1. Introduction

The polarization of light contains a lot of information that cannot be directly detected, which has attracted widespread attention from researchers [1,2]. The polarization imaging ideas are mainly divided into three categories: division of amplitude, division of the aperture [3], and division of the focal plane [4–6]. The technology of the division of the focal plane, where the metasurface capable of collecting specific polarization signals and the photosensitive element of the detector are directly integrated together, has quickly become an interesting research direction due to its advantages such as real-time imaging and system stability. Meanwhile, one of the core technologies of the compact full-polarization camera is the development of the circular dichroic metasurface with the large bandwidth, the high extinction ratio (ER) and the high circular dichroism (CD). The extinction ratio and the circular dichroism correspond to the most essential polarization perception, and the effective bandwidth affects the strength of the signal in the signal-to-noise ratio of the imaging system.

In the past ten years, the circular dichroic waveplate based on the metasurface that has a completely different modulation effect on RCP and LCP have developed rapidly [7–22]. The design ideas are mainly divided into two categories: the chiral geometric structure assembly method [23–27] and wave plate combination method [28–30]. The chiral geometric structure assembly method mainly uses a large amount of computational power to scan the parameter groups of the chiral cells such as z-shaped ones, which is an empirical design approach. The wave plate combination method mainly draws on the combination of a quarter wave plate and a 45-degree linear polarizer in traditional optics. More than 80% of the circular dichroism and an ultra-high extinction ratio of nearly 35:1 have been achieved based on the nature-inspired chiral metasurface using the wave plate combination method [28]. However, there are relatively few research reports on polarization photodetectors that have already integrated the circular dichroic wave-plate. In 2012, Afshinmanesh [15] proposed a silicon (Si) photodetector that integrates a two-dimensional helical plasmonic microstructure, and the extinction ratio of the linearly polarized and circularly polarized states is 25 and 1.13 at 830 nm operation wavelength, respectively. In 2015, Li [7] prepared an ultra- compact circularly polarized Schottky photodetector whose photosensitive unit cell is a Z-shaped metal block, and the quantum efficiency and circularly polarized extinction ratio are 0.2% and 3.4:1, respectively.

In this article, we numerically propose the 0-,45-, 90-and -45-degree linear polarizer photodetector, and they are composed of the sio2 support layer deposited on the detector buffer layer and the silicon grating with the specific orientation. The external quantum efficiency of the linearly polarized photodetectors in TM and TE modes is 0.003 and 0.52, respectively. In addition, the circular polarization photodetectors based on the hexagonal lattice Si metasurface can be approximated as the combination of the EQ and the MQ for the RCP mode and the MQ for the LCP mode. The fully polarized sensing large Stokes pixel composed of three pairs of orthogonal polarization detection pixels with small errors can almost accurately obtain arbitrary polarization information of the incident light.

2. Structure and analysis

It is shown in Fig. 1(a) that the geometric parameters of the six proposed InGaAs/InP photodetector integrating the Si metasurface modulating specific polarization are specified respectively. The pixel P1, P2, P3, P4, P5 and P6 represent the 0-degree, 90-degree, -45-degree, 45-degree polarizers, the left and right circular dichroic device, respectively. The pixel P2 can be rotated by 90 °, 45 °, and −45 ° to obtain pixels P1, P3, and P4. The P5 can be transformed into P6 by performing a mirror image transformation on the YZ cross section. As shown in Fig. 1(b), The InGaAs/InP detector chip is a typical PIN structure, consisting of the p-doped 500 nm thick InP contact layer, a 2 ${\mathrm{\mu} \mathrm{m}}$ thick InGaAs absorption layer, the n-doped 500 nm thick InP contact layer, and the InP substrate. Wet etching removes all InP substrates, grows 3 ${\mathrm{\mu} \mathrm{m}}$ thick sio2 and 650 nm amorphous silicon, and then uses Electron-beam lithography technology to transfer the patterns in the silicon layer. The incident light enters the metasurface from the air above. Figure 1(c) shows the period and width of the 0-degree polarizer. Figure 1(d) shows the top view of the unit cell of the pixel P5. The refractive index of the SiO2 layer and InP in the near infrared are set to 1.46 and 3.15, respectively. The dielectric constant of the silicon is derived from Ref. [31]. The refractive index of the InGaAs is shown in Table 1. The commercial software comsol multiphysics is employed to analyze the optical properties of these metasurfaces. We use the perfectly matched layer (PML) and the waveguides port as the boundary condition in the z-axis direction. In addition, the periodic boundary condition is applied along the surrounding boundaries, and the S-parameters of the mode are extracted to get the corresponding amplitude and phase information. The transmitted (reflected) light intensities $\textrm{T}(\textrm{R} )$ are obtained by integrating the power flux P over the transmission (reflection) port ${S_1}({{S_2}} )$, and $\textrm{T} = \smallint P \cdot d{s_1}$, $\textrm{R} = \smallint P \cdot d{s_2}$. The absorption rate ${A_{InGaAs}}$ of the InGaAs can be expressed as 1 $- $ (T + R+${Q_{InP}})/I$. Here, I is the incident light power intensity, ${Q_{InP}}$ is the resistance loss of the InP and equals $\smallint j \cdot E{\; }dv$, the j is the body current density and E is the electric field.

 

Fig. 1. (a) shows a schematic diagram of six small pixel unit cells. The P1, P2, P3, P4, P5 and P6 represent 0-degree, 90-degree, -45-degree polarizers, 45-degree polarizers, a left circular dichroic device and a right circular dichroic device, respectively. (b) is the front view of the metasurface. ht = 500 nm, hi = 2000nm, hb = 500 nm, hs = 3000 nm, h1 = 650 nm. Figure 1(c) is the top view of the pixel P2. P0 = 880 nm. a0 = 480 nm. (d) is the top view of the unit cell of the pixel P5. dh = 54 nm, a1 = 390 nm, b1 = 240 nm, b2 = 127 nm. k2 = b1/a1, k2 = b2/(a1-b1). A-plane is composed of the red dashed line and the z-axis. The slit corresponding to the width dh is named Tunnel A.

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Table 1. The refractive index of the InGaAs: n-i*k

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The design tunability of device by scaling up or down the dimensions is very important to follow. The effects of different parameters of the structure on the performance of different polarizations in the wavelength range of 1.3–1.8 ${\mathrm{\mu} \mathrm{m}}$ are firstly investigated. When one parameter is studied, the remaining parameters are consistent with those in Fig. 1. Figure 2(a) shows the effect of the side length a1 of the pixel P5 on the absorption of LCP and RCP incidences, and the absorption of the device for LCP is greater than 50% in the 1.3-1.6 ${\mathrm{\mu} \mathrm{m}}$ wavelength range. It is seen that the resonant valleys of the RCP polarization shift sensitively towards longer wavelengths with the increased a1. Figure 2(b) shows the effect of the thickness of the amorphous silicon on the absorption of LCP and RCP. There are both one slight change in the absorption spectrum in the LCP and RCP incidences. In contrast to the effect of h1, the thickness of InGaAs absorption layer hi plays a more dominant role on the operating bandwidth of the absorption dichroism. As the parameter hi decreases, the bandwidth of the absorption valley of the RCP increases, but unfortunately, the absorption of the LCP decreases significantly. The trade-off phenomenon between bandwidth and dichroism is very similar to the concept of the response bandwidth product of the PIN detectors. Figure 2(d) shows the absorption spectra of RCP and LCP both remain almost unchanged, which may indicate that the upper silicon metasurface and the lower PIN detection structure are decoupled. The absorption of the LCP does not vary with the scaling factor K1, as shown in Fig. 2(e). On the contrary, the absorption valley of the RCP that is accompanied by a decrease in effective bandwidth redshifts with the increase of K1. Figure 2(f) shows that the absorption valley of the RCP redshifts with the increase of the scaling factor K2, and the effective bandwidth increases. In addition, Fig. 2(g-i) show the modulation effect of the grating in the pixel P2 on linearly polarized light (LPL). Figure 2(g) shows that the modulation of the period p0 is very weak, but the manipulation behavior of the grating width (thickness) in Fig. 2 h (i) is relatively complex. Figure 2(h) shows the absorption valley of the TM light widens and redshifts as the grating width a0 increases, and the severe absorption attenuation also exhibits in the case of the specific TE wavelength incidence. This phenomenon means that the width of the grating must be accurately controlled during the process of processing, otherwise there will be no high absorption extinction ratio peak corresponding to good TM absorption valley and TE absorption peak. Figure 2(h) shows the absorption valley of the TM light narrows down and redshifts as the grating thickness h0 increases. For a qualified polarization detector, it should have a high response to the specific polarization (absorption > 60%), but the lowest response to the orthogonal polarization modes in order to guarantee a large extinction ratio. Finally, an optimal circular polarization detector whose a1, h1, hi, hs, k1, and k2 are 390 nm, 650 nm,2 µm,3 µm,0.84 and 0.61, respectively, is achieved.

 

Fig. 2. Absorption spectra of the InGaAs layer of different polarized incident lights. Transmission spectra (RCP and TM: solid line, and LCP and TE: dot dashed line) as a function of (a) a1; (b) h1; (c) hi; (d) hx; (e) k1; (f) k2; (g) p0; (c) a0; and (e) h0. (a-f): Absorption spectra for the pixel P5. (g-i): Absorption spectra for the pixel P2.

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The appearance of the circular dichroism is mainly caused by the chiral dislocation formed by the displacement of two mirrored isosceles trapezoids in opposite directions. Therefore, it is necessary to decompose the pixel P5 in Fig. 1(a) into two independent modules: the hexagonal lattice dielectric metasurface composed of the amorphous silicon and the sio2 substrates, and the non-polarized selective PIN detector that only perceives light intensity. Figure 3 studies the physical mechanism of the high circular dichroism of transmission existing in separate hexagonal lattice dielectric metasurface. Figure 3(a) shows electric field energy spectrum in the case of circular polarization incidence, and the energy peaks are both at 1550 nm wavelength. The electric field energy can be calculated by formula $\smallint |E |\mathrm{\Delta }V/\smallint |{{E_0}} |\mathrm{\Delta }V$, where the integral range is the volume occupied by two dislocation isosceles trapezoid blocks, and ${E_0}$ is the electric field of the incident light. The origin of the large circular dichroism can also be verified by a simple inspection of the mode profile at the three different cross sections on Si metasurface. The illustration in Fig. 3(a) is the electric field intensity distribution diagram of the XY section corresponding to the thickness of 1/4, 1/2 and 3/4 of the amorphous silicon. The electric field energy localization under RCP incidence is much larger than that under LCP incidence, which is consistent with the two energy peaks in Fig. 3(a). Meanwhile, the region with the higher electric field appears in Tunnel A in the case of the 3/4 and 1/4 cross-sections under RCP incidence, and almost all energy is compressed in the air gap surrounded by the silicon on both sides. The physical image is very matched with the FP cavity composed of a high -low -high refractive index ternary system. In addition, the multipole moment expansion method is also an effective method to study the optical metasurface [32], which can equate the device with a series of the radiant power sources, such as the electric dipole (ED), magnetic dipole (MD), electric quadrupole (EQ), magnetic quadrupole (MQ), etc. In the calculation of the multipolar decomposition, the total scattering power can be expressed as

 

Fig. 3. (a)The integral of the spatial volume electric field in amorphous silicon of the unit cell of the Si metasurface. 1/4: the XY cross-section of z = 1/4 * h1, 1/2: the XY cross-section of z = 1/2 * h1, 3/4: the XY cross-section of z = 3/4 * h1. Figure 3(b): the multipole expansion in the case of circular polarization (CP) incidence. Figure 3(c, d): The electric field intensity distribution diagram and the current direction distribution diagram of plane A in the case of CP incidence. The white dashed line represents the boundary of amorphous silicon. Figure 3(e, f): The 2D transmission spectrum depending on the width dh of the Tunnel A. A-plane is determined by the red dashed line in Fig. 1(d) and the z-axis.

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Here, P, M, ${Q_{\alpha \beta }}$, ${M_{\alpha \beta }}$ represent scattering from ED, MD, EQ and MQ, respectively. The j represent current density and c is light speed, and $\mathrm{\alpha \;\ and\;\ \beta }$ represents two of the three mutually orthogonal projection directions. Figure 3(b) shows the multipole expansion of the Si metasurface. The device may be manipulated by the bright mode that is composed of a combine of the electric quadrupole and the magnetic quadrupole in the case of the RCP incidence, and controlled by the magnetic quadrupole that is a typical dark mode in the case of the LCP incidence. In addition, it is easy to note that plane A can almost pass through all areas with the strong electric field energy in the illustration of Fig. 3(a), which includes the Tunnel A and the energy circle at the center of two isosceles trapezoids. Figure 3(c, d) shows the distribution diagram of the electric field intensity and the electric current direction in the CP incidence. For the RCP incidence, the electric field is mainly localized in the air gap surrounded by silicon medium on both sides, and there are two standing wave nodes with different strengths in the z-direction. Due to the weak correlation between the absorption valley of RCP and the thickness of the silicon metasurface as shown in Fig. 2(b), the lateral spacing of the air gap should naturally be considered an important role in the FP resonance. In addition, the two cross marks at the top of Fig. 3(c) represent the counterclockwise rotating current half loop, which indicates that the direction of the equivalent magnetic dipole is shooting out of the screen, and the small black circle in the middle represents the clockwise current loop, whose magnetic current direction is shooting into the screen. The reverse electric (magnetic) dipoles with some spacing is the physical image of a typical electric (magnetic) quadrupole, which is highly consistent with the multipole moment expansion in Fig. 3(b). For the LCP incidence, the electric field energy is also mainly localized in the air gap, and the two opposite rotating current loop indicate that the magnetic quadrupole controls the device. Figure 3(e, f) shows the 2D transmission spectrum depending on the lateral spacing dh of the air gap. There is a strong transmission valley in the RCP incidence, where the resonance wavelength and the width of the Tunnel A are linearly related. The modulation effect of the Tunnel A is very intense, and the resonance wavelength can cover 1400 nm- 1700nm with a size change of the air gap of less than 20 nm. On the contrary, the FP mode supported by air gap can exhibit strong transmission peaks in LCP mode. Obviously, the main source of the large circular dichroism of the silicon metasurface is the strong FP mode resonance in the narrow Tunnel A.

3. Result and discussions

In the preceding sections, we have discussed the extinction capabilities of the corresponding optics components, and we have thoroughly studied the optical properties of the Si metasurface with the sio2 substrate, whose unit cell is formed by the displacement of two mirrored isosceles trapezoid silicon blocks in opposite directions, and we also studied the influence of the geometric parameters of pixels P2 and P5 on the optical absorption of the orthogonally polarized light. In this section, we are more inclined to evaluate the comprehensive quality of the metasurfaces. The sharp corner of the isosceles trapezoid will become a circle in the practical processing process, so it is necessary to estimate the damage degree of the corner radius to the silicon metasurface index. Figure 4(a) shows half of the CD and ER peaks appear at the corner radius of 90 nm and 40 nm, respectively. In addition, the angle of incidence of the metasurface is also crucial for practical use in imaging polarimetry. The incidence angle in the XZ and YZ planes has a significant impact on the Si metasurface, as shown in Fig. 4(b). CD will disappear at an incidence angle of 20 ° in both plane of incidence, and ER will both disappear at 10 °. Figure 4(c) shows the influence of the incident angle on the performance of the Si grating in the pixel P2. Half of the linear dichroism (LD) peak corresponds to an incident inclination angle of 40 °. When the inclination angle of the XZ plane is less than 20 °, it is independent of the linear extinction ratio (LER) of the silicon grating, and when the inclination angle is 40 °, LER decreases by half. The incidence angle of the YZ plane has no effect on the extinction ratio of the silicon grating. A typical evaluation indicator for photodetectors is responsiveness: ${R_i} = \alpha {\eta _{int}}e/\hbar \mathrm{\omega }$, which directly maps the conversion relationship between the optical signals and electrical signals. Here, $\mathrm{\alpha }$ is the optical absorptivity of the detector, ${\eta _{int}}$ is the internal quantum efficiency, which is generally 100% by default in photovoltaic devices without gain, ${\eta _{ext}} = \mathrm{\alpha }\ast {\eta _{int}}$ is the external quantum efficiency, e is the elementary charge, $\hbar $ is the reduced Planck constant, and $\mathrm{\omega }$ is the angular frequency. Figure 4(d) shows that the external quantum efficiency of the pixel P2 is 0.002 and 0.52 in TM and TE incidence modes at 1550 nm operation wavelength, respectively, and the external quantum efficiency of the pixel P5 is 0.018 and 0.78 in RCP and LCP incidence modes, respectively.

 

Fig. 4. (a, b) The influence of the corner radius and incident angle on the performance of the Si metasurfaces in the pixel P5. Figure 4(c): The influence of the incident angle on the performance of the Si grating in the pixel P2. Figure 4(d): The external quantum efficiency spectrum of the pixel P2 and P5 under orthogonal polarization incidence.

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Due to the inconsistent external quantum efficiency between the linear and circular polarization detection pixels, the derivation formula of the corresponding Stokes vector will change. The components of the Stokes parameter can be defined as:

Here, $I{(\mathrm{\omega } )_0}$, $I{(\mathrm{\omega } )_{90}},\; I{(\mathrm{\omega } )_{ - 45}}$, $I{(\mathrm{\omega } )_{45}},\; I{(\mathrm{\omega } )_{rcp}}$ and $I{(\mathrm{\omega } )_{lcp}}$ are the photocurrent of the 0-degree, 90-degree, 135-degree, 45-degree polarization photodetector, the right and left circular dichroic device at the specific frequency, respectively. ${\eta _L}$ and ${\eta _C}$ are the external quantum efficiencies of the linear and circular polarization detection pixels at specific operating wavelengths, respectively. We used the linearly polarized light that is represented by KK and $\textrm{Theta}(\mathrm{\theta } )$ to illuminate the six small pixels. Here, KK is the quotient of the projection of the electric field amplitude in the X and Y directions, and $\mathrm{\theta }$ is the phase difference between the electric field in the Y-axis and X-axis directions. The external quantum efficiency is brought into Eqs. (6∼9) to get the full Stokes parameter. In addition, a quantitative comparison is necessary by extracting the average errors for S1, S2 and S3. The theoretical Stokes parameter can be represented by (${D_0},{D_1},{D_2},{D_3}$), and the Stokes parameter obtained by the finite element algorithm is (${S_0},{S_1},{S_2},{S_3}$). Moreover, errors for the degree of linear and circular polarizations are defined as $\left|{\sqrt {S_1^2 + S_2^2} /{S_0} - \sqrt {D_1^2 + D_2^2} /{D_0}} \right|$ and $|{{S_3}/{S_0} - {D_3}/{D_0}} |$, respectively. Here, $|\textrm{x} |$ indicates that the absolute value operator acts on the element x. The error of the degree of linear polarizations (Dolp) are less than 0.01 at 1550 nm operation wavelength range, and the average error of the degree of circular polarizations (Docp) are less than 0.08, as shown in Fig. 5. Figure 5(b) also show that the minimum error of the Docp is less than 0.01. Such a low error polarization camera is likely to be widely used in the field of biosensor and detection. Figure 5(c) and (d) show the effect of the mesh density and the finite element polynomial degree on the circular dichroism of the circularly polarized detector, respectively. The maximum mesh size of the InGaAs is in the range of 40 nm −120 nm. The maximum mesh size for the materials without optical loss is the incident wavelength divided by the refractive index divided by the ratio, and the ratios are 4, 6, 8, 10, 12. Figure 5(c) shows that the CD is almost independent of the mesh size of the InGaAs. When the ratio is greater than or equal to 6, the CD also shows almost no change. In the comsol software, the discretization of the electric field is generally in the form of a cubic type and a default quadratic type. Figure 5(d) shows the effect of the quadratic and cubic discretization on the circular dichroism of the device, and the maximum value of their absolute error is very small at 1.4%. In addition, Fig. 5(e) also demonstrates the effect of doping concentration on the absorption coefficient of the InP materials, whose specific data comes from the literature [33]. Figure 5(f) shows that the doping concentration is almost independent on the circular dichroism of the device.

4. Conclusion

In conclusion, we utilize the Si metasurface consisting of the InGaAs/InP photodetector, the SiO2 support layer and the Si grating to realize the function of 0- degree, 45-degree, 90-degree and 135-degree polarized photodetector, and they all have the large average ER (160:1) of external quantum efficiency at 1550 nm operation wavelength. In addition, a circularly polarizing dichroism photodetector is numerically proposed by using the chiral metasurface whose unit cell is two trapezoidal blocks with some dislocations, and the circular polarization dichroism ($\textrm{CPD} = {\eta _{ext}}_{RCP} - {\eta _{ext}}_{LCP}$) of the external quantum efficiency at 1550 nm wavelength reaches 78% and the extinction ratio is 30:1. We also numerically demonstrate that the full Stokes large pixel composed of six small pixels can almost accurately measure arbitrary polarized light at 1550 nm operation wavelength. We believe that the large pixel designed by us may be easy to apply to various circularly polarized scenes, which can extend our detection dimension from intensity to polarization.

 

Fig. 5. (a,b) the error for degree of linear and circular polarizations at 1550 nm operation wavelength. KK: 5, 3, 1, 1/3, 1/5. Figure 5(c,d): the effect of the mesh density and the finite element polynomial degree on the CD of the pixel P5. Figure 5(e,f): the effect of doping concentration on the absorption coefficient of the InP materials and the circular dichroism of the device.no absorption in Fig. 5(f) represents the case where the imaginary part of the refractive index of the InP is zero.

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