Titanium dioxide metasurface manipulating high-efficiency and broadband photonic spin Hall effect in visible regime

1 Introduction

Spin Hall effect (SHE) is the physical phenomenon associated with the spin-dependent trajectories of electric current due to spin-orbit interaction (SOI) [1], [2], [3]. Photonic spin Hall effect (PSHE) is the photonic analogy of SHE which refers to the transverse spin-split of light trajecroty [4], [5], [6], [7]. The transverse splitting of trajectory of light originates from the opposite geometric phases for the two spins/polarizations through the interactions of photonic spin angular momentum and orbital angular momentum [8], [9]. The spin-orbit coupling is rising as a promising platform for novel photonic functions such as beam generator and detectors, hologram, polarization control and lens [10], [11]. In that it is highly desirable to achieve high efficient control of spin-orbital coupling especially in visible regime, where many medium including noble metals and silicon show nonignorable damping. Furthermore, it has provided new degrees of freedom to control spin photonics and is potentially useful for exploiting multifunctional spin photonics devices.

Recently, metamaterial with rationally designed building blocks have enabled the realization of many phenomena and functionalities unavailable through use of naturally occurring materials [12], [13], [14], [15], [16]. Many basic and anisotropic metamaterial structures, such as metal split-ring resonators, exhibit birefringence suitable for polarization conversion [17], [18], [19], [20], [21], [22], [23], [24]. Metasurfaces, the two-dimensional counterpart of the metamaterials have also be developed for high-efficiency light manipulations [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37]. Compared to metamaterials composed of complex three-dimensional structures, metasurfaces can be easily fabricated by using the photolithography or nanoprinting. As the operation wavelength goes to the optical regime, metasurfaces made of metals are always suffered from the severe ohmic loss, which usually results in high damping and low efficiency, especially in transmissive metasurfaces.

All-dielectric metasurfaces with building blocks of high-refractive and low-loss dielectrics have been proposed as an alternative route, where the ohmic damping could be avoided [38], [39], [40], [41], [42], [43], [44], [45], [46], [47]. Most of the all-dielectric metasurfaces demonstrated so far are made of silicon because it is compatible with current fabrication processing technology. The dielectric loss of silicon is negligible in terahertz and infrared regime, while it increases rapidly at visible wavelength [48]. The titanium dioxide (TiO₂) has emerged as a promising candidate for manipulating visible light with high-efficiency over nanoscale dimensions because its refractive index (∼2.5) is high and dielectric loss (∼0) is negligible at visible wavelength [49], which is suitable for fabricating high-efficiency and broadband dielectric metasurfaces in visible regime [48], [49], [50], [51], [52], [53].

In this work, we propose and experimentally demonstrate an all-dielectric metasurface capable of achieving high-efficiency and broadband PSHE with a transmissive configuration in visible regime. The PSHE is rising from the opposite geometric Pancharatnam-Berry phases of two spins in polarization space. Compared to the silicon metasurfaces with aspect-ratio (1:3) Si nanofins, the metasurface with building blocks of rationally rotated high-aspect-ratio (1:7.5) TiO₂ nanofins standing on a quartz substrate is fabricated through highly precise electron beam lithography (EBL) and atomic layer deposition (ALD) procedures. The TiO₂-based dielectric metasurface shows a symmetric transverse spin-dependent trajectory of transmitted left-handed circular polarization (LCP) and right-handed circular polarization (RCP) with high efficiency (97.6% [calculated] and 86% [measured] at wavelength 514 nm) due to the strong SOI. It is also found that the metasurface can realize high-efficiency spin-dependent photonic functions in a broadband manner. The proposed SOI metasurface is miniaturized to subwavelength scale and increases additional internal degrees of freedom, which is promising in future integrated on-chip devices with multichannel information processing.

2 Results and discussion

Figure 1A shows the designed transmissive all-dielectric metasurface that exhibits transverse spin-dependent trajectories due to the SOI in a broadband manner. The building blocks of our metasurface are high-aspect-ratio TiO₂ nanofins (Figure 1B) standing on a quartz substrate. The required phase is imparted by rotation of nanofin by an angle θ based on the geometric Pancharatnam-Berry phase. To split the two spins (LCP and RCP) in the transverse of light trajectory, the phase profile φ of the metasurface needs to follow

where λ is the design wavelength, x is the coordinate of each nanofin, Λ is the periodic dimension of each supercell, and the sign of “±” is for RCP (LCP) incidence. This phase profile is acquired by rotating each nanofin by an angle

Figure 1:

Design of a metasurface exhibiting high-efficiency PSHE. (A) Schematic diagram of the metasurface showing spin-splitting, and its building block of TiO₂ nanofins on a quartz substrate. (B) Side and top views of the supercell of nanofin grating with periodic dimension Λ × S. Each supercell consists of eight nanofin elements. Top views of a nanofin showing width W, length L with unit cell dimension S × S and the rotation of nanofin by an angle θ results in the required phase (geometric Pancharatnam-Berry phase). Side view of a TiO₂ nanofin on a quartz substrate showing height H. Incident plane wave propagates along the z direction. The geometric parameters are: Λ = 3120 nm, S = 390 nm, W = 80 nm, L = 230 nm, H = 600 nm. PSHE, photonic spin Hall effect.

In our metasurface, every eight nanofins that rotate by θ = 1/8π make up a supercell with periodic dimension Λ × S. In order to achieve the maximum polarization conversion efficiency (PCE), every nanofin with birefringence originating from the asymmetric cross section is supposed to operate as a half-waveplate. We measured the optical constant of TiO₂ film by utilizing ellipsometer (see Figure S1 in the supplementary material) and employed a finite difference time domain (FDTD) method for investigating the birefringence effect. The PCE under several different illumination wavelengths were firstly determined via simulations as functions of the length and width of the nanofin (see Figure S2 in the supplementary material). Since the results for parameter L = 230 nm and W = 80 nm exhibit high efficiency in a broadband manner, we select these optimized parameters to further design and fabricate the metasurface. The simulated PCE can be greater than 90% in a broad wavelength ranging from 502 to 528 nm and as high as 98% in the desired wavelength 514 nm (Figure 2A), indicating the high-efficiency and broadband performance of the TiO₂-based photonic device. Displacement electric field distribution for x-component (Figure 2B) and y-component (Figure 2C) in a nanofin at the wavelength 514 nm under circular polarization (CP) illumination show that a phase retardation between the x and y polarizations as π can be achieved, further confirming the role of TiO₂ nanofin as a half-waveplate. For these simulations, periodic boundary conditions are applied at the x and y directions and perfectly matched layers (PMLs) are applied at the z directions. We calculate the PCE as the ratio of the transmitted opposite helicity power to the incident power.

Figure 2:

Birefringence effect of a TiO₂ nanofin metasurface. (A) Simulated and measured polarization conversion efficiency as a function of wavelength. (B and C) Simulated displacement electric field (x-component and y-component) distribution in a nanofin at the wavelength 514 nm with circular polarization illumination.

For normal incidence of CP light, the transmitted electric field (EL/Rt) of the nanofin rotated by an angle θ (Figure 1b) can be deduced through Jones matrix as follows [54]:

where ϕ represents the phase retardation between the length and width of the nanofin along the propagating direction, e^L/R=(e^x±ie^y)/2 is the Jone’s vector of LCP or RCP. The two terms in Equation (3) represent the transmitted CP waves with the same and opposite helicity compared to the incident wave, respectively. Note that the opposite helicity radiation carries an additional phase delay of φ = ±2θ, which is known as Pancharatnam-Berry phase and is crucial for constructing a metasurface with phase gradient. The signs of “+” and “−” are for RCP and LCP incidence, respectively. This spin-dependent Pancharatnam-Berry phase in the polarization space leads to the opposite trajectory of the two spins, resulting in spin-splitting and PSHE. The transmitted phase can be tuned from 0 to ±2π as the nanofin is rotated from 0 to π. In our metasurface, the ϕ is approximately equal to π at the wavelength 514 nm. Therefore, the transmitted electric field (EL/Rt) can be expressed as EL/Rt=ie±i2θe^R/L, indicating that nearly total incident CP light is converted into opposite handness radiation.

To construct our metasurface, 8-phase levels from 0 to 2π with 1/8π step under RCP normal incidence were chosen as shown in Figure 3A. According to wave vectors momentum conservation law, the refraction can be expressed as generalized Snell’s law:

where k_t,x and k_i,x represent the x-component of the incident and transmitted transverse wave vector, and ±∂φ/∂x is the spin-dependent phase gradient (here the sign “±” for RCP (LCP) incidence). This spin-dependent phase gradient can cause the spin-dependent orbit angular momentum. To conserve the total angular momentum, the orbit angular momentum along the z direction will be reduced due to the SOI. It is significant that the sign of the phase profile will be totally flipped if the helicity of the incident CP light is changed to the opposite one, which is critical to achieve a transverse spin-split of light trajectory. The electric field maps in Figure 3B and C shows that the incident RCP and LCP are refracted in two symmetric angular directions, further confirming the spin-dependent trajectory propagation. This angle of refraction can be calculated by the generalized Snell’s law as θ′=sin−1(∂φ/∂x2π/λ)=sin−1(λΛ)=9.48∘. Since the geometric phases of the two spins are opposite, the proposed metasurface supports a symmetric spin-splitting of the propagating direction under linear polarization (LP) illumination with normal incidence.

Figure 3:

Angular dependence of phase and polarization conversion efficiency of nanofin and electric field maps. (A) Simulated polarization conversion efficiency (red points) and phase (blue points) of a nanofin with θ varying from 0° to 180°. (B and C) Simulated electric field maps for RCP and LCP illumination, respectively.

2.1 Metasurface fabrication and far-field measurements

Scanning electron micrograph (SEM) of the fabricated TiO₂ metasurface is shown in Figure 4. The top view SEM of the fabricated metasurface is presented in Figure 4A, where an enlarged supercell is denoted by a dashed red rectangular. Correspondingly, Figure 4B shows the side view SEM of the fabricated metasurface, in which the high-aspect-raito TiO₂ nanofins are clearly displayed. The as-fabricated TiO₂ nanofins metasurface agrees well with the design, and the detailed fabrication process is described in Methods Section.

Figure 4:

Fabricated titanium dioxide metasurface and comparison between simulations and measurements with different polarization states illumination at 514 nm. Scanning electron micrograph (SEM) of a fabricated metasurface, top (A) and side (B) view, and an enlarged image of the supercell is marked and inserted in (A). Simulated and measured far-field intensity profiles of m = −1, m = 0 and m = +1 orders with incident polarization states of (C) LP, (D) RCP and (E) LCP, respectively. (F) Optical measurement setup for the metasurface, consisting of a laser with desired wavelength whose beam is passing through a linear polarizer and a quarter-waveplate to generate the input light with desired polarization to illuminate the metasurface, and the transmission light is measured by a charge-coupled device (CCD) camera. Scale bar: 1 μm.

Figure 4C–E shows the comparison of far-field intensity distributions between simulation and experiment under LP, RCP and LCP illumination with normal incidence. The LP light can be considered as the superposition state of LCP and RCP. These two spins will be refracted into transverse symmetric propagating directions after passing through the metasurface. Under LP illumination (Figure 4C), as expected, the transmitted wave is splitted into two symmetric angular direction of m = −1 and m = +1, respectively. The transmitted power of m = −1, m = 0 and m = +1 orders are 48.8, 0.4 and 48.8% in simulation, and 42.6, 0.09 and 43.4% in experiment. For RCP illumination (Figure 4D), the simulated (measured) power of m = 0 does not change but the m = +1 order increases to 97.6% (86%) while the m = −1 decreases to 0%, indicating the high-efficiency PSHE of our metasurface. The simulated trend agrees well with the measured results. For LCP illumination (Figure 4E), we can observe opposite trend. The simulated (measured) power of m = 0 does not change but the m = −1 order increases to 97.6% (86%) while the m = +1 decreases to 0%. The reason that the measured efficiency cannot reach to the expected value in simulation is mainly due to the inevitable imperfection in device fabrication. These simulations are performed using the FDTD method for a supercell of eight nanofins with periodic conditions along x and y directions and PML long z directions. It is worth mentioning that the high-efficiency PSHE can also be achieved in a broadband manner. To further confirm the spin-dependent splitting of the PSHE, the Stokes parameter S₃ was also measured in experiment (see Figure S3 and Note 3 in the supplementary material). The opposite spin accumulation is observed for the two symmetric angular direction of m = −1 and m = +1. Figure 4F shows the optical measuremental setup to test far-field intensity distributions of our fabricated metasurface, and the related descriptions are given in Methods Section.

We characterized the working performance of the metasurface under several different illumination wavelengths, as shown in Figure 5A. The incident beam can be splitted with larger offset with the wavelength increasing from 450 to 670 nm. Figure 5B showed the results for the beam-centroid shift versus transimission distance under different illumination wavelength according to generalized Snell’s law. As the wavelength increases from 450 to 670 nm, the beam-centroid shift increases correspondingly. This trend agrees well with measured results shown in Figure 5A. Note that the metasurface can exhibit high-efficiency and broadband PSHE for almost the entire visible regime from 450 to 670 nm. We measured the working efficiency for several discrete illumination wavelengths of 450, 488, 532, 633 and 670 nm, and the corresponding efficiencies are 33.6, 50.0, 78.7, 73.9 and 62.6%, respectively. The detailed measured power intensities are shown in Figure 5C.

Figure 5:

Broadband performance of the metasurface. (A) Experimentally measured far-field intensity distributions in linear scale, where false colors correspond to their respective wavelengths. (B) Calculated results for the beam-centroid shift versus transmission distance with different illumination wavelength. (C) Measured incident power intensity and operating efficiency under different illumination wavelengths. The inset shows the transmitted power intensity for each diffraction orders m = 0 (gray points and red area), m = −1 (red points and blue area) and m = +1 (green points and yellow area) with different illumination wavelength.

3 Conclusions

In summary, we have demonstrated a titanium dioxide based all-dielectric metasurface capable of realizing high-efficiency and broadband PSHE in visible regime. The metasurface composed of high-aspect-raito TiO₂ nanofins with spatially variant orientation was perfectly fabricated on a quartz substrate. Under LP, LCP and RCP illuminations, we found that this metasurface enabled spin-dependent propagation due to the opposite geometric Pancharatnam-Berry phases in polarization space. The designed and measured maximum operating efficiencies (at λ = 514 nm) reach up to 97.6 and 86%, respectively. Moreover, high-efficiency PSHE can also be achieved in a broadband manner for almost entire visible regime. The controllable manipulation of strong SOI of light with tailored nanofins paves the avenue to spin-controlled photonics devices, which promises important applications in optical communications, quantum information processing and photonic devices in the future.

4 Methods