Highly Efficient Polarization Control Based on All-dielectric Metasurfaces

In recent years, metasurfaces have been widely used in the manufacture of various optical components. Based on all-dielectric metasurfaces, we proposed broadband, high-efficiency (over 83%) quarter-wave plates (QWP) and half-wave plates (HWP), respectively. The structure of the HWP we designed is equivalent to the superposition of two QWPs. The proposed QWP and HWP have high transmission efficiency, with bandwidths of 1376-1624 nm and 1411-1584 nm, respectively. Furthermore, based on the three-layer all-dielectric metasurfaces structure, we proposed a reversible bifunctional metasurfaces, which can realize the function of QWP and the effect of light deflection. This work may be conducive to the miniaturization and integration of polarization conversion devices.


I. INTRODUCTION
The polarization control technology of electromagnetic waves has been widely used in various fields, such as communication, instrument measurement, and imaging [1]- [3]. Traditional polarizing devices are mostly realized by using natural materials or man-made three-dimensional metamaterials [4], which usually exhibit shortcomings such as large period size, complex configuration structure, and low work efficiency. These shortcomings greatly limit its application in photonic integrated equipment [5], [6].
Metasurfaces is a two-dimensional planar array composed of sub-wavelength-sized unit structures [7]. While maintaining the excellent electro-magnetic properties of the metamaterial, it is easier to manufacture and process than three-dimensional metamaterials. It has excellent characteristics such as easy preparation, low loss, and good compatibility with actual engineering equipment. The metasurfaces can control phase [8]- [11], amplitude [12], [13] and polarization [14]- [16] response at sub-wavelength resolution, showing excellent electromagnetic wave control ability. In recent years, dielectric metasurfaces have been widely used in focusing [17], [18], nano-grating [19]- [21], holograms [22], [23], polarization modulation [24]- [26], nonlinear effects [27], [28], etc. Various functional devices based on metasurfaces are proposed. For example, Ding et al. [29] designed an ultra-thin, broadband HWP that works in the near-infrared band based on the plasma metasurfaces, conversion efficiency is greater than 97%. Li et al. [30] proposed broadband, high-efficiency reflective HWP and QWP that work at infrared wavelengths. Xu et al. [31] proposed a high-efficiency bifunctional metasurface that works at visible wavelengths, which can achieve beam anomalous refraction and focusing. Previous research on metasurfaces functional devices started with metal nanostructures, but transmissive metal metasurfaces have very low working efficiency in the visible and near-infrared bands, and they can generally only be used for reflective structures. The proposal of all-dielectric metasurfaces avoids the ohmic loss of metals and has high transmission amplitude, which can realize the large-scale industrial production of metasurfaces devices.
In this paper, we propose three polarization control devices based on the all-dielectric metasurfaces. The first is a QWP device based on a double-layer structure, and the other is a HWP device. Different from the traditional two-layer structure of HWP [32], the HWP we proposed is a three-layer structure, which is designed on the basis of QWP. The proposed HWP is equivalent to the superposition of two QWPs. The two types of wave plates work in the near-infrared band and have the characteristics of broadband and high efficiency. The superposition of two simple structures can achieve the functions we want, which can greatly reduce the difficulty of design, and it is also conducive to actual manufacturing. Furthermore, we can design polarization devices that can achieve different functions at the same time based on this idea. By carefully designing the three-layer all-dielectric metasurfaces, we propose a bifunctional polarization control device that can simultaneously achieve the function of a quarter wave plate and the deflection effect of light. The transmission amplitude of the polarization control device is greater than 83%. In this paper, the design of using simple metasurfaces to construct multifunctional metasurfaces will be conducive to the miniaturization and integration of polarization conversion devices.

II. PRINCIPLE AND DESIGN
Here, we use silicon nanomaterials to construct the metasurfaces polarizers. We can achieve complete control of the amplitude, phase, and polarization of light by picking a proper set of parameters of silicon nanostructures. In this article, we deposit silicon on the silicon dioxide layer to obtain the structure we need. Fig. 1A depicts a simulation diagram of the structural unit of a transmissive QWP. The top layer is a rectangular silicon antenna with a height of h, and its length and width are denoted by a and b respectively. The fast axis and slow axis of the silicon antenna are perpendicular to the yaxis and the x-axis, respectively. The bottom layer is a dielectric layer made of silicon dioxide with a thickness of t. P is the width of the silicon dioxide dielectric layer along the xand y-direction. Fig. 1B depicts a simulation diagram of the structural unit of a transmissive HWP. It is composed of two unit cells in Fig. 1A. Fig. 1C depicts the simulation diagram of the structural unit of the proposed highly efficient bifunctional metasurfaces. It is a super unit cell composed of eight unit cells arranged along the x-axis. We decompose the linearly polarized (LP) light into the xaxis (x-LP light) and the y-axis (y-LP light). In order to realize the functions of the transmissive QWP and HWP, the x-LP light and the y-LP light must have approximately the same transmission amplitude and have a higher transmittance. For the QWP, the transmission phase difference must be equal to π/2. For the HWP, the transmission phase difference must be equal to π. Use Jones matrix to represent the incident LP light: where θ represents the angle formed between the plane of polarization and the x-axis. For QWPs and HWPs, the Jones matrix can be expressed as: where α represents the transmission phase difference between the x-direction and the y-direction. When θ is equal to 45°, LP light passing through the QWP and HWP can finally be written as: From Equation (3) and (4), it can be concluded that when LP light with an angle of 45° to the x-axis is incident on the QWP, the transmitted light is converted into circularly polarized (CP) light, and when it is incident on the HWP, the transmitted light is deflected by 90° around the x-axis.
The basic principle of beam deflection is that the designed nano-rectangular silicon antenna array can simultaneously generate two different transmission phase for incident x-LP light and y-LP light. When a light beam enters a metasurface structure, its refraction obeys the generalized Snell's law [6]: where represents the angle of refraction. represents the angle of incidence. is the wavelength in vacuum. and represent the refractive indices of the incident surface and the transmission surface, respectively. ⁄ represents the phase gradient. We can achieve light deflection by changing the transmission phase of the two polarized lights to have the same phase gradient. Through this principle, combined with the designed QWP, we designed a bifunctional metasurfaces polarizer with a three-layer all-dielectric structure.
Here, we simulate the three polarization devices using finite difference time domain (FDTD) method. During the simulation, we use periodic boundary conditions in the x-and y-direction, and perfect matching layer (PML) boundary conditions in the z-direction. The optical constants of silicon dioxide and silicon are taken from Palik's data. For QWP and HWP, after parameter scanning, the lattice constant of the structural unit is set as p = 700 nm, the thickness of the silicon dioxide dielectric layer is set as t = 300 nm, the height, length, and width of the silicon nano-antenna are set as h = 750 nm, a = 281 nm, b = 354 nm.
For the bifunctional metasurfaces super cell, the silicon nano-antenna on the top has the same parameters as the QWP, and the thickness of the silicon dioxide dielectric layer remains unchanged. For the bottom silicon nano-antenna array, we scan the length and width of the silicon nano-antenna at the incident wavelength of 1550 nm, and list the unit cells that can cover the phase gradient from 0 to 2 . The scan result is shown in Fig. 2. We select eight rectangular nano-antennas (as shown in Fig. 2D)

A. QWP ANALYSIS DISCUSSION
When the x-LP light and the y-LP light are incident on the QWP we designed, the simulated transmission amplitude ( , ) and transmission phase ( , ) changes are shown in Fig. 3A and B, respectively. The simulated wavelength range is 1300-1800 nm. Through simulation calculation, we can find that the transmission amplitude is greater than 85% in the range of 1376 nm to 1624 nm for two orthogonally polarized lights incident on the metasurfaces. At the same time, the phase difference (Δφ) between the two orthogonally polarized lights is about 90 ° ± 7 °. The results of the simulation are consistent with our theory, so we can get a broadband, high-efficiency QWP, which can convert LP light into CP light. Its working wavelength range is 1376-1624 nm and the bandwidth is 248 nm.

FIGURE 3. (A) Transmission amplitude and (B) phase variations in the x-and y-direction when x-LP light and y-LP light are incident on the QWP. (C) Ellipticity (θ = 45°), and transmission amplitude in the x-and y-direction when p-LP light is incident on the QWP. (D) Ellipticity variations with the different polarization directions of the incident light.
In order to verify the performance of our proposed QWP, we use the ellipticity χ to evaluate the transmitted light. As shown in Fig. 3C, when LP light along the p-direction (p-LP light) is incident on the metasurfaces (the angle θ is 45°), χ can be expressed by (6).
where and represent the transmission amplitude in the x-and y-direction, respectively. and represent the transmission phase in the x-and y-direction, respectively. = 1 and = -1 represent perfect right-handed circularly polarized (RCP) light and left-handed circularly polarized (LCP) light, respectively. We can observe that in the wavelength range from 1376 nm to 1624 nm, when the incident light is at a 45° angle to the x-axis, the ellipticity of the transmitted light is greater than 0.9. This means that LP light is converted into nearly perfect RCP light after it is incident on the metasurfaces we designed. Fig. 3D shows the ellipticity of the transmitted light under different incident angles. It can be seen that when the incident light is at an angle of 45° or -45° with the x-axis, the transmitted light is RCP light or LCP light, respectively. When the polarization angle is other angles, the transmitted light is converted into elliptically polarized light. For the QWP we designed, it can also convert CP light into LP light. The principle is the same as that of LP light into CP light. We will not repeat it here.

B. HWP ANALYSIS DISCUSSION
When the x-LP light and the y-LP light are incident on the QWP we designed, the simulated transmission amplitude and transmission phase changes are shown in Fig. 4A and B, respectively. The simulated wavelength range is 1300-1800 nm. Through simulation calculation, we can find that for two orthogonally polarized lights incident on the metasurface, the transmission amplitude in the wavelength range of 1411 nm to 1584 nm is greater than 83%. At the same time, the phase difference between the two orthogonally polarized lights is about . The results of the simulation are consistent with our theory, so we can get a broadband, high-efficiency HWP. Its working wavelength range is 1411-1584 nm and the bandwidth is 173 nm.

FIGURE 4. (A) Transmission amplitude and (B) transmission phase variations in the x-and y-direction when x-LP light and y-LP light are incident on the HWP. (C) Transmission amplitude in the x-and y-direction when p-LP light is incident on the HWP, and (D) calculated AoLP and DoLP.
Further, we use the angle of linear polarization (AoLP) and the degree of linear polarization (DoLP) to evaluate the performance of the HWP proposed in this article. AoLP represents the angle between the polarization direction of LP light and the x-axis. DoLP describes the linearity of transmitted light, and the DOLP of perfect linearly polarized light is equal to 1. Here, we allow an error of 0.1.
The LP light along the p-direction is incident on the metasurfaces we designed, as shown in Fig. 4C, where the angle between the p-and x-axis is 45°. The AoLP and DoLP are calculated according to (7) and (8) are shown in Fig. 4D. We can observe that in the wavelength range of 1411-1584 nm, the transmission amplitudes of p-LP incident light in the x-and y-direction are approximately equal, and the simulated DoLP is greater than 0.9. This shows that after LP light is incident on the metasurfaces we designed, it is still nearly perfect LP light. Within the designed bandwidth, the simulated AoLP is 135°, indicating that the 45° LP light rotates 90° around the x-axis. The result verifies that the metasurfaces we designed can realize the function of HWP. For LP light incident in any polarization direction (assuming the angle of the polarization plane is θ), according to the characteristics of the designed HWP, we can easily know that the transmitted light will rotate around the x-axis by an angle of 2θ. According to this feature, we can adjust the polarized light to any direction we need

C BIFUNCTIONAL METASURFACES
Here, we performed simulation calculations on the proposed bifunctional metasurfaces. The bifunctional polarization regulator we designed is a three-layer continuous structure metasurfaces, which can avoid functional interference between unit structures. The overall transmission amplitude exceeds 83% when the incident wavelength is 1550 nm. The upper structure is equivalent to the QWP we designed, which realizes the conversion of CP light to LP light. The structural design of the bottom layer realizes the deflection of light. Fig. 5A and B depict the transmission amplitude of each three-layer structure unit under the incidence of x-LP light and y-LP light, respectively. The transmission amplitude of each unit structure is different, which is caused by the different sizes of the selected silicon nano-antennas. For x-LP light incidence, the lowest transmitted amplitude is 0.88, and for y-LP light incidence, the lowest transmitted amplitude is 0.73. Each structural unit we designed has a high transmission amplitude for incident light. same, that is, the phase delay is basically zero. This indicates that the transmitted light is converted into LP light. Fig. 5D depicts the distribution of the transmission phase in the x-and y-direction when 45° LP light is incident on the metasurfaces. The simulation shows that the transmitted light has a phase delay approximately equal to /2 in the propagation direction. Therefore, we can realize the conversion of LP light to CP light.   . 6A depicts the electric field distribution of LP light transmitted when CP light is incident. It can be observed that the propagation direction of the transmitted light is deflected by an angle of θ. Fig. 6B shows the deflection angle of the transmitted light and the energy distribution in this direction. The transmission angle obtained by the simulation is 15.8°. According to the generalized Snell's law, we can get = arcsin ( /( )). N is the number of unit cells contained in a super unit cell. The calculated angle is 16.1°, and the simulation result is relatively close to the theoretical calculation result. In addition, we incident 45° LP light onto the designed metasurfaces, and the transmitted light electric field distribution is shown in Fig. 6C. We can see that the transmitted CP light is deflected. The transmission angle is also 15.8° as shown in Fig. 6D. The above simulation results show that we have successfully designed a high-efficiency bifunctional metasurface.

IV. CONCLUSION
We proposed broadband and efficient transmissive QWP and HWP, and further designed a high-efficiency bifunctional metasurfaces. The QWP is a double-layer metasurfaces composed of rectangular silicon and silicon dioxide layers, with a bandwidth of 1376-1624 nm. HWP is a three-layer metasurfaces composed of two QWPs, with a bandwidth of 1411-1584 nm. The designed bifunctional metasurfaces adds a refraction layer on the basis of QWP, which can realize the function of QWP and the refraction of transmitted light at the same time. Our design realizes the polarization control of light, which can be used in the manufacture of other optical instruments. This work may contribute to the miniaturization and integration of polarization conversion devices.