1. Introduction

Photon spin provides an extra degree of freedom to control light, and enables potential applications in spin-based photonics [1]. How to manipulate spin photons is the key issue in spin-based applications, which is similar to those in the spintronics [2]. In general, spin filter is employed in the spintronics to address this issue [3]. Metasurfaces exhibit exceptional abilities for controlling spin states of photons [4, 5] and various spin-based photonics applications have been developed, such as ultrathin flat lenses [6–8], holograms [9,10], wave-front engineering [11,12], and spin photonic splitters [13, 14].

In this paper, we propose a photonic spin filter based on dielectric metasurfaces. In our scheme, the metasurface is designed by writing a space-variant nanograting in a glass substrate which results in a space-variant effective birefringence. By suitably designing the local orientation of the nanograting, the desired Pancharatnam-Berry (PB) phase lens can be achieved. The structure of the spin filter is similar to that of conventional spatial filter [15], but the two plano-convex lenses are replaced by the PB phase ones. The experimental results show that the photonic spin filter can effectively sort the desirable spin photons from input photons with mixed spin states.

2. Schematic diagram for photonic spin filter

Figure 1 shows the schematic diagram of the photonic spin filter. Similar to the conventional spatial filter, the photonic spin filter is constructed by replacing two plano-convex lenses with PB phase ones [Fig. 1(a)]. The first PB phase lens focuses photons with desired spin state. Diaphragm lets focused photons pass through and the second PB phase lens is used to recover the original spin state. The experimental setup of the photonic spin filter is shown in Fig. 1(b). A fundamental-mode Gauss beam is generated by the He-Ne laser, and then passes through a collimation system (Lens1 and Lens2). The half-wave plate (HWP) is used to control the intensity of light and to prevent the charge-coupled device (CCD) from saturation. The combination of the Glan laser polarizer (GLP) and the quarter-wave plate (QWP), is used to produce photons with mixed polarization (spin) states. By simply rotating the transmission axis of the GLP and the optical axis of the QWP, the mixed spin states are prepared. The photonic spin filter is composed of two confocal metasurface lens (MS1 and MS2) and a diaphragm. The intensity pattern is captured by the CCD.

In our scheme, the dielectric metasurface works as PB phase lens. It is convenient to use Jones calculus to describe the PB phase. By applying the optical rotation matrix R(θ) on the Jones matrix J, we can obtain a transmission matrix [16]

 

Fig. 1 Schematic diagram and experiment setup for the photonic spin filter. (a) Schematic illustration of the photonic spin filter composed of two Pancharatnam-Berry (PB) phase lenses and a diaphragm. The beam propagates along the z axis. The left PB phase lens focuses photons with desired spin state. Diaphragm lets focused photons pass through it and the right PB phase lens is used to recover the original spin state. (b) Experiment setup. The light source is a 21 mW linearly polarized He-Ne laser at 632.8 nm. A collimation system is composed of Lens1 and Lens2 (two lenses with effective focal length 25mm and 75mm, respectively). HWP, half-wave plate (for adjusting the light intensity); GLP, Glan laser polarizer; QWP, quarter-wave plate; MS1 and MS2, metasurfaces; D, diaphragm; CCD, charge-coupled device (for recording the distribution of light intensity). MS1 and MS2 work as PB phase lenses. The combination of the GLP and QWP is used to produce photons with mixed polarization (spin) states.

Download Full Size | PDF

Here, θ is the space-variant orientation of the local optical axis in the metasurface, and

We consider the input beam with circular polarization (spin), and its electric field described by a Jones vector

After the beam passing through the metasurface, the electric of output beam E_out(x,y) = T(x,y)E_in(x,y) can be written as

From Eq. (4) we find that the output photons reverse their spin states and acquire a space-variant phase which depends on the orientation of local optical axis. This space-variant phase is purely geometric in nature, and is the so-called PB phase Φ_PB = 2σθ. The direction of local optical axis can be designed to cover the range of 0 ≤ θ ≤ π, and therefore the phase shift covers the range of 0 ≤ Φ_PS ≤ 2σπ. By suitably engineering the geometry of optical axis θ, a PB phase lens can be achieved [17].

To focus an input plane wave to the focal point f, a hyperboloidal phase profile is needed to be constructed, as shown in Fig. 2(a). A phase shift Φ_PS should be introduced in the optical path between point A(x,y,0) on a plane wavefront and the focal point F(0,0, f), and is given by

 

Fig. 2 Schematic illustration of the design of the PB phase lens with metasurface. (a) A hyperboloidal equiphase surface should be constructed to focus a plane wavefront onto focal point. (b) The corresponding orientation of local optical axes in the metasurface. (c) and (d) plot the phase shift introduced by the metasurface illuminated by the plane wave with left-handed and right-handed circular polarizations, respectively. (e) The cross-polarized microscopic image of metasurface between two crossed linear polarizers. P_in and P_out denote the input and output polarization states of light. The short lines below the microscopic image indicate the local orientations of optical axes in the metasurface.

Download Full Size | PDF

where λ is the wavelength in free space. The above equation shows that the desired phase shift varies with the transverse distance $r\left(r=\sqrt{x^2+y^2}\right)$.

It has been demonstrated that the dielectric metasurface can create continuous PB phase covering from 0 to 2π [18]. Hence, the phase shift can be created by PB phase with dielectric metasurface, i.e. Φ_PB = Φ_PS. From Eqs. (4) and (5), the local orientation of optical axis in the metasurface for the spin state σ = +1 can be determined as

Equation (6) shows that the local optical axes change along radial direction which is also shown in Fig. 2(b). The phase shifts present opposite characteristics since the PB phases are spin-dependent [Fig. 2(c) and 2(d)]. It means that the one spin component is focused and the other is defocused. Similar method can be used to design the metasurface lens for focusing the other spin state of σ = −1. The local optical axes in the two cases possess opposite rotation directions respecting to radial direction.

The metasurfaces are fabricated by writing space-variant nanograting in a silica glass substrate using femtosecond laser [19, 20]. The retardation and the distribution of the slow axis can character the birefringent, which can be independently controlled during the fabrication process [20]. The glass substrate is mounted onto XYZ linear air-bearing translation stage system, and the stage is computer controlled. The fused glass (SiO₂) decomposes into porous glass (SiO_2(1−x) + xO₂) under the laser irradiation, whose refractive index is controlled by the laser intensity [19]. The phase retardation is ϕ = 2π(n_e − n_o)d/λ, where d is the writing depth and n_e − n_o the induced birefringence. The effective ordinary and extraordinary refractive indices can be written as [20]

Here, f is the filling factor, n₁ and n₂ are the refractive indices of the two media which form the nanograting structure. At the wavelength of 633 nm, the homogenous retardation of the prepared sample is π with a certain direct writing depth, the filling factor is 0.1–0.2 and the line width is 30–50 nm. The structured area with the diameter of 8 mm is centered on the glass substrate with the diameter of 25.4 mm (Altechna R&D). The azimuth of the slow optical axis is controlled by XY stage position and the laser beam polarization azimuth which is manipulated by an achromatic HWP [21].

The cross-polarized optical image of the sample is an effective method to character the structures of space-variant birefringence embedded in silica glass substrate. The cross-polarized microscopic image exhibits a series of concentric bright, which suggests the rotation angles for local optical axes change alone radial direction [see Fig. 2(e)]. Between two bright rings the local optical axis changes π/2, and thereby the central position of bright rings r_n can be calculated as

3. Experimental results of spin filter

We first measure the focusing characteristics for a single metasurface lens. Figures 3(a) and 3(b) show that the intensity of input beam is focused by the metasurface lens to a small spot at the focal plane. Here, the focal length of metasurface is 200 mm. Figures 3(c) and 3(d) plot the corresponding Stokes parameters. We find that the left-handed circular polarization of the input beam is converted into the right-handed circular one after it passes through the metasurface. When the input polarization is switched from left-handed polarization to right-handed one, the metasurface works as a diverging lens. This is due to the PB phases are spin-dependent.

 

Fig. 3 The distribution of intensity and Stokes parameter S₃ for the metasurface lens. Left column: input beam; Right column: output beam at the focal plane.

Download Full Size | PDF

To examine the efficiency of the photonic spin filter, the input beam with a mixed spin states is considered. The linear polarization can be viewed as a superposition of two oppositive spin states with equal magnitudes. The distributions of intensity and Stokes parameter of the input beam are plotted in Figs. 4(a) and 4(b), respectively. From Fig. 1(a) we can find an interesting feature: either spin state (σ = +1 or σ = −1) can be obtained by exchanging the places of the left PB phase lens and the right PB phase lens in the spin filter. It means that the two PB phase lenses (metasurfaces) can construct two types of filters: one only selects left-hand circularly polarized component to pass through it; the other selects the right-hand circularly polarized component. Hence, the left-hand polarized component (σ = +1) [Figs. 4(c) and 4(d)] or the right-hand polarized component (σ = −1) [Figs. 4(e) and 4(f)] can be obtained by modulating the structure of photonic spin filter.

 

Fig. 4 (a) and (b) show the intensity and Stokes parameter S₃ of the input beam with linear polarization, respectively. The desired spin state of output beam, such as left-handed component [(c) and (d)] or right-handed one [(e) and (f)], can be obtained by modulating the structure of the spin filter. S₃ = 0,1,−1 represent linear, left circular, and right circular polarization, respectively.

Download Full Size | PDF

We next consider an elliptical polarized light normally impinges onto the the photonic spin filter. The input beams can be viewed as a superposition of two circular polarization components with unequal magnitudes. When input beams with different elliptical polarization ranging from left-handed to right-handed polarizations, the quantity of the former gradually decreases while the latter increases. So the output intensity gradually decreases, due to only the phontons with left-handed circular polarization pass through the filter as shown in Figs. 5(a)–5(d). As a comparison, the photonic spin filter only allows the photons with right-handed circular polarization to pass through it as shown in Figs. 5(e)–5(h). The experimental results show that the photonic spin filter can select the desirable spin state photons from input photons with mixed spin states.

 

Fig. 5 The output intensity of photonic spin filter for the input beam with different ellipticity e. The white ellipses with arrows show the polarized states of incident beams. (a)–(d) The desirable spin state of photons is left-handed polarization. (e)–(h) The desirable spin state of photons is right-handed polarization. When input beams with different elliptical polarization ranging from left-handed to right-handed polarizations, the quantity of the former gradually decreases while the latter increases. So the output intensity gradually decreases, due to only the phontons with left-handed circular polarization pass through the filter (upper panels). As a comparison, when the photonic spin filter only selects the photons with right-handed circular polarization to pass through it, the output intensity gradually increases (lower panels).

Download Full Size | PDF

The principle of photonic spin filter is based on PB phase which originates from local changes in polarization and is not affected by the incident wavelength. Therefore, the proposed filter can work in the broadband. However, the conversion efficiency of prepared sample depends on incident wavelength, and the dispersion affects the performance of the spin filter. Achromatic metasurface reported by Aieta et al [22], may provide a route to realize achromatic PB phase lens. With further improvement in the performance of single metasurface lens, spatial filtering and spin filtering can be simultaneously realized by the photonic spin filter. In addition, PB phase lens based on liquid crystal may offer an alternative choice to realize the spin filter. Furthermore, the two lenses can be replaced with only one element which integrates PB phase lens into a conventional concave lens. A more detailed analysis and an experimental demonstration are the subject of a future work.

4. Conclusions

In conclusion, we have proposed a photonic version of spin filter based on dielectric metasurfaces. Similar to the conventional spatial filter, the photonic spin filter is constructed by replacing two plano-convex lenses with PB phase ones. The dielectric metasurfaces work as PB phase lens, resulting in a spin-dependent focusing. The photonic spin filter can select the desired spin state of photons from input photons with mixed spin states. We believe that our proposed scheme have potential applications in spin-based applications.