, H. Luo, S. Wen, and Z. Liu, “Optical edge detection based on high-efficiency dielectric metasurface,” Proc. Natl. Acad. Sci. U. S. A. 116(23), 11137–11140 (2019).
[Crossref]

Rep. Prog. Phys. (1)

X. Ling, X. Zhou, K. Huang, Y. Liu, C. W. Qiu, H. Luo, and S. Wen, “Recent advances in the spin hall effect of light,” Rep. Prog. Phys. 80(6), 066401 (2017).
[Crossref]

Sci. Rep. (1)

X. Zhou, L. Sheng, and X. Ling, “Photonic spin hall effect enabled refractive index sensor using weak measurements,” Sci. Rep. 8(1), 1221 (2018).
[Crossref]

Science (2)

N. Shitrit, I. Yulevich, E. Maguid, D. Ozeri, D. Veksler, V. Kleiner, and E. Hasman, “Spin-optical metamaterial route to spin-controlled photonics,” Science 340(6133), 724–726 (2013).
[Crossref]

H. Onur and K. Paul, “Observation of the spin hall effect of light via weak measurements,” Science 319(5864), 787–790 (2008).
[Crossref]

Tech. Phys. Lett. (1)

P. A. Belov, S. I. Maslovski, K. R. Simovski, and S. A. Tretyakov, “A condition imposed on the electromagnetic polarizability of a bianisotropic lossless scatterer,” Tech. Phys. Lett. 29(9), 718–720 (2003).
[Crossref]

Other (2)

J. D. Jackson, Classical Electrodynamics (Wiley, 2001).

S. Yushanov, J. S. Crompton, and K. C. Koppenhoefer, “Mie scattering of electromagnetic waves,” https://cn.comsol.com/paper/download/181101/crompton_paper.pdf .

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Figures (5)

Fig. 1.
Fig. 1. The three-dimensional schematic of the system and polarization dependence of light scattering. (a) The blue and red rotatory arrows represent the incident left and right circularly polarized lights, respectively. The incident directions are all in the $y$-$z$ plane. $\beta$ is the angle between the incident light and the $z$-axis. The blue and red lines represent the scattering directions of left and right circularly polarized lights, respectively. (b) The far-field scattering diagram of a metallic (Au) ellipsoidal Rayleigh particle in ${Oxy}$ plane simulated in COMSOL Multiphysics software for different incident polarized lights. The radii of the particle in the $x$, $y$ and $z$ directions are 10 nm, 3 nm and 30 nm, respectively. The wavelength of the incident light is 650 nm and the incident angle $\beta$ is $45^\circ$. $\sigma \equiv 0$, +1, and -1 indicate the linear, right-circular and left-circular polarizations, respectively.
Fig. 2.
Fig. 2. The simulated cosine values of azimuthal angles and elevation angles for the centroids of scattering far-field. The material of the ellipsoidal Rayleigh particle is metallic (Au). The wavelength of the incident light is 650 nm. The incident angle is $45^\circ$. (a) and (b) The changes in the cosine values of azimuthal angles and elevation angles for the centroids of scattering far-field with the radius of the particle in $y$ direction ($a_y$) through simulation. The radii of the particle in the $x$ and $z$ directions are 10 nm and 30 nm, respectively. (c) and (d) The changes in the cosine values of azimuthal angles and elevation angles for the centroids of scattering far-field with the radius of the particle in $x$ direction ($a_x$) through simulation. The radii of the particle in the $y$ and $z$ directions are 10 nm and 30 nm, respectively.
Fig. 3.
Fig. 3. The dependences of the cosine values of azimuthal angles for the centroids of scattering far-field on the incident angle. The radii of the particle in the $x$, $y$ and $z$ directions are 10 nm, 20 nm and 30 nm, respectively.
Fig. 4.
Fig. 4. The simulated optical forces exerted on the metallic (Au) ellipsoidal Rayleigh particle. The wavelength of the incident light is 650 nm. (a) - (c) The changes in the $x$, $y$ and $z$ components of optical forces with the radius of the particle in $y$ direction ($a_y$). The radii of the particle in the $x$ and $z$ directions are 10 nm and 30 nm, respectively. The incident angle is $45^\circ$. (d) - (f) The changes in the $x$, $y$ and $z$ components of optical forces with the incident angle. The radii of the particle in the $x$, $y$ and $z$ directions are 10 nm, 20 nm and 30 nm, respectively.
Fig. 5.
Fig. 5. The simulated optical torques exerted on the metallic (Au) ellipsoidal Rayleigh particle. The wavelength of the incident light is 650 nm. (a) - (c) The changes in the $x$, $y$ and $z$ components of optical torques with the radius of the particle in $y$ direction ($a_y$). The radii of the particle in the $x$ and $z$ directions are 10 nm and 30 nm, respectively. The incident angle is $45^\circ$. (d) - (f) The changes in the $x$, $y$ and $z$ components of optical torques with the incident angle. The radii of the particle in the $x$, $y$ and $z$ directions are 10 nm, 20 nm and 30 nm, respectively.

Equations (21)

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E inc = E 0 ( σ i x ^ + cos β y ^ + sin β z ^ ) exp [ i k 0 ( sin β y + cos β z ) ] ,
H inc = H 0 ( x ^ + σ i cos β y ^ + σ i sin β z ^ ) exp [ i k 0 ( sin β y + cos β z ) ] ,
E sc = k 0 2 4 π ϵ 0 e i k 0 r r [ ( n ^ × p ) × n ^ 1 c n ^ × m ] ,
H sc = 1 η 0 ( n ^ × E sc ) ,
p = α ¯ ee E inc ,
m = α ¯ mm H inc ,
α ¯ ee = ( α ee1 x x + i α ee2 x x 0 0 0 α ee1 y y + i α ee2 y y 0 0 0 α ee1 z z + i α ee2 z z ) ,
α ¯ mm = ( α mm1 x x + i α mm2 x x 0 0 0 α mm1 y y + i α mm2 y y 0 0 0 α mm1 z z + i α mm2 z z ) .
S = 1 2 Re ( E sc × H sc ) .
cos φ = cos φ S r r 2 sin θ d θ d φ S r r 2 sin θ d θ d φ ,
cos θ = cos θ S r r 2 sin θ d θ d φ S r r 2 sin θ d θ d φ ,
cos φ σ sin 2 β η 0 W 3 η 0 2 W 1 + ( 1 / c 2 ) W 2 ,
cos θ cos β η 0 W 4 η 0 2 W 1 + ( 1 / c 2 ) W 2 ,
W 1 = ( α ee1 x x 2 + α ee2 x x 2 ) + ( α ee1 y y 2 + α ee2 y y 2 ) cos 2 β + ( α ee1 z z 2 + α ee2 z z 2 ) sin 2 β ,
W 2 = ( α mm1 x x 2 + α mm2 x x 2 ) + ( α mm1 y y 2 + α mm2 y y 2 ) cos 2 β + ( α mm1 z z 2 + α mm2 z z 2 ) sin 2 β ,
W 3 = ( α mm2 z z α ee1 y y α mm1 z z α ee2 y y ) ( α mm2 y y α ee1 z z α mm1 y y α ee2 z z ) ,
W 4 = ( α mm1 y y α ee1 x x + α mm2 y y α ee2 x x ) + ( α mm1 x x α ee1 y y + α mm2 x x α ee2 y y ) .
cos φ = σ sin 2 β C 1 C 2 + C 3 cos 2 β ,
F = S n ^ T ¯ d S ,
T ¯ = 1 2 Re [ ϵ E E + μ H H 1 2 ( ϵ E E + μ H H ) I ¯ ] ,
Γ = S n ^ ( T ¯ × r ) d S ,

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