1. Introduction

Polarization is a fundamental property of light. Detecting the polarization state of light is critical for a wide range of applications, including communication [1,2], target detection [3–5], astronomy [6], and biomedical diagnosis [7,8]. Infrared polarization detection is potentially advantageous to identify faint or even camouflaged targets in complex backgrounds [9–11]. Evaluating polarization states typically involves measuring the Stokes parameters, which can be obtained through various methods such as using rotating polarizers and wave plates in front of the detector [12] or using multiple polarizers and detectors to conduct parallel measurements [13]. However, these conventional approaches suffer from drawbacks such as bulky sizes, long acquisition time, complex optical systems, and difficult alignment. Thus, there is an urgent need for miniaturized polarimeters. Flat optics based on metamaterials and metasurfaces opens a new path for miniaturized polarization detection as a result of their compact form factors, great design flexibility, and broad wavelength coverage [14–20]. While promising, the implementation of flat optics for polarization detector miniaturization is hindered by the sophisticated alignment required during heterogeneous integration and the reduction in light flux received by the photosensitive regions. Thus, filterless monolithic polarimeters [21–23] have become a research hotspot recently. In such devices, polarization selective light coupling structures are directly integrated on the detection material. The polarization selective light coupling structures preferably not only provide polarization discrimination but also enhance the light absorption in the detection material. Full-Stokes detection provides complete description of any partial or total polarization state. So, it becomes a crucial technique for target identification, 3D reconstruction, and robotic vision in a wide range of applications such as remote sensing, communication, and medical diagnostics. For full-Stokes polarimetry, several subpixels with different polarization selective light coupling structures are designed for different principles detection polarization states, including linear and circular polarization. Although pixel-level monolithic linear polarimetry has been realized by integrating wire grid polarizers [24–30], achieving efficient linear and circular polarimetry simultaneously on the same detection material chip still remains a challenge. In addition, how to achieve sufficient polarization extinction ratio in each subpixel and how to avoid reduction in photoresponse are the essential problems of this type of devices.

Here, we present a novel proposal for a compact, high-performance quantum well (QW) long-wavelength infrared (LWIR) polarimeter for full-Stokes polarization detection on the same detection material chip. The device consists of six subpixels with different principles detection polarization states to achieve linear and circular polarization selective responses, including 0°, 90°, 45°, 135° linear polarization, left circular polarization, and right circular polarization. The linear polarization selectivity is provided by a subwavelength metal grating and the circular polarization selectivity is provided by a two-layer twisted metamaterial. All the subpixels are based on the same GaAs/AlGaAs quantum well chip, and compatible with the architecture of focal plane arrays. With the help of dual polarization selection provided by the structure and the QWs, linear polarization extinction ratio (LPER) is above 2.6 × 10⁶ and circular polarization extinction ratio (CPER) reaches 150. In addition, the polarization selective light coupling structures induce surface plasmon polarization waves that enhance the absorption efficiency, defined as the absorptance of the QWs [31]. Compared with the absorption efficiency of a 45° edge facet coupled quantum well infrared photodetector (QWIP) as a standard reference, the absorption efficiency of the QWIP integrated with the linear-polarization-selective light coupling structure is enhanced by more than 16 times to over 67.6%. The absorption efficiency of the QWIP integrated with the circular-polarization-selective light coupling structure is enhanced by more than 18 times to 72.2%. Through simple subtracting and normalization operations on the photocurrents of the subpixels, the Stokes parameters (S₁, S₂, S₃) are obtained with small root mean square errors of 4.88 × 10⁻⁵, 0.036%, and 1.66%, respectively. In addition, over the incident angle range of ±5°, the polarization extinction ratios of the device are maintained at a very high level (LPER > 10⁵ and CPER > 139) and the absorption efficiency does not reduce. Concerning a practical device structure, where the subpixel size is limited to 60 µm × 60 µm, although the errors of the extracted Stokes parameters (S₁, S₂, S₃) increases to 2.46%, 3.48% and 6.74%, respectively, due to light diffraction and scattering, the accuracy of full-Stokes detection is still high enough for many applications. The results presented in this manuscript are all based on simulation by the FEM method, while the parameters such as the geometry of the device and the dielectric function of the materials are all extracted from experimental results. Thus, our design is ready for device fabrication. The novel design of the on-chip full-Stokes LWIR QWIP holds immense promise as a superior solution for infrared polarization detection and polarimetric imaging.

2. Results and discussion

We report on the innovation of a compact LWIR full-Stokes polarization detection chip based on anisotropic and chiral metamaterials integrated QWs. Our device incorporates six subpixels (Fig. 1(a), P1 to P6) arranged in a 2 × 3 array. There are four linear polarization (LP) subpixels with subwavelength metal gratings oriented at 0° (P1), 45° (P2), 135° (P3), and 90° (P4) to the x-axis, corresponding to the principle detection polarization states of 90°, 135°, 45°, and 0° linear polarization, respectively. In addition, there are two subpixels (P5 and P6) with two chiral metamaterials of opposite handednesses, corresponding to the principle detection polarization states of LCP and RCP, respectively. Here, we employ a widely used method to obtain the Stokes parameters (S₀, S₁, S₂, S₃) by measuring the intensity of linear and circular polarization components through the photocurrents (I₁ to I₆) of the subpixels, and doing subtraction and normalization operations on them [32].

I₁ to I₆ denote the photocurrents of subpixels P1 to P6, respectively. I₀ is calculated as the sum of I₁ and I₄. Subpixel P1 and P4 share the same structure and each of them is at 90° to the other within the x-y plane. As shown in Fig. 1(b), subpixel P4 is composed of a heavily doped GaAs bottom contact layer (h₁ = 600 nm), a reflective subwavelength grating carved out of the contact layer (h₂ = 550 nm, s = 1 µm) and coated with Au, an active region (h₃ = 610 nm) of 10 GaAs/AlGaAs QWs, and a top GaAs contact layer (h₄ = 650 nm). The period of the Au subwavelength grating is 3.8 µm. Figure 1(c) presents the diagram of subpixel P3. Subpixel P2 is at 90° to subpixel P3. All the layers in subpixel P3 and P2, namely the bottom contact layer (h₁), the active region (h₃), and the top GaAs contact layer (h₄), are the same as those in subpixel P1 and P4. The subwavelength grating is oriented 135° to the x-axis. The grating height (h₂ = 550 nm) and metal ridge width (s = 1 µm) are also the same as those of subpixel P1 and P4. The grating period along the 135° direction is 3.8 µm, so the period along the x-axis (P_x) and that along the y-axis (P_y) are both 5.374 µm. As diagrammed in Fig. 1(d), subpixel P5 features a two-layer twisted metamaterial. The thicknesses of the GaAs contacts and the active region (h₁, h₃, and h₄) are identical to those for subpixel P1-P4. The two-layer twisted metamaterial contains two subwavelength gratings. The top grating is made of a 1.45 µm thick GaAs layer oriented at 45° to the x-axis. The period (P₁) along the direction of 45° to the x-axis is 1.29 µm. The ridge width of the grating (W₁) is 0.7 µm. The bottom grating is similar to those in subpixel P1-P4. It is along the y-axis. The grating period is 3.65 µm, the grating height (h₂) is 550 nm, and the ridge width is 0.84 µm. Subpixel P6 is a mirror image of subpixel P5 about the y-axis. The fabrication of these subpixels can follow the flip-chip process [24–26,30,33,34]. Before the flip, the bottom GaAs contact layer is at the very top. Then, the Au grating for each subpixel is made by carving the GaAs contact layer and coating it with Au. After the flip-chip bonding, the Au grating moves to the bottom. Then, a substrate removal process is applied to remove most of the substrate [25,33]. After that, for subpixel P1-P4, a complete layer (1.45 µm thick) needs to be etched away from the top. For subpixel P5 and P6, the dielectric grating (1.45 µm thick) needs to be carved out of the top layer. In this sense, our design is compatible with the flip-chip process, and the superpixle containing the six subpixels can be expanded into a focal plane array for full-Stokes polarimetric imaging.

 

Fig. 1. Long-wavelength infrared (LWIR) full-Stokes polarization detection (a) Schematic diagram of the 3D structure of on-chip quantum well long-wavelength infrared polarimeter. The device incorporates six subpixels arranged in a 2 × 3 array. There are four linear polarization (LP) subpixels with subwavelength metal gratings oriented at 0° (P1), 45° (P2), 135° (P3), and 90° (P4) to the x-axis. There are two subpixels (P5 and P6) with two-layer twisted metamaterial of opposite handednesses, corresponding to the principle detection polarization states of LCP and RCP, respectively. (b) Schematic diagram of the 3D structure of linear polarization (LP) QWIP (P4). The inset figure shows the schematic diagram of a gold nanograting unit cell in the x-y view. Structural parameters: P_x= 3.8 µm, s = 1 µm. The thicknesses of the bottom contact layer, the grating, the QWs, and the uncarved part of top contact layer are h₁= 600 nm, h₂= 550 nm, h₃= 610 nm, h₄= 650 nm. (c) Schematic diagram of the 3D structure of LP QWIP (P3). The inset figure shows the schematic diagram of three gold nanogratings structure in the x-y view. The subwavelength grating is oriented 135° to the x-axis. Structural parameters: P_x= 5.374 µm, P_y= 5.374 µm, P = 3.8 µm, s = 1 µm. The thickness of the bottom contact layer (h₁), the grating (h₂), the active region (h₃), and the top GaAs contact layer (h₄) are the same as those in subpixel P4. (d) Schematic diagram of the 3D structure of circular polarization (CP) QWIP (P5). The inset figure shows the schematic diagram of the dielectric grating in the x-y view. Structural parameters: P_x= 3.65 µm, P_y= 3.65 µm, P = 1.29 µm, W₁= 0.7 µm, and s = 0.84 µm. The thicknesses of the GaAs contacts, the grating height and the active region (h₁, h₃, h₂ and h₄) are identical to those for the subpixel P4. The top grating is made out of GaAs layer (h₅= 1.45 µm) and oriented at 45° to the x-axis. The dielectric grating is drawn in green. (e) The active region with a total thickness of 610 nm contains ten AlGaAs (50 nm)/GaAs (6 nm) QW stacks. (f) Real and imaginary parts of $\varepsilon $_z. The dielectric constant of the effective medium of the QWs is diag ($\varepsilon $_x, $\varepsilon $_y, $\varepsilon $_z). (g) Absorption efficiency of a 45° edge facet coupled device.

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The active region, depicted in Fig. 1(e), has a total thickness of 610 nm and comprises 10 AlGaAs (50 nm)/GaAs (6 nm) QW stacks. Due to the selection rule of the intersubband transition, the QWs only absorb the light with a z-component electric field. Thus, the QWs can be treated as an uniaxial effective medium with a permittivity tensor like $\varepsilon $_QW = diag ($\varepsilon $_x, $\varepsilon $_y, $\varepsilon $_z), where $\varepsilon $_x = $\varepsilon $_y = $\varepsilon $_GaAs and ${\varepsilon _\textrm{z}} = {\varepsilon _{GaAs}} + \frac{{{\varepsilon _{GaAs}}{f_{12}}\omega _p^2}}{{\omega _{12}^2 - {\omega ^2} - i\omega \gamma }}$ [35]. In the x-y plane, the optical response of the QWs is comparable to that of GaAs, which is a transparent dielectric in the long wave infrared range. In the z-direction, $\varepsilon $_z conforms to the Lorentz formula. $\varepsilon $_GaAs is the refractive index of the GaAs, f₁₂ the oscillator strength, ω_p the two-dimensional effective plasma frequency, ω₁₂ the transition frequency in optics, and γ the relaxation frequency [36]. Figure 1(f) shows Re ($\varepsilon $_z) and Im ($\varepsilon $_z) of the QWs in a typical LWIR QWIP with the peak detection wavelength of 10.55 µm. Since the QWs do not respond to normally incident light, they are usually made into a 45° edge facet coupled device for photoresponse characterization [31]. The absorptance of the QWs in the 45° edge facet coupled device serves as a standard reference. Figure 1(g) demonstrates the absorption efficiency spectra of a standard 45° edge facet coupled device, with the absorption peak at 10.55 µm being 4.1%. The dielectric constant of Au is derived from the Drude model [37].

Figure 2 presents the polarization dependent optical responses of subpixel P4, P3, and P5. The absorptance and reflectance spectra of subpixel P4 under x- and y-polarized illumination are presented in Fig. 2(a)-(b). The x-polarized light induces a surface plasmon polariton (SPP) wave at the interface between the metal grating and the bottom GaAs contact layer, resulting in an absorption efficiency of 67.6% at the designated central detection wavelength (10.55 µm) (Fig. 2(a)). In contrast, the y-polarized light does not effectively excite the SPP wave, leading to a low absorption efficiency of 2.56 × 10⁻⁷ at the same wavelength. With the help of dual polarization selection provided by the structure and the detection material, the QWs only absorb the light with a z-component electric field, and the SPP wave excited by the x-polarized light is efficiently absorbed by the QWs. The y-polarized light directly incident on the QWs and that diffracted or scattered into the QWs are hardly absorbed, leading to an ultrahigh LPER of 2.6 × 10⁶. It is worth noting that this subwavelength metal grating not only provides a high polarization discrimination but also enhances the absorption efficiency by the resonantly excited SPP waves and critical coupling [38,39]. Under x-polarized illumination, the reflectance approaches zero at the wavelength of 10.55 µm, indicating that the incident power is 100% coupled into the SPP wave. Thus, an intensified local field is built up (Fig. 2(c)). As a result, the absorptance of the QWs is enhanced by more than 16 times, compared with that of the same QWs in a 45° edge facet coupled QWIP as a standard reference.

 

Fig. 2. (a) Absorptance and reflectance spectra of subpixel P4 under x-polarized light illumination. A_{QW, x} denotes the absorption efficiency of the QWs, A_{m, x} denotes the absorption efficiency of the metal, R_x denotes the reflectance of x-polarized light. (b) Absorptance and reflectance spectra of subpixel P4 under y-polarized light illumination. A_{QW, y} denotes the absorption efficiency of the QWs, A_{m, y} denotes the absorption efficiency of the metal, R_y denotes the reflectance of y-polarized light. (c) Field distributions on the x-z cross section of subpixel P4 under x- and y-polarized light illumination, respectively. The wavelength of the incident light is 10.55 µm. The colored surfaces represent |E_z|²/|E₀|². (d) Absorptance and reflectance spectra of subpixel P3 under 45°-polarized light illumination. A_{QW, 45°} denotes the absorption efficiency of the QWs, A_{m, 45°} denotes the absorption efficiency of the metal, R_45° denotes the reflectance of 45°-polarized light. (e) Absorptance and reflectance spectra of subpixel P3 under 135°-polarized light illumination. A_{QW, 135°} denotes the absorption efficiency of the QWs, A_{m, 135°} denotes the absorption efficiency of the metal, R_135° denotes the reflectance of 135°-polarized light. (f) Field distributions on the 45° cross section of subpixel P3 under 45°- and 135°-polarized light illumination, respectively. The wavelength of the incident light is 10.55 µm. The colored surfaces represent |E_z|²/|E₀|². (g) Absorptance and reflectance spectra of subpixel P5 under LCP illumination. A_{QW, LCP} denotes the absorption efficiency of the QWs, A_{m, LCP} denotes the absorption efficiency of the metal, R_LCP denotes the reflectance of LCP. (h) Absorptance and reflectance spectra of subpixel P5 under RCP illumination. A_{QW, RCP} denotes the absorption efficiency of the QWs, A_{m, RCP} denotes the absorption efficiency of the metal, R_RCP denotes the reflectance of RCP. (i) Field distributions on the x-z cross section of subpixel P5 under LCP and RCP illumination, respectively. The wavelength of the incident light is 10.55 µm. The colored surfaces represent |E_z|²/|E₀|².

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The case of subpixel P3 is almost the same of subpixel P4 except that the principle detection polarization state becomes 45° linear polarization. As shown in Fig. 2(d)-(f), 45° linearly polarized light resonantly excites the SPP wave at the wavelength of 10.55 µm, which enhances the absorption efficiency to 67.7%. In contrast, the 135° linearly polarized light does not efficiently excite the SPP wave and is mostly reflected. Especially at the central detection wavelength of the QWs (10.55 µm), the absorption efficiency is only 1.63 × 10⁻⁷, and the LPER at this wavelength is as high as 4.2 × 10⁶.

For subpixel P5 or P6, the dielectric grating at the top partially plays the role of a quarter wave plate. After the incident light passing through the dielectric grating layer, the x-component light field accumulates a π/2 phase more (or less) than the y-component. When LCP light is incident at subpixel P5, it is converted into x-polarized light after passing through the dielectric grating, while the RCP light is converted into y-polarized light. Then the x-polarized light can induce a SPP wave at the bottom metal grating, resulting in a prominent absorption enhancement at the resonant wavelength of 10.55 µm. As shown in Fig. 2(g)-(i), the absorption efficiency reaches 72.2% and the reflectance decreases to 0.8%. In contrast, the y-polarized light converted from the RCP light does not efficiently excite the SPP wave, resulting in high reflection and low absorption. In addition, the circular polarization discrimination is enhanced by the multiple reflection between the metal grating at the bottom and the dielectric grating at the top. Concerning P5, for RCP light, the excited SPP waves during the multiple reflections in this film destructively interfere with each other, while for LCP light the excited SPP waves during the multiple reflections constructively interfere with each other. The multiple reflection interference mechanism has been reported in detail in previous works [39,40]. Further, the circular polarization discrimination is magnified by the additional polarization selection provided by the QWs. The QWs only absorb the light with a z-component electric field, so the SPP wave excited by the LCP is efficiently absorbed by the QWs. The RCP light directly incident on the QWs and that diffracted or scattered into the QWs has little z-component electric field, and thus it is hardly absorbed. At the peak detection wavelength of the QWs (10.55 µm), the absorption efficiency is only 0.48%, and the CPER at this wavelength is as high as 150. The absorption efficiency of LCP is 72.2%, which is 18 times higher than that of a 45° edge facet coupled device, indicating that the two-layer twisted metamaterial integrated QWIP not only has a high circular polarization discrimination but also has an enhanced absorption efficiency.

The geometry of the dielectric grating is a critical factor for the absorption efficiency and the CPER. The geometry of the dielectric grating (θ = 45°, W₁ = 0.7 µm) as we presented in the previous context is optimized. However, due to fabrication imperfection, the angle between the dielectric grating and the x-axis may deviate from the wanted value of 45°. As shown in Fig. 3(b), when θ becomes 40°, the absorption efficiency for the principle detection polarization (LCP) at the wavelength of 10.55 µm drops from 72.2% to 67.1%. In addition, the change in θ breaks the destructive interference of multiple reflections, leading to a higher absorption for RCP light. As a result, the CPER decreases from 150 to 95. Likewise, when the angle of the grating to the x-axis is 50°, the absorption efficiency of LCP light decreases from 72.2% to 70.1% at the wavelength of 10.55 µm, and the CPER decreases to 103. Thus, in the range of ±5° around θ = 45°, the performance of subpixel P5 does not decline too much. The ridge width (W₁) of the grating is another geometric parameter that needs to be analyzed. As shown in Fig. 3(d), the absorption peak caused by the SPP wave changes as W₁ changes. On one hand, the change in W₁ affects the phase difference introduced between E_x and E_y by the dielectric grating, reducing the conversion capability to circularly polarized light. On the other hand, it affects the interference between the principle-polarization radiation and the cross-polarization radiation of the two-layer twisted metamaterial during multiple reflections, weakening the destructive interference with RCP light. Concerning the circular polarization discrimination, a smaller W₁ such as 0.675 µm slightly improves the CPERs from 150 to 172 (Fig. 3(d)), but reduces the LCP light induced absorptance of the QWs from 72.2% to 71.8% at the designated wavelength (10.55 µm). Reducing W₁ further to 0.55 µm, the CPER is substantially reduced to 48 at a wavelength of 10.55 µm. Increasing W₁ to 0.8 µm substantially reduces the CPER to 43 at the wavelength of 10.55 µm. The width (W₁) of the grating ridge is a key factor affecting the circular polarization characteristics. By using electron beam lithography to define the patterns, the deviation of θ can be controlled within 1° and that of W₁ within several tens of nanometers [17,41,42], thus ensuring the robustness of subpixel P5 and P6.

 

Fig. 3. (a) Schematic diagram of the angle (θ) of the dielectric grating to the x-axis. (b) Absorption efficiency and CPER spectra for LCP and RCP light at 10.55 µm of dielectric grating angle (40°- 50°). (c) Schematic diagram of the dielectric grating width (W₁). (d) Absorption efficiency and CPER spectra for LCP and RCP light at 10.55 µm of the dielectric grating width (0.55 µm – 0.8 µm).

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The influence of the grating ridge width (s) is also studied. We analyzed the dependence of the QW absorptance spectra on s for subpixel P3, P4, P5. Regarding the spectra induced by the principle polarization state and the unwanted polarization state, subpixel P1, P2, P6 are expected to be the same as subpixel P3, P4, P5, respectively. Regarding subpixel P4, the optimized s value is 1.0 µm as reported in the manuscript. Figure 4 (a) presents the QW absorptance spectra at three different s values. As s changes from 0.9 to 1.1 µm, the resonance induced by the principle polarization (θ = 0°) shifts to longer wavelengths. On the other hand, the variation in s from the optimized value causes a decrease in the peak absorptance, indicating that the system is deviated from the critical coupling condition. Due to these two factors, as s changes from 1.0 to 0.9 or 1.1 µm, the absorption efficiency for x-polarized light at the central detection wavelength (10.55 µm) decreases from 67.6% to 64.5% or 63.2%. For the unwanted polarization state, various s values all lead to very low absorption efficiencies around 10⁻⁸ to 10⁻⁶ (Fig. 4 (b)). Thus, the LPERs are all above 10⁶ for s varying from 0.9 to 1.1 µm. For subpixel P3, the dependence of the absorption spectra on s (Fig. 4 (c-d)) is almost the same as that of subpixel P4. For subpixel P5, the optimized s is 0.84 µm. As s changes from 0.74 to 0.94 µm, the resonant peak of the QW absorptance almost remains unchanged. And the peak absorptance also changes slightly. For the unwanted polarization state, the three s values all lead to low absorption efficiencies. Thus, when s changes from 0.84 to 0.74 µm, the CPER is slightly decreased from 150 to 143. When s changes from 0.84 to 0.94 µm, the CPER is slightly increased from 150 to 158. Therefore, a ± 100 nm variation in s does not significantly degrade the performance of all the subpixels. Moreover, by using electron beam lithography to define the patterns, the deviation of s can be controlled within 30 nm. Based on the above analysis, our device shows a good tolerance to fabrication imperfections.

 

Fig. 4. (a) Absorption efficiency spectra for x-polarized light of subpixel P4 with the width of the Au grating. (b) Absorption efficiency spectra for y-polarized light of subpixel P4 with the width of the Au grating. (c) Absorption efficiency spectra for 45°-polarized light of subpixel P3 with the width of the Au grating. (d) Absorption efficiency spectra for 135°-polarized light of subpixel P3 with the width of the Au grating. (e) Absorption efficiency spectra for LCP light of subpixel P5 with the width of the Au grating. (f) Absorption efficiency spectra for RCP light of subpixel P5 with the width of the Au grating.

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Based on our device, we performed full-Stokes detection. As shown in Fig. 5 (a), 26 distinct polarization states are picked for full-Stokes detection test. The 26 polarization states are distributed on four longitudes of the Poincare sphere corresponding to four different orientation angles (φ = 0, π/8, π/4, 3π/8). The input (red solid line) and measured (star shaped) Stokes parameters (S₁-S₃) of the polarization states on the four longitudes are presented in Figs. 5(b)-(e). For each incident polarization state, we obtain the absorption efficiencies of the six subpixels and calculate the Stokes parameters based on Eq. (1). The root mean square errors for S₁, S₂, and S₃ as small as 4.88 × 10⁻⁵, 0.036%, and 1.66%, respectively, are achieved. It is revealed that of S₁ and S₂ are lower that the errors of S_3, probably due to the fact that the LPER (above 2.6 × 10⁶) is much higher than the CPER (150).

 

Fig. 5. (a) Schematic illustration of the full-Stokes information in a Poincare sphere. S₁ and S₂ are the linear parameters that characterize the direction of the linear component. S₃ is the circularly polarized parameter that quantifies the circular component. Stokes parameters (S₁–S₃) calculated for 26 different polarization states. (b)-(e) The input (red solid line) and measured (star shaped) Stokes parameters (S₁-S₃) for different orientation angles (φ = 0, π/8, π/4, 3π/8) and ellipticity angles (χ).

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The influence of the incident angle is crucial for practical applications, as the light passing through the optical system usually involves a certain range of incident angles at the detector. Figure 6(a) displays a tiny blue-shift of 0.025 µm of the SPP resonance when subpixel P4 is subjected to an oblique incidence of 5° in the x-z plane. Accordingly, the absorption efficiency for x-polarized light at the central detection wavelength (10.55 µm) slightly decreases from 67.6% to 66.8%, while the y-polarized light is still near 100% reflected. The decrease in LPER from 2.6 × 10⁶ to 1.95 × 10⁶ is attributed to the reduction in the absorption efficiency of x-polarized light, as shown in Fig. 6(b). The oblique incidence of 5° in the y-z plane did not blueshift the SPP resonance. Thus, the absorption efficiency for x-polarized light remains the same at the wavelength of 10.55 µm. However, this oblique incidence in the y-z plane slightly disrupts the total reflection of y-polarized light, thereby reducing the LPER from 2.6 × 10⁶ to 9.64 × 10⁴, as depicted in Fig. 6(b). When subpixel P3 is subjected to 5° oblique incidence in the x-z plane, the SPP resonance also undergoes a tiny blue-shift of 0.025 µm, leading to an absorption efficiency from 67.7% to 67.3% for 45°-polarized light. On the other hand, for 135°-polarized light, the reflectivity of the grating is reduced, resulting in a reduction of the LPER from 4.2 × 10⁶ to 1.82 × 10⁵, as displayed in Fig. 6(d). The cases of subpixel P1 and P2 are similar to those of subpixel P4 and P3. When subpixel P5 is subjected to oblique incidence of 5° in the x-z plane, the resonance intensity is only slightly reduced, resulting in a slightly decrease of the absorption efficiency from 72.2% to 71.7% for LCP light. However, for RCP light, the oblique incidence disrupts the destructive interference among multiple reflections, and the suppression of absorptance becomes less effective. The CPER of the device is reduced from 150 to 139, as shown in Fig. 6(f). The oblique incidence of 5° in the y-z plane did not blueshift the SPP resonance, resulting in the same absorption efficiency at the wavelength of 10.55 µm. Nonetheless, this oblique incidence increases the absorption efficiency for RCP, thereby the CPER is slightly reduced to 142. Although slightly reduced due to the 5° oblique incidence, the performance of our device still surpasses most integrated circularly polarized detectors: The absorption efficiency of subpixel P1, P2, P3 or P4 remains above 66.8% and LPER remains above 10⁵. The absorption efficiency of subpixel P5 or P6 remains above 71.7% and the CPER remains above 139.

 

Fig. 6. (a) Absorption efficiency spectra for x- and y-polarized light at an oblique incidence of 5° in the x-z and y-z plane in the subpixel P4. (b) LPER spectra for oblique incidence of 5° in the x-z and y-z plane in the subpixel P4. (c) Absorption efficiency spectra for 45°- and 135°-polarized light at an oblique incidence of 5° in the x-z and y-z plane in the subpixel P3. (d) LPER spectra for oblique incidence of 5° in the x-z and y-z plane in the subpixel P3. (e) Absorption efficiency spectra for LCP and RCP light at an oblique incidence of 5° in the x-z and y-z plane in the subpixel P5. (f) CPER spectra for oblique incidence of 5° in the x-z and y-z plane in the subpixel P5.

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Pixel size is another important factor affecting the performance of polarization detection. The above discussions are based on large pixel sizes (e.g. larger than 200 µm × 200 µm). When the size of each subpixel shrinks to 60 µm × 60 µm, the performance of polarization detection inevitably declines due to light diffraction and scattering. Figure 7(a) depicts the absorptance spectra of subpixel P4 with a size of 60 µm × 60 µm under x- and y- polarized light illumination. Specifically, the x-polarized light elicits a resonance at 10.55 µm, which leads to a device absorption efficiency of 57.4%. Under y-polarized light illumination, the absorption efficiency is 1.33%. Thus, the LPER becomes 43. As shown in Fig. 7(b), the 45°-polarized light generates a prominent resonance at 10.55 µm in absorptance spectra of subpixel P3, leading to the peak device absorption efficiency of 62.1%. For 135°-polarized light, the absorption efficiency at the wavelength of 10.55 µm is 2.04%. As a result, the LPER is 30. Finally, Fig. 7(c) illustrates the absorptance spectra of the subpixel P5 under LCP and RCP illumination. Here, the LCP light leads to a significant resonance at 10.55 µm, resulting in a device absorption efficiency of 54.7%. At the peak detection wavelength of 10.55 µm, the absorption efficiency for RCP light is 3.08%, leading to the CPER of 18.

 

Fig. 7. (a) Absorptance spectra of the subpixel P4 under x- and y-polarized light illumination about 60 µm focal plane array. (b) Absorptance spectra of the subpixel P3 under 45°- and 135°-polarized light illumination about 60 µm focal plane array. (c) Absorptance spectra of the subpixel P5 under LCP and RCP illumination about 60 µm focal plane array.

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Although the LPER and CPER declines as the subpixel size shrinks to 60 µm × 60 µm, the accuracy of the full-Stokes detection is still considerably high. The selection of the polarization states for full-Stokes parameter detection based on 60 µm × 60 µm subpixels is consistent with that in Fig. 5. For each incident polarization state, the absorption efficiency of each subpixel is also obtained first, and then the Stokes parameters are calculated based on Eq. (1). Compared with the input polarization states, the root mean square errors of S₁, S₂, and S₃ are 2.46%, 3.48%, and 6.74%, respectively. We observe that the small pixel size leads to increase errors of the extracted Stokes parameters, as shown in Fig. 8. This increase in full-Stokes detection error is due to the decrease in polarization extinction ratio caused by diffraction and scattering of light. Nevertheless, the accuracy of full-Stokes detection is still high enough for many applications.

 

Fig. 8. Stokes parameters (S₁–S₃) calculated for 26 different polarization states at 60 µm focal plane array. (a)-(d) The input (red solid line) and measured (star shaped) Stokes parameters (S₁-S₃) for different orientation angles (φ = 0, π/8, π/4, 3π/8) and ellipticity angles (χ).

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3. Conclusion

In this study, we propose an on-chip quantum well long-wavelength infrared polarimeter for full-Stokes polarization detection. The device comprises six subpixels with different principles detection polarization states, including 0°, 90°, 45°, 135° linear polarization states, and two circular polarization states. The linear polarization selectivity is provided by a subwavelength metal grating and the circular polarization selectivity is provided by a two-layer twisted metamaterial. All the subpixels are based on the same GaAs/AlGaAs quantum well chip, and compatible with the architecture of focal plane arrays. With the help of dual polarization selection provided by the structure and the detection material, the device demonstrates a linear polarization extinction ratio (LPER) above 2.6 × 10⁶ and a circular polarization extinction ratio (CPER) of 150 in the LWIR range. In addition, the polarization selective light coupling structures induce SPP waves that enhances the absorptance of the QWs by more than 16 times. Through simple subtracting and normalization operations on the photocurrents of the subpixels, the Stokes parameters (S₁, S₂, S₃) are obtained with small root mean square errors of 4.88 × 10⁻⁵, 0.036%, and 1.66%, respectively. In addition, the polarization extinction ratios of the device (LPER > 10⁵ and CPER > 139) maintains at a very high level over the incident angle range of ±5°. Concerning a limited subpixel size of 60 µm × 60 µm, although the root mean square errors of the measured Stokes parameters (S₁, S₂, S₃) increases to 2.46%, 3.48% and 6.74%, respectively, due to light diffraction and scattering, the accuracy of full-Stokes detection is still high enough for a lot of applications. Our findings offer a promising direction for the development of high-performance monolithic full-Stokes polarization detectors.