Photonic spin Hall effect in metasurfaces: a brief review

2.1 Spin-orbit interaction

It is well known that light carries both energy and momentum. The momentum of light can be divided into linear and angular contributions [41]. In paraxial approximation, the angular momentum of light has a spin part associated with circular polarizations [42] and an orbital part associated with the direction of wave vector or phase front [43], [44]. Spin-orbit interaction describes the mutual influence between the spin and orbit angular momenta of light [41], [45], [46], [47], [48], [49]. Generally, the trajectory of beam is associated with the external part of the orbit angular momentum. As a result of spin-orbit interaction, the variation of trajectory is always accompanied with the transverse spin-dependent deflection, namely, the photonic SHE. In experiments, this effect is so weak that a precise measurement technique is required to observe it [7] or it can be observed under an enhanced interaction led by the multireflection in an isotropic material [15]. Additionally, the helical structure of optical wavefront around the beam axis (i.e. the optical vortex located at the beam axis) is associated with another internal form of orbital angular momentum [50], [51]. With the rapid development in generating and manipulating the optical vortex beams, the interaction between spin and this internal orbital angular momentum gathers more and more interests in recent years.

Geometric phases are the performances of spin and orbit angular momentum interaction, which are different from the traditional dynamic phases as they are not integrated as the increase of optical propagation length [52], [53]. It is the change of geometric properties of beam which contributes a phase difference to the light [51], [52], [53], [54], [55], [56], [57], [58]. Polarization and spatial propagation are the major geometric properties of beam. Therefore, two kinds of geometric phases are found in the early researches in succession [59], [60]. The first class is spin-redirection phase, which was found by Rytov in 1938 [61] and then developed by Vladimirskii [62] and Berry [63]. The variation of propagation direction in SO(3) space (position space) will lead to the phase difference in wave function. The other kind of geometric phase is dubbed as Pancharatnam-Berry (PB) phase [64], [65], [66], [67], which is named after its finders, Pancharatnam and Berry. Differently, it is related to the polarization variation in SU(2) space, namely, the polarization space. Both the spin-redirection and PB phases are the manifestations of spin-orbit interaction.

Spin and orbit angular momenta are the intrinsic freedoms of light, which can basically extend the capacity of information encoding and provide a brand-new way to manipulate light. Spin-orbit interaction relates them and gives a feasible approach to utilize them. Efforts in this topic have shown great potentials in communication, particle manipulation, optical design, and optical computation. Geometric phases are the quantitative representations of spin-orbit interaction and are the reasons of spin-dependent behaviors of light in propagation. Therefore, simple descriptions of geometric phases are firstly presented in the following.

2.2 Spin-redirection phase

Berry phase is well known as a phase difference acquired when a quantum system described by a Hamiltonian is subjected to a cycle of time-dependent adiabatic parameter, which is first pointed out by Berry in 1984 [63]. However, the findings about phase difference in optical systems were presented long before it [61], [62]. Propagation and polarization are the vector properties of a light beam. For the first category, the variation of propagation direction contributes to the spin-redirection phase. In particular, it induces an additional term in the equations of motion (ray equations) which describes a polarization-dependent shift of the beam trajectory.

Figure 1 shows the evolution of a light beam. Triad vector (x, y, z) is the laboratory coordinate frame, where the momentum direction of light beam t is recorded. An attached coordinated frame (t, v, w) is applied to describe the transverse properties. As shown, the polarization state e will rotate with the evolution of light beam. This effect can also be represented in a unit sphere, where each point on the surface stands in a unique direction in position space. The evolution trajectory of momentum direction is depicted in Figure 2. For a loop trajectory, marked by a green dash line in the sphere, the polarization state rotated from e to e′. Under the spin-orbit interaction, polarization rotation in the beam transverse section will lead to a back-action on the orbital angular momentum of light, namely, the spin-redirection phase. This geometric phase is different for the spectra components in a light beam, which will finally lead to the transverse shift of light beam.

Figure 1:

The polarization evolves along a twisted ray trajectory, obeying the parallel transport law. The wave polarization is measured in a coordinate frame with basic vectors (t, v, w) accompanying the ray, where t=p/p is the tangent to the trajectory.

Figure 2:

The parallel transport of the polarization vector e⊥t on the unit t-sphere in momentum space. For a loop trajectory, the polarization states rotate from e to state e′.

2.3 Pancharatnam-Berry phase

The PB phase is associated with the polarization variation of light. To trace out the variation, Poincaré sphere is the most valid representation. The polarization of light can be characterized by the Stokes parameters (S₀, S₁, S₂, S₃) in general [68]. For a totally polarized beam, these parameters will fulfill the relationship S02=S12+S22+S32, where S₀=1 as the field is normalized. Thus, a unit sphere can be constructed based on the coordinates (S₁ , S₂ , S₃ ); each point on the surface of Poincaré sphere will be solely related to a general polarization state. Figure 3 shows a general Poincaré sphere. The poles represent circular polarizations; equatorial points are linear polarizations; and the other points between the poles and equator are elliptical polarizations. Four linear polarizations are marked on the equator of Figure 3, and the poles are assigned with opposite circular polarizations (σ=±1). It is clear that the diametrically opposite points on Poincaré sphere represent the orthogonal polarizations.

Figure 3:

The polarization evolution is represented by the precession of the Stokes vector (S1, S2, S3) on the Poincaré sphere about the S3 axis. The Stokes parameters are applied to characterize the polarizations of light; for a polarized beam, they hold relationship S12+S22+S32=1. Poles of this unit sphere represent circular polarizations, the equatorial points represent the linear polarizations, and the internal points are elliptical polarizations. The polarization states on the coordinate axes are marked by arrow lines.

For a cyclical evolution on the Poincaré sphere, just for example as the route C described in Figure 3, the PB phase Φ_B included can be deduced as the half of solid angle Ω enclosed by the route on the surface. Therefore, it is a feasible approach to manipulate the phase of light by controlling polarization, which is currently attracting growing attention.

Polarization is the fundamental feature of electromagnetic waves. The studies of polarization have been extended to a wide category in the past decades. However, Poincaré sphere is still limited to the representation of most simple and primary homogeneous plane polarization states. To adjust the general Poincaré sphere to more complicated situations, higher-order Poincaré sphere [69], [70], orbital Poincaré sphere [71], and hybrid order Poincaré sphere [72] are developed recently. The transverse phase structure of light beam is associated with the internal orbital angular momentum of light, which provides an additional degree of freedom for beam manipulation and data encoding. Thus, the orbital angular momentum carrying beams also requires a prominent geometrical representation. Orbital Poincaré sphere is the analogy of general polarization Poincaré sphere in phase space. Cylindrical vector (CV) beams are light beams of which the polarization states are arranged with cylindrical symmetry in the beam cross section, which is the higher-order solution of Maxwell’s vector wave equation. Many unique properties originating from the special intrinsic symmetry of CV beams have distinguished them from the general optical beams with homogeneous polarization. Similar to Poincaré sphere, higher-order Poincaré sphere is lately developed to describe the CV beams.

Figure 4 shows the representation of higher-order Poincaré sphere (l=σ=1), and each point (θ, ϕ) along the surface describes a higher-order polarization state, where the poles represent circularly polarized optical vortexes with orthogonal chiralities and opposite topological charges; the points on equator represent polarization states that are linearly polarized and azimuthally arranged, and the intermediate points between the poles and equator represent elliptically polarized vector states. For more general cases, the higher-order Poincaré sphere will be reduced to the standard Poincaré sphere when l=0. Moreover, the handedness of optical vortex and circular polarization at each pole can be adjusted in the same or opposite senses. As a consequence, the polarization state collection in each order (l) can be enclosed by two spheres with opposite σ. In this geometric representation, higher-order PB phase is demonstrated by cyclic transformation of the CV beams on the higher-order Poincaré sphere. The resulting geometrical phase is then given by [69]

where Ω is the solid angle subtended by the area enclosed in the evolving route; l and σ are the topological charge and spin assigned to the sphere, respectively.

Figure 4:

Higher-order Poincaré sphere (l=1): the poles (θ=0, π) represent orthogonal circular polarizations with different optical vortex (l=±1). Equatorial points (θ=π/2) represent generalized cylindrical vector beams; (ϕ=0; θ=π/2) and (ϕ=π; θ=π/2) represent radial and azimuthal vector beams, respectively; (ϕ=π/2; θ=π/2) and (ϕ=3π/4; θ=π/2) represent spiral polarizations. Intermediate points between the poles and equator represent elliptically polarized cylindrical vector beams.

From the three kinds of Poincaré spheres mentioned above, the orthogonal eigenstates of the whole state-space are settled at the opposite poles of the sphere. For the standard Poincaré sphere, poles are marked with the opposite spin states σ=±1; for the orbital Poincaré sphere, poles are assigned with the contrary topological charges ±l; and for the higher-order Poincaré sphere, poles are ruled with both the opposite spin and topological charges ±l, σ=±1. All in all, the states on the poles of sphere are orthogonal but in a value, i.e. the same order. Then, what will be the evolution of phase and polarization states between different orders? To describe this situation and find out the PB phase involved, a hybrid-order Poincaré sphere is recently developed. Figure 5 describes the representation of a hybrid-order Poincaré sphere [72]. It is based on the finding that the representation of the polarization states in inhomogeneous anisotropic media has a similar expression of polarization states on the higher-order Poincaré sphere with only the orbital states being different. Therefore, the polarization and phase evolution in inhomogeneous anisotropic media with special geometry can be conveniently described by the evolution of states along the geodesic lines on the hybrid-order Poincaré sphere. The PB phase associated within this process are discussed as well

where l and m are the topological charges of the north and south poles, respectively; σ is the primary spin state; and Ω represents the solid angle faced by the encompassed area.

Figure 5:

Schematic illustration for the evolution of phase and polarization states on hybrid-order Poincaré sphere. Insets in the right row show the phases of points A, B, and C, respectively. Insets in the left row show the polarization states of the three points. Here, we assume the north pole with state σ=±1 and l=0, while the south pole is with σ=-1 and l=1.

2.4 Metasurfaces based on subwavelength structure

The manipulation of wavefront is generally realized by introducing the changes of phase and polarization of light [73], [74]. Traditional optical devices are based on the reflection, refraction, or diffraction effects in media to accumulate these variations for light manipulations [75], [76], [77]. Thus, the volume size of traditional devices is limited by the propagation effects. To expand functionality and miniaturize the optical elements, metasurfaces with a reduced dimensionality are developed in recent years, which breaks the restriction of light propagation by introducing feature variations in the scale of operating wavelength [21], [27], [29]. Additionally, the metasurfaces made of arrays of scatters can be arranged with a spatially varied geometry (size, orientation, and shape). Hence, the spatially varied responses of the beam wavefront can be artificially managed.

Two kinds of scatters are applied in the up-to-date phase designing of metasurfaces based on subwavelength structure. This first kind uses the dispersion of scatters to add abrupt phase changes in light propagation [22], [78], [79], [80], [81], [82]. A canonical example is the V-shape antennas as shown in Figure 6A [23], [30], [83], [84], [85], [86], [87]. When a light beam impinges on a metallic antenna, the light wave will couple with the surface wave and the electron oscillation in the antennas, namely, with the surface plasmons. The phase difference induced in the propagation wave of metasurface is a result of strong interaction between light and the local surface plasmon polaritons (SPPs). When metallic antenna geometry satisfies the resonance requirement, the incident field will keep in phase with the excited surface current. The surface current will lead or lag the incident field. As with the accordance of surface current and the scattered field, the phase of scattered field can be controlled by altering the geometry of metallic scatters, as the example in Figure 6B. Additionally, V-shape antennas allow one to design the amplitude, phase, and polarization state of the scattered light, since two orthogonal modes can be excited by the incident field. According to Babinet’s principle, the V-shape slits milled in a thin metallic film can also be applied to manipulate the features of light [88].

Figure 6:

(A) The SEM image of metasurface based on the V-shape antennas. (B) The scattered electric field corresponds to the individual antennas in the left picture. Adapted from Ref. [23].

Another kind of scatter introduces phase change by controlling the local polarization states of the light beam [38], [57], [58], [89], [90], [91], [92], [93], [94], [95], [96], [97], [98]. As introduced in the last section, the polarization evolution will lead to phase change in waves. By locally tailoring the evolving routes of polarization, a desired phase distribution can be expected in the scattered field. The most used polarization devices in traditional optics is the polarizer and waveplate. The former one is a filter which chooses a specific polarization component from the incident field, while the last one can convert the polarized beam to a certain polarization state. By designing the geometry of scatters, both the function of polarizer and waveplate can be realized in the subwavelength scale, as the examples shown in Figure 7. The rectangular apertures milled in a metallic thin film functions like a miniature polarizer. And the polarization of transmitted light is primarily perpendicular to the long axis of aperture. Thus, the metasurface shown in Figure 7A will lead to the phase variation around the center axis, namely, an optical vortex as shown in Figure 7B [93]. Figure 7C and D exhibit the structure and experimental results of another optical vortex generator, which is based on the rectangular antennas serving as miniature waveplates [57]. Therefore, the continuous tailoring of wavefront is feasible by engineering the polarization.

Figure 7:

The metasurfaces based on the PB phase scatters. (A) and (B) The schematic and phase distribution of a rectangular apertures comprised metasurface, which serves as a vortex beam generator. Each rectangular aperture can be regarded as a polarizer working at a fixed wavelength. (C) and (D) The SEM image and intensity distribution obtained from a dipolar antenna array. The antennas have the same geometry but varied orientations. Each antenna can be treated as a nano-waveplate. Adapted from Refs. [57], [93].

The dielectric metasurfaces constructed by continuous or quantized subwavelength gratings can also be applied to modulate the polarization states of the light beam [58], [90]. When the period of grating is much smaller than the wavelength of incident beam, only the zeroth order is propagating, while the others are suppressed. Homogeneous gratings are operating as a uniaxial crystal with its optical axes parallel and perpendicular to the gratings. It means that the electric fields oscillating along or orthogonally across the grating will obtain the different phase shifts. Therefore, it leads to the so-called form birefringence, contrasting to the birefringence originating from the anisotropy of oriented molecules [91]. By designing a spatially varying subwavelength grating, the polarization can be manipulated in each exact location. Thus, a metasurface with sophisticated function can be realized. The quantization of subwavelength grating will sufficiently alleviate the difficulty in designing and fabricating [58], [90].

3.1 Spin-dependent splitting in position space

As mentioned above, the variation of propagation orientation will lead to the phase change in wave beam, which is the spin-redirection phase [59], [62], [63]. For different angular spectral components, the introduced phase changes are different as well. Therefore, a phase gradient is presented between the different spectral components. The phase gradient of angular spectral component will lead to a spin-dependent shift in position space,

where ∇Φ_G(k_x, k_y) is the gradient of geometric phase and is a function of transverse wave vectors (k_x, k_y). The z-direction is assumed as the direction of normal incidence, where xz plane is the incident plane of light. Thus, the spin-dependent splitting in y-direction is the expected photonic SHE lead by spin-redirection geometrical phase.

The magnitude of induced spin-redirection phase can be found in the reflection or refraction equation of light, where the component of k_y is the reason for spin-dependent splitting in y-direction, which is in the following form:

where σ refers to spin of incident light, δ∝cotθ_i/k₀, θ_i is the incident angle, and k₀ is the wave number in a vacuum. The magnitude of δ is related to the physical parameter of interface [108]. For example, the thickness of interface can be modulated to enhance the effect. Bliokh et al. proposed an efficient way to directly observe the photonic SHE by guiding the light beam in a glass cylinder as shown in Figure 8. The long propagation route in glass cylinder amplifies the spin-dependent splitting [15].

Figure 8:

A laser beam enters the glass cylinder at a grazing angle through the input prism, coils along the cylinder surface, and leaves it by means of the output prism. The liquid-crystal variable retarder (LCVR) is used for generating and switching between the circularly polarizations, whereas the quarter-wave plate (QWP) and polarizer P2 are intended for measurement of the Stokes parameters. The inset shows a real picture of the spiral light beam inside the cylinder. Adapted from Ref. [15].

Metasurfaces can also be applied to manipulate the spin-dependent splitting in position space by enhancing the spin-orbit interaction [22]. By designing a two-dimensional (2D) electromagnetic nanostructure as shown in Figure 9A, an in-plane phase retardation is introduced in wavelength scale at the beam transverse section. The phase retardation makes the anomalous scattering of passing light, which therefore dramatically changes the related physical parameters of this artificial interface. Thus, the photonic SHE can be directly observed in the experiment. Figure 9 shows the experimental apparatus and observed S₃ results. This work shows the possibility of controlling the photonic SHE by designing the metasurfaces, which not only provides a novel application of ultrathin metasurfaces but also exhibits a new degree of freedom in information transfer between spin and orbital angular momenta of photons.

Figure 9:

The photonic SHE related to spin redirection phase is directly observed by introducing an ultrathin metasurface. (A) The scanning electron microscope image of metasurface designed by arranging the V-shape antennas in x-direction. (B) The schematic illustration of the observing setup. (C) and (D) are the measured S₃ when polarization of incident beam is changed from linear polarization in x direction to y direction. Adapted from Ref. [22].

3.2 Spin-dependent splitting in momentum space

PB phase is the other kind of geometric phase introduced by the spin-orbit interaction of light. As shown above, the cyclic polarization state variation in parameter space will create the spin-dependent geometric PB phase. Thus, if we can spatially design the evolving routes of polarization states on Poincaré sphere, a desired phase distribution can be acquired. In traditional optics, the evolution of polarization can be modulated by a waveplate with a fixed retardation. The orientation of optical axis reference to the incident polarization state α(x, y) and the phase retardation ψ can both be adjusted to change the output state. The state transform in a waveplate can be concluded as

The above equation indicates that a fraction sin²(ψ/2) of the incident photons reverses their handedness and that the other cos²(ψ/2) remains unchanged. For the transformed polarization part, ψ and α(x, y) determine the ellipticity and its orientation, respectively. Circular polarizations are the eigenstates of standard Poincaré sphere and essentially corresponded to the orthogonal spin states (σ±=±1). As Eq. (5) shows, only the opposite circular polarizations σ_∓ get the different phase factor 2σα(x, y). Hence, the opposite circular polarizations are just considered in the designing of metasurfaces. For ψ=π, i.e. a half-wave phase retardation, all photons reverse their handedness.

Therefore, the orientation of optical axis of waveplate will restrict the evolving route of polarization state on Poincaré sphere. Figure 10 shows the example of state evolution on Poincaré sphere along different routes and directions. Four different routes following the longitudes are marked with arrow lines; green and red represent the direction toward or backward to the south pole. The blue arrows on the equator are the representations of optical axis orientation. As what we have deduced above, PB phase is equal to half of the solid angle enclosed by the routes on the surface; thus, the induced PB phase would be

where σ is the direction of evolving route. It can be seen that the phase difference ΔΦ_G=Φ_G-Φ₀=2σα(x, y) is in agreement with Eq. (4). By this way, the orientation of local optical axis can be tailored to design the PB phase.

Figure 10:

The accumulations of PB phase for the opposite spin components, the left picture (A) shows the transformation from left circular polarization (σ=+1) to right one (σ=-1). Oppositely, the right picture (B) shows the transformation in a different direction. As the reversal of incident polarization, the sense of generated PB phase will be changed.

In the above section, the phase gradient in k-space leads to the photonic SHE in the position space. Here, a spin-dependent splitting in k-space will be desired as the PB phase can be tailored by arranging the orientation of local optical axis in position space. A shift of wave vector will arise due to the phase gradient,

where ex^ and ey^ are the unit direction vectors in x axis and y axis of space coordinate.

Following the above analysis, for circularly polarized light passing through the metasurface with designed local optical axes and the phase retardation of medium set to be π, the spin of incident light beam will be totally reversed and the shift of wave vector can be deduced as

where Λ_x=∂α(x, y)/∂x and Λ_x=∂α(x, y)/∂y are the rotational speed of local optical axes in x and y axes. Moreover, the shift of wave vector in momentum space will cause an angular shift in position space after propagation. For linearly polarized beam, which is the superposition of right circular polarization and left circular polarization, the splitting distance of orthogonal spin components in the observing distance z can be derived as

The spin-dependent shift in momentum space has been reported by Shitrit et al. in 2011 [38], where the transmission spectra of coupled localized plasmonic chains are studied. The photonic SHE is observed under the interaction with a curved chain constructed by isotropic unit cells or with a straight line comprising rotated rectangular cells as shown in Figure 11. Moreover, the plasmonic chains can be changed to modulate the phase front of beam. A wavefront phase dislocation was observed in a circular curvature, in which the dislocation strength was enhanced by the locally anisotropic effect. A vortex with topological charge l=2 is acquired in the spin-flip component when the circular curvature is constructed by the isotropic building blocks, and vortex with topological charge l=4 is observed when the circular curvature is constructed by the arranged anisotropic cells.

Figure 11:

SEM images of a plasmonic chain with identical unit cells but arranged in a curve with period a (A) and another chain with rotated rectangular cells in a straight line (B). (C) and (D) are the spin-dependent momentum deviations for these two different arranged plasmonic chains, respectively. The red and blue lines stand for incident spin states σ=+1, respectively. Adapted from Ref. [38].

Studies on the spin-dependent effect modulated by PB phase have been carried out for several years, and all their results are valuable. However, the observable photonic SHE of propagated light is still a huge topic. Ling et al. reported a giant photonic SHE recently [39]. The gradient metasurface was fabricated by the femtosecond laser self-assembly of nanostructures in fused silica. The rotated local optical axes in horizontal direction endowed the metasurface with a spin-dependent phase gradient. Thus, the angular splitting in position space can be detected directly after the glass. The transparent silica glass promised the high transport efficiency of transmission mode. The polariscopic analysis result and SEM picture are used to describe the inner structure (Figure 12A and B), and Figure 12C–F show the observed intensity and S₃ results. This effect operated at the transmission mode and the Ohmic loss of metallic plasmonic structure is avoided. Based on the PB phase metasurfaces, the direction of spin-dependent splitting can also be modulated by arranging the pattern of local optical axes. Photonic SHE occurring in radial direction and longitudinal direction have been reported lately [109], [110], [111].

Figure 12:

The far field giant photonic SHE observed after a linearly polarized beam passes through two structured metasurfaces. (A) and (B) are the polariscopic analysis result and SEM image picture of the applied metasurface. (C) and (D) show the intensity and S₃ parameter for the metasurface with a rotation rate of Ω=π/20 rad μm^-1, respectively. (E) and (F) are the corresponding results for another sample with the exactly opposite rotational rate of Ω=-π/20 rad μm^-1. The observation distance is 10 cm away from the metasurface. Adapted from Ref. [39].

Another work is devoted to enhance the efficiency of photonic SHE in metallic plasmonic metasurfaces [40]. A certain criterion is developed from the general Jones matrix analysis. Such a criterion is approachable from two different routes, leading to two types of metasurfaces with distinct symmetry properties. While the idea is realizable at general frequencies, as a proof of concept, the fabricated two realistic microwave samples and performed experiments demonstrate that both can realize photonic SHE with ≈90% efficiency within a broad frequency bandwidth. Finally, the experiment demonstrates that the metasurfaces can work as efficiently, and broadband polarization detectors are one illustration of many potential applications of our findings.

Many primary works about the PB phase-caused photonic SHE is focused on the propagating electromagnetic surface waves, where the PB phase gradient will guide the spin-dependent splitting in the metallic interface [24], [48], [59], [112], [113], [114], [115], [116]. The collective oscillation of the electrons at the surface of a metal caused by the coupling with light is dubbed as the SPPs. The SPPs can be closely related to the composition and structure of materials and therefore has led to many advances in the control of light at the nanoscale. The photonic SHE involved in this effect may provide a polarization-dependent sensitivity in controlling the directionality of SPPs devices [117], [118]. However, it is substantially different with photonic SHE of light beam; thus, it was not mentioned in this review. Breaking the rotational symmetry of PB phase elements may be the basic requirement for observing the photonic SHE [119], [120], and the rotation rate of local optical axes in metasurfaces is related to magnitude of splitting [38], [121], [122].

4.1 Spin-dependent splitter

Polarizing beam splitter can separate the orthogonally polarized components of beam into different propagation directions. A birefringence crystal with considerable thickness is required for the conventional polarizing beam splitter. Therefore, it cannot be integrated in a compact optical system. Particularly, the circular polarization beam splitter is further limited with the absence of natural materials with sufficient circular birefringence [123], [124]. However, spin angular momentum essentially corresponds to the circular polarization of light; thus, the generator of photonic SHE can be instinctively regarded as a circular polarization beam splitter.

As discussed in the earlier section, PB phase gradient can make a photonic SHE with controllable splitting angle in position space, which thus can be treated as a circular polarization beam splitter. However, the intensity pattern of beam is also a major issue for applications in spin-based optical information processing and imaging systems. Figure 13 shows the intensity separation of a modulated light beam [125]. The left column shows intensity patterns generated by a phase-only spatial light modulator. And the right column shows the splitting results; red and blue represent the orthogonal circular polarizations (σ=±1). The splitter is fabricated by femtosecond laser writing subwavelength grating in a fused silica glass. Thus, a high transmission efficiency, 50.1%, and a high conversion efficiency, 96.3% (note that the transmission losses are not taken into account when evaluating the conversion efficiency), at 632.8 nm wavelength are measured by a laser power meter.

Figure 13:

Left column shows the intensity patterns of three typical linear polarization beams (vortex beam, Hermite-Gaussian beam, and Airy beam in the order from top to bottom) and the superposition of a right-handed circular polarization plane Gauss beam and a left-handed circular polarization Airy beam. Right column is the corresponding normalized Stokes parameter S₃ after the spin-dependent splitter. Blue color represents the right polarization and red for left polarization. Adapted from Ref. [125].

4.2 Pancharatnam-Berry phase lens

As a most frequently used element in optics, a lens is an indispensable part of most optical systems. To make a lightweight and small-volume lens, a variety of schemes have been proposed in the past. Fresnel lens is the most popular solution which introduced a gradual phase gradient in the radial direction to focus light. However, it is still restricted to a thickness comparable to the wavelength (λ₀/n, the effective wavelength in medium), as the requirement of a whole period phase retardation 2π. The development of metasurface offers an efficient way to directly manage the spectral responses of light and thus can be applied to further reduce the thickness of lenses [86], [87], [126], [127]. Moreover, the PB phase elements possess different responses to the orthogonal circularly polarized light [56], [88], [128], [129] and thus will endow the lens novel freedom for light manipulation.

Figure 14 is the PB phase lens proposed by Hasman et al. in 2003 [90]. A discrete structure realized by using the computer-generated space-variant subwavelength dielectric grating is equal to a Fresnel lens. This structure operates at infrared radiation wavelength 10.6 mm. A dielectric lens working in the visible spectrum is reported in 2014 by Lin et al. [58]. These works follow a general strategy to design the PB phase elements. The subwavelength grating features linear phase dependence with the orientation of grating, as shown in Figure 14A; thus, any phase distribution can be accessed by patterning the subwavelength gratings. The phase profile required for a desired optical field can be determined by the Fourier optics. Therefore, by discretizing the phase profile, such a planar lens was obtained in the mentioned works.

Figure 14:

(A) The relationship between the designed phase and the discrete local grating orientation. Inset is the SEM image of a region on the subwavelength structure of the focusing lens. (B) Illustration of a PB phase lens with varying subwavelength structures in the radial direction. (C) The geometric phase distribution and the measured light spot. Inset is the measured (dots) and calculated intensity (solid curve) cross section. Adapted from Ref. [90].

Also, the metallic structure can be applied to realize the PB phase lens. Metal is firstly used as the resonance antenna of metasurface, because of the requirement of loss materials whose imaginary part of the complex refractive index is comparable to the real part. However, ohmic losses in the metal and the limited scattering cross sections of the antennas have constrained the efficiency of metasurfaces operating in transmission mode. Moreover, It has been theoretically shown that only the transmitted cross polarization wave can acquire the geometric phase change range from 0 to 2π, and the cross-polarization coupling efficiency is fundamentally limited to stay below 25% (with respect to the total incident energy) for ultrathin metasurfaces operating with linearly polarized fields, although the power efficiency of metallic metasurfaces can be increased by making the metasurfaces work at reflection mode or by designing the gap plasmon-based metasurfaces [82], [130], [131], [132]. Figure 15 reports an ultrathin linear metasurface lens with maximal cross-polarization transmission efficiency reaching 24.7%, where the thickness is about λ/1000 (λ is the operating wavelength); only tangential electric currents are supported [129].

Figure 15:

Geometry of the Ding’s high efficient metallic metasurface lens. (A) Schematic of the metasurface lens. (B) Geometric parameters of the unit cell. Adapted from Ref. [129].

The spin-related feature of PB phase provides a fresh degree of freedom for light manipulation. Thus, multifunctionality is anticipated in the PB phase lenses. Multifoci diffractive lens has been widely used in various optical systems, which allows a single incident beam to focus at different positions along the longitudinal axis or along the transverse direction. However, the conventional realizations of such a multifoci lens are complex and cumbersome. To miniaturize the multifoci lens and make the focusing controllable, the PB phase-based metasurfaces are applied. Figure 16A shows the schematic metasurface lens with three different focal points along the longitudinal direction [133]. Different polarization states arranged from left to right are listed with linear, right circular, and left circular polarizations. The focused spots are shown in Figure 16B. To realize this function, the metasurface is actually divided into three regions in the radial direction. Different phase profiles are imparted in these regions to focus the different components of linear polarized incident beam, and the focal length is set to be apart. Hence, the position and the polarization of the focal points can be controlled by changing the helicity of the incident light.

Figure 16:

(A) The schematic illustration of the designed longitudinal three-foci metasurface lens; each focal point is the focusing of different polarization components. (B) The observed light spots correspond to the three focal points. Adapted from Ref. [133].

To realize the lens with transverse multifoci, a novel idea is proposed by Wang et al. [134]. Figure 17A is the schematic illustration of the metasurface which is fabricated by etching rectangular slits on a gold film. The substrate is a high-resistance Si wafer. Compared with the design of longitudinal multifoci lens, the antennas are not divided into several distinct regions, but the distribution seems relatively in disorder. This is because the phase profiles supporting the focusing of right and left spin components are simultaneously imprinted on the metasurface. Moreover, to make sure that the two phase profiles are working at the same time, the adjacent slits are working for the different spin components. Therefore, the lens will achieve a giant transverse shift and focus the photons with different spin states to separate spots, when working with a linearly polarized incident beam, as shown in Figure 17B.

Figure 17:

Schematic illustration of the transverse two-foci metasurface lens. (A) The distribution of rectangular silt antennas in metasurface. (B) The metasurface lens focus the incoming beam to two apart spots according to the sense of circular polarization. Adapted from Ref. [134].

4.3 Novel spin-Hall devices

With the development of nanofabrication techniques, a variety of flat devices with more complex and multifunctionality are conceived. The spin-Hall devices based on the PB phase can either work at the linearly polarized incident beams or at a circularly polarized beam but possess distinct responses to the incidences. Apart from the devices developed from the traditional counterparts, such as the polarization beam splitter, laser mode converter [135], and optical lens mentioned above, some novel devices with unprecedented functions are realized. A circular dichroism (CD) spectrometer is an important tool in sensing chiral molecules possessing differential optical responses to circular polarization of light. These molecules are very common in biological and organic compounds. Hence, the CD spectrometer is widely used in biological material studies, protein and DNA structural analysis, and stereochemical detection. Typical CD spectrometers are cumbersome and expensive. Shaltout et al. proposed a novel and integratable CD spectrometer based on the gap-plasmon metasurface with broadband response and one-dimensional phase gradient [132]. The left and right circular polarizations of light are reflected to the opposite directions in position space due to photonic SHE, and the reflection angles for the wavelength components are varied, as shown in Figure 18. Thus, using a broadband detect source, the right and left polarization spectra of samples are obtained in the same time. Additionally, the real-time sensing of chiroptical spectroscopy can also be built in this scheme.

Figure 18:

Illustration of a proposed circular dichroism spectrometer. The components with different polarizations are reflected in opposite directions, and each wavelength component is reflected at a different angle. Colors represent the different wavelength values. Adapted from Ref. [132].

Another spin-Hall device with novel function is the Stokes parameters detector which is proposed by Pors et al. [136]. Polarization is one of the most important features of electromagnetic waves, which is generally characterized by the Stokes parameters (S₀, S₁, S₂, S₃). However, for each of the Stokes parameter, a single measurement is needed in the experiment. Thus, it is not easy to determine the polarization state of beam in real time. Pors et al. carefully designed a metasurface for simultaneous determination of the normalized Stokes parameters. Figure 19 shows the schematic of their Stokes parameters detector. It was realized by interweaving three distinct metasurfaces which can separately probe the normalized Stokes parameters of wave.

Figure 19:

The Stokes parameter detector proposed by Pors et al. |u〉 is the incoming state with unknown polarization, (|x〉, |y〉), (|a〉, |b〉), and (|r〉, |l〉) can determine the Stokes parameters S₁, S₂, and S₃, respectively. Adapted from Ref. [136].

To extend the multifunctionality of flat optical devices, Veksler et al. proposed a disorder structure most recently [137]. Apparently, the optical spin provides an additional degree of freedom in the gradient metasurfaces based on the PB phase by breaking the rotational symmetry. However, the unidirectional arrangement of building blocks can only provide a feasible channel for the directional responses. To overcome this disadvantage, the channels arising from the symmetry breaking can be increased by constructing a disorder structure. A metasurface with three applicable wavefronts is demonstrated in Figure 20. Light components with different topological charges are deflected to different directions.

Figure 20:

Schematic of spin-controlled far-field phase functions with different orbital angular momenta generated by a disorder gradient metasurface. The inset shows the mixed antenna groups, where each color corresponds to a different wavefront. Adapted from Ref. [137].