GaAs Linear Polarizer with a High Extinction Ratio for Extended Short-Wave Infrared Detection

Abstract

Metasurfaces have shown an unprecedented ability to modulate electromagnetic waves at subwavelength scales, especially polarized optical metasurfaces, applied for imaging, navigation and detection. In this work, a kind of efficient all-dielectric diatomic metasurface for polarization and phase changing, consisting of a pair of GaAs nanopillar and nanocube, is proposed. By adjusting the unit cell structural parameters, the polarization state can be controlled and adjusted at the short-wave infrared (SWIR) band (1~3 μm). At the wavelength of 2125 nm, the maximum transmission efficiency, the extinction ratio and the linear polarization degree can reach 93.76%, 40.99 dB and 0.99, respectively. Overall, this all-dielectric diatomic metasurface has broad application potential in extended SWIR polarization detection.

1. Introduction

The short-wave infrared (SWIR) band (1~3 μm) is one of the “atmospheric transmission windows”; therefore the detector working in this band can obtain more radiation energy from the target. In addition, the SWIR detector can operate at room temperature, avoiding an expensive and sizable refrigerator [1] and its imaging effect is as good as the reflective imaging of visible light. Moreover, in addition to its capability to penetrate through the smoke for imaging [2], SWIR can detect the details that the mid-wave and long-wave infrared detection lack. In addition, as the information can be carried on the state of polarization, polarization detection can expand the amount of information. Polarizers have a broad application in imaging, navigation and detection [3,4,5]. Optical systems in practical polarization detection applications are moving towards miniaturization and multifunctional integration. However, traditional optical polarizers are usually bulky. Furthermore, the working band for 1–1.7 μm is exploited and the extended SWIR (1.7~2.5 μm) polarizer is not to be covered yet [6]. Although there have been reports indicating that subwavelength metal grating structures based on surface plasmon resonance can achieve broadband and high transmission polarization converters in the terahertz range, these single -layer metal -grating-based polarizers exhibit high optical losses in the visible and near-infrared wavelength regimes, which may result in low transmittance of the polarizer [7,8,9,10]. Fortunately, the all-dielectric metasurface relying on the Mie resonance effect can easily solve the problem of high optical loss [11].

Optical parameters such as phase, amplitude and polarization state of incident light can be controlled by designing arrays of nanostructures, which makes it possible for metasurfaces to manipulate the properties of light in the subwavelength range. On one hand, ${\mathrm{S}\mathrm{i}\mathrm{O}}_2$ has ultralow loss in the short-wave infrared band and also has a low refractive index. On the other hand, as a typical III-V compound semiconductor, GaAs has a high refractive index at the SWIR band. At the same time, GaAs has a band gap at 1.441 eV and a cut-off wavelength of around 861 nm, which is far away from our operating wavelength; therefore, GaAs has low transmission loss at the SWIR band [12]. In addition, GaAs can be easily fabricated by electron beam lithography (EBL) and dry etching. Moreover, as GaAs is based on a 6.1 Å family InAs/GaSb/AlSb material system that is the same as existing type-II superlattice materials, in-situ growth can be achieved. Therefore, this GaAs-based linear polarizer can be utilized for subsequent superlattice InAs/GaSb/AlSb integrated polarization detectors. Considering the extinction coefficient, the operating wavelengths of different materials should be selected to obtain high transmission efficiency. $\mathrm{S}\mathrm{i}{\mathrm{O}}_2$ and GaAs are selected as metasurface materials in our design. The polarization-dependent component can be processed by mature technologies of GaAs materials growing on $\mathrm{S}\mathrm{i}{\mathrm{O}}_2$ substrates using molecular beam epitaxy (MBE) equipment [13]. Recently, according to a report, the incorporation of multiple meta-atoms in a single unit cell is expected to provide more degrees of freedom for metasurfaces [14]. Previous research has also shown that using diatomic metasurfaces can obtain applications such as polarization perfect absorption and vectorial holographic imaging [15,16]. At present, some scholars have studied metasurfaces designed with rectangular nanopillars and these optical components have functions such as polarization, beam splitting and phase manipulation with superior performance [17,18,19,20,21]. In addition, metasurfaces with controllable polarization angles also have applications in information encryption and anticounterfeiting identification [22,23].

The extended SWIR (1.7–2.5 μm) polarizer has not been explored and only the working band of 1–1.7 μm is covered [24]. Thus, this paper presents a state-of-the-art general implementation of nanoscale linear polarizers based on all-dielectric GaAs diatomic metasurfaces for applications in the SWIR (1–3 μm). A single unit cell of the linear polarizer comprises a nanocube polarization-change meta-atom (PCM) and a nanopillar phase-shift meta-atom (PSM). By adjusting the rotation of the PCM, the size of the PSM and the spatial distance of the PCM and PSM with appropriate parameters, they can work together to become a linearly polarized component with high transmittance, high extinction ratio and controllable angle of polarization.

2. Structure and Theoretical Analysis

The desired metasurface structure (polarizer) shown in Figure 1a consisted of the period unit cell. It can change random light into linear polarized light with a desired direction, such as 0°, 45° 90° and 135°. The unit cell comprises one PCM and one PSM, made of GaAs, which are placed on a $\mathrm{S}\mathrm{i}{\mathrm{O}}_2$ substrate. PCM and PSM are placed on the diagonal line of unit cells, respectively. A PCM that is GaAs material with a subwavelength-thick nanopillar can functionally operate as truncated waveguides allowing certain modes with polarization-dependent effective indices to propagate. By carefully designing the lateral dimensions and orientation of the PCM, π phase difference between two orthogonal polarizations can be obtained. Therefore, it is possible for PCM to achieve a metamaterial half-wave plate with the function of linear polarization conversion. At the same time, PSM plays an important role in improving the efficiency and accuracy of polarized light transmission, which can be used for large-scale and high-precision phase modulation while maintaining the polarization state of incident light. In addition, by combining PSM with PCM into one unit cell, this structure can not only adjust the major polarization angle of the outgoing light with quite small steps (<1°), but also can hold the promise of providing a greater degree of freedom in metasurface design. Furthermore, compared to existing metamaterial structures [9,12,18], our diatomic metasurface based on GaAs has a comparative advantage in transmittance efficiency. In addition to that, by carefully designing a diatomic metasurface composed of PSM and PCM, there are broad potential applications in the integration of waveplates and some optical components, such as lenses, beam splitters, parabolic reflectors and so on.

A transfer matrix can represent any optical device as:

$$M=\left(\begin{array}{cc}{J}_{XX}& J_{XY}\\ J_{YX}& J_{YY}\end{array}\right)$$

(1)

where $J_{XX}$ and $J_{YY}$ are the complex scattering coefficients of incident light polarized along the two axes of the element atom, respectively, determined by the size of the element atom along the two axes with a confirmed material. The complex $J_{XY}$ represents the conversion coefficient by which the optical device converts the y-polarization component of the incident light into the x-polarization component. The optical device can only transfer the x(y) polarization component in the incident light to the x(y) polarization component in the outgoing light. Thus, $J_{XY}$ = $J_{YX}$ = 0. The complex number J can also be expressed as a combination of transmission amplitude and phase. ${|t}_{xx}\left|{\left(\right|t}_{yy}\right|$) and ${\phi }_{xx}$(${\phi }_{yy}$) represents the transmission amplitude and phase of light polarized along the x(y) axis. Thus, the metasurface Jones matrix of symmetrical structures can be expressed as:

$$M_1=\left(\begin{array}{cc}\left|t_{xx}\right|e^{i{\phi }_{xx}}& 0\\ 0& \left|t_{yy}\right|e^{i{\phi }_{yy}}\end{array}\right)$$

(2)

As we know, by applying an angle of rotation α relative to the x-axis of the optical device, the Jones matrix can be described as:

$$M_2=\left(\begin{array}{cc}cos\alpha & -sin\alpha \\ sin\alpha & cos\alpha \end{array}\right)\left(\begin{array}{cc}\left|t_{xx}\right|e^{i{\phi }_{xx}}& 0\\ 0& \left|t_{yy}\right|e^{i{\phi }_{yy}}\end{array}\right)\left(\begin{array}{cc}cos\alpha & sin\alpha \\ -sin\alpha & cos\alpha \end{array}\right)$$

(3)

Due to the rotationally symmetrical structure of the cylindrical PSM, the Jones matrix of PSM can be described by Equation (1). For the polarized light transmission, the amplitude of cubical PCM along the x-axis and y-axis is equal and the phase difference between the x-direction and the y-direction is π. Thus, ${|t}_{xx\_PCM}|=|t_{yy\_PCM}|$, ${\phi }_{yy\_PCM}-{\phi }_{x{x}_{PCM}}=\pi$, the Jones matrix of PSM and PCM can be simplified to:

$$M_{\mathrm{P}\mathrm{S}\mathrm{M}}=\left(\begin{array}{cc}\left|t_{xx\_PSM}\right|e^{i{\phi }_{xx\_PSM}}& 0\\ 0& \left|t_{xx\_PSM}\right|e^{i{\phi }_{xx\_PSM}}\end{array}\right)$$

(4)

$$M_{PCM}=\left(\begin{array}{cc}\left|t_{x{x\_}_{PCM}}\right|e^{i{\phi }_{x{x\_}_{PCM}}}({cos}^2\alpha -{sin}^2\alpha )& 2\left|t_{x{x\_}_{PCM}}\right|e^{i{\phi }_{x{x\_}_{PCM}}}cos\alpha sin\alpha \\ 2\left|t_{x{x\_}_{PCM}}\right|e^{i{\phi }_{x{x\_}_{PCM}}}cos\alpha sin\alpha & \left|t_{xx\_PCM}\right|e^{i{\phi }_{xx\_PCM}}({sin}^2\alpha -{cos}^2\alpha )\end{array}\right)$$

(5)

Because this metasurface integrates two meta-atoms in a single unit cell, the Jones matrices of PSM and PCM can be added directly. The influence of PCM and PSM on the transmission amplitude and phase of the light along the x-axis polarization is the same. Thus, the Jones matrix of the diatomic metasurface under the condition of $\left|t_{xx\_PSM}\right|=\left|t_{xx\_PCM}\right|$, ${\phi }_{xx\_PSM}={\phi }_{xx\_PCM}$ can be expressed as:

$$M_{UC}=M_{PSM}+M_{PCM}=2\left|t_{x{x\_}_{PSM}}\right|e^{i{\phi }_{x{x\_}_{PSM}}}\left(\begin{array}{cc}{cos}^2\alpha & sin\alpha cos\alpha \\ sin\alpha cos\alpha & {sin}^2\alpha \end{array}\right)$$

(6)

From Equation (6), it can be seen that this diatomic metasurface can not only realize the function of a polarizer; if the design here is α=0°, the matrix of the $M_{UC}$ is $\left(\begin{array}{cc}1& 0\\ 0& 0\end{array}\right)$ and this metasurface can be regarded as a horizontal linear polarizer. If α = 45°, the matrix part of the $M_{UC}$ is $\frac{1}{2}\left(\begin{array}{cc}1& 1\\ 1& 1\end{array}\right)$ and this metasurface can be seen as a linear polarizer of +45°.

We know that when the incident light is elliptically polarized, the Jones matrix is $J_{in}=\left(\begin{array}{c}{A}_{ox}{e}^{i{\phi }_{ox}}\\ A_{oy}{e}^{i{\phi }_{oy}}\end{array}\right)$. After the incident light passes through a diatomic metasurface, the Jones matrix of the transmitted light can be expressed as:

$$J_{out}=M_{\mathrm{U}\mathrm{C}}{J}_{in}=2\left|t_{x{x\_}_{PSM}}\right|e^{i{\phi }_{x{x\_}_{PSM}}}\left(A_{ox}{e}^{i{\phi }_{ox}}cos\alpha +A_{oy}{e}^{i{\phi }_{oy}}sin\alpha \right)\left(\begin{array}{c}cos\alpha \\ sin\alpha \end{array}\right)$$

(7)

By analyzing the equation of $M_{UC}$ and $J_{out}$, it can be concluded that a suitable PSM and PCM combination can be equivalent to a linear polarizer with a polarization angle equal to the rotation angle of the PCM. The schematic diagram of the transmission matrix is shown in Figure 2.

3. Design and Numerical Simulation

As described above, PCM and PSM are made of GaAs and placed on a $\mathrm{S}\mathrm{i}{\mathrm{O}}_2$ substrate. The finite-difference time-domain (FDTD) method is utilized to construct and optimize an all-dielectric diatomic metasurface structure for achieving a linear polarizer with a high extinction ratio suitable for extended SWIR detection. A mesh accuracy of two is chosen in the simulation and periodic boundary conditions are applied in the x- and y-directions. A perfectly matched layer with a thickness of 18 is used in the z-direction.

3.1. Determine the Operating Wavelength

Here, the working wavelength ranges from 2100 nm to 2200 nm to verify its function at extended SWIR detection. Following the principles of metasurface structure, the period of a single unit cell should be approximately half the wavelength. Too large a unit cell period would affect the transmittance and other properties of the metasurface. Nevertheless, too small a unit cell period would not only cause the near-field coupling effect between PCM and PSM but also be unfavorable for actual processing. Therefore, in this simulation, the period of a single unit cell is 1500 nm (P = 1500 nm). The PSM and PCM are located at the diagonal of the unit cell. Thus, the center-to-center distance S = $750/\left(\sqrt{2}/2\right)$ = 1060.66 nm.

The length, width and height of the PCM are iteratively optimized. Optimal results are obtained at the operating wavelength. The heights of PCM and PSM are chosen as 500 nm (H = 500 nm). The PCM length and width are designed to be 600 nm and 378 nm(L = 600 nm, W = 378 nm). Appropriate structural parameters of the PCM will make the transmittance of the polarizer reach the peak value. Here, we fix the PSM radius to 245 nm and we will continue to discuss the influence of the PSM radius on the metasurface polarization and phase in Section 3.2.

To obtain the selected operating wavelength, the incident light source was selected from 2100 nm to 2200 nm and the parameters scanned the effect of the polarization angle of the light source from 0° to 180° on their transmittance, as shown in Figure 3a. When the linear polarizer is near the wavelength of 2125 nm, the contrast between the transmittance and the polarization angle of the incident light source is relatively large. Therefore, the 2125 nm light source is selected as the incident light source in the follow-up work to design a higher-performance linear polarization device.

To explore the effect of the rotation direction of the PCM on the function of the polarizer, in the simulation, we designed metasurfaces in four directions. As shown in Figure 3, the maximum transmittance (the red area in the figure) and the minimum transmittance (the purple area in the figure) of the linear polarizer change continuously with the change in the rotation of the PCM. Different PCM rotation angles cause the linear polarizer we designed to achieve different modulation effects on the incident light source ${\mathsf{\theta }}_{in}$ with different polarization angles. As far as polarization regulation is concerned, the PCM rotation angle of 0° can be taken as an example in Figure 3a. The linear polarizer achieves the maximum and minimum transmittance when the polarization angles of the light source are 0° and 90°, respectively, and it can be regarded as a horizontal linear polarizer. This result is in line with our previous theoretical analysis.

3.2. Performance Evaluation with the Transmittance and Extinction Ratio

The change in the PSM radius can not only tune the polarization performance of the metasurface linear polarizer but can also have a great influence on the phase of the metasurface. Based on the previous numerical simulation parameters, the rotation angles 45° and 135° of the PCM are taken as examples as follows and the impact of the change in the PSM radius and the incident polarization angle on polarizer performance for the metasurface is investigated under the wavelength of the light source at 2125 nm.

As shown in Figure 4a,c, the change in transmittance is largest when the PSM radius is around 245 nm, which maintains the performance of the polarizer optimized. The transmittances obtained under incident polarization angles 45° and 135° in the above two figures also show that PCMs with different rotation angles of 45° and 135° have reversed modulation effects. In Figure 4b,d, considering the loss, the characteristics of polarizers are relatively consistent with Malus’ Law ($\mathrm{I}=\mathrm{I}\left(0\right){cos}^2\theta$).

Figure 5 shows that the transmittance and extinction ratio of the metasurface linear polarizer change with the PSM radius. The maximum (minimum) transmittance Maxt (Mint) here is defined as the transmittance obtained when the polarization direction of the incident light is orthogonal (paralleled) to the long axis of the PCM and the extinction ratio is defined as $\mathrm{E}\mathrm{R}=10\mathrm{*}\mathrm{l}\mathrm{g}(\mathrm{M}\mathrm{a}\mathrm{x}\mathrm{t}/\mathrm{M}\mathrm{i}\mathrm{n}\mathrm{t})$. As illustrated in Figure 5, it is shown that when the PSM radius is 245 nm, the performance of the metasurface linear polarizer is optimal. When the PCM rotation angle is 45° (Figure 5a) and 135° (Figure 5b), the maximum transmittance can reach 93.83% and 93.76%, respectively, and the extinction ratio is up to 34.487 dB and 40.99 dB, respectively. However, the small size of meta-atoms will carry some difficulties in fabrication processing. Moreover, in Figure 5, it can also be found that the performance of the polarizer becomes very poor when the PSM radius is larger than 260 nm and the minimum transmittance exceeds the maximum transmittance at this time. Therefore, it is necessary to consider the trade-off among the polarization performance, component size and difficulties in fabrication comprehensively to select the appropriate radius of PSM. In addition, the near-field coupling affects the transmittance and polarization responses of the PSM and PCM. As the radius of the PSM increases, mutual near-field coupling between the PSM and the PCM enhances. Thus, the reasonable unit cell size for the metasurface should be designed to obtain polarization states with high transmittance.

3.3. Performance Optimization with the Major Polarization Angle and the Degree of Linear Polarization

The polarization ellipse is an effective and direct method to describe the polarization state of transmitted light. The performance of the metasurface linear polarizer can be evaluated by the polarization state of the transmitted light. The impact of the PSM radius on the transmitted polarized light is explored at the light wavelength of 2125 nm. Here, the PCM rotation angles are still selected as 45° and 135° and the polarization angle of the incident light is 0°. To understand the impact of PSM radius on the linear polarizer more directly, the range of PSM radius increases from 230–270 nm to 230–300 nm. To explore the impact of the PSM radius on the transmitted light, the change in the major polarization angle and the degree of linear polarization of (DOLP), the transmitted light is illustrated by the polarization ellipse in Figure 6. The major polarization angle is defined as the angle between the horizontal direction and the major axis of the polarization ellipse, which describes the polarization direction of transmitted light and also indicates the manipulation of the polarization angle of the transmitted light for the linear polarizer. Herein, the degree of polarization (DOP) that represents the proportion of polarized light in the total light intensity is used to quantitatively analyze the polarized and nonpolarized components of light. The DOP can vary from 0 (natural light) to 1 (fully polarized) and the DOLP, which represents the purity of linearly polarized light, of the perfect linearly polarized light is greater than 0.9. This DOLP can be calculated by $\mathrm{D}\mathrm{O}\mathrm{L}\mathrm{P}=1–2\mathrm{*}\mathsf{\gamma }/(1+{\mathsf{\gamma }}^2)$, where γ represents the ratio of the major axis to the minor axis of the polarization ellipse.

Figure 6a,b are polarization ellipses as a function of the PSM radius. The relationships between the major polarization angle and DOLP at the PCM rotation angles of 45° and 135° are shown in Figure 6c,d, respectively. It can be seen that when the PCM rotation angle is 45° (Figure 6c) and 135° (Figure 6d), the main polarization angle of the linear polarizer changes from 45° to −45° and from −45° to 45° as the PSM radius increases. For the combination of PSM and PCM, the major polarization angle of the outgoing light can be adjusted from 45° to −45° with quite small steps less than 1°, which can bring high precision polarization modulation to the incident light. In addition, when the PCM rotation angle is 45° (135°) and the PSM radius is 245 nm (288 nm), the major polarization angle is 45.02° (46.14°) and the degree of linear polarization is 0.9933 (0.9942). In this situation, the polarization effects are almost the same for both PCM rotation angles of 45° and 135°. From the above phenomenon, it can be concluded that the polarization effect of the polarizer can also be modulated by the changing radius of the PSM.

This metasurface can not only alter polarization and phase modulation by changing the rotation angle of the PCM but also achieve the same effect by controlling the radius of the PSM. Moreover, the PCM and PSM can work together with appropriate dimensions to provide a large degree of freedom for the metasurface, which can become a linearly polarized component with high transmittance, high extinction ratio and controllable polarization angle.

SWIR detector is a type of detector that can detect the near-infrared and short-wave infrared bands. Common infrared detection materials include InGaAs, InSb and Type-II superlattices. InGaAs is a III-V semiconductor with good optoelectronic conversion performance and response speed. Its bandgap energy ranges from 0.75 to 0.95 eV, which allows it to be used for detecting the near-infrared and SWIR bands. The response range of InGaAs detectors is typically between 0.9 and 1.7 μm, making it useful for many applications in military, medical, industrial and scientific research fields. InSb is a III–V semiconductor with a smaller bandgap energy range from 0.17 to 0.23 eV. Its response range is between 1 and 5 μm, making it suitable for detecting SWIR and mid-wave infrared bands. InSb detectors exhibit better performance at high temperatures due to their higher carrier mobility. In addition, there is a new type of material called “type II superlattice”, which is composed of multiple different semiconductor materials stacked together. Unlike InGaAs and InSb, the bandgap energy of type II superlattice materials can be adjusted by designing and controlling the lattice structure, allowing for detection in a wider range of infrared bands. Furthermore, type II superlattices have lower noise and higher temperature operating capabilities. In summary, InGaAs and InSb are commonly used detection materials in SWIR detectors, exhibiting excellent performance in different bands. Type II superlattices represent a new and promising detection material with the potential to detect in a wider range of infrared bands, but further research and development are still needed [25,26,27].

4. Conclusions

In this paper, a type of single-layer, all-dielectric and diatomic metasurface composed of GaAs-based PCM and PSM operating in the SWIR atmospheric window (1–3 μm) is proposed. Using theoretical analysis and Lumerical FDTD numerical simulation, the changes of transmittance, extinction ratio and DOLP with the operating wavelength, incident polarization angle, PSM diameter and PCM rotation angle are systematically studied. The unit cell PCMs with different rotation angles of 45° and 135° are numerically simulated. The results show that this diatomic metasurface can be used as a linear polarizer whose polarization angle is related to the PCM rotation angle and the PSM radius. The maximum value of transmittance, the extinction ratio and the DOLP for this polarizer can reach 93.76%, 40.99 dB and 0.99, respectively. Furthermore, by adjusting the rotation of the PCM, the size of the PSM and the spatial distance of the PCM and PSM with appropriate parameters, the phase-tuning range of the incident light can be expanded to achieve varieties of wavefront shaping and this metasurface can be potentially applied to extend SWIR polarization detection.