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Abstract
A dynamically reconfigurable metasurface grating is proposed in this work based on the phase change material Ge2Sb2Te5 (GST). The metasurface grating keeps as the 0° polarizer that allows only x-polarized light to pass when the GST is in the crystalline state, and switches to the 90° polarizer (only y-polarized light passes through) while the GST transforms into the amorphous state. Furthermore, the circular polarization dichroism could be achieved using a double-layer metasurface consisting of this dynamic grating and a large broadband plasmonic quarter-wave plate. We can expect to achieve fully polarized detection with the ultra-high spatial resolution using only three components. In addition, we can obtain the largest bandwidth (300 nm) of the full Stokes large-image-element to date in the near infrared band by using the six-image-element technique with the crystalline phase GST.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The polarization of light contains much useful information that is difficult to detect directly, such as surface shape, roughness, chemical properties, and it has a broad prospect in photonic communications [1], satellite remote sensing [2] and bio-optical imaging and sensing [3]. The polarization imaging ideas are mainly divided into three categories: division of amplitude [4], division of the aperture [5], and division of the focal plane [6–8]. Division of the focal plane based on the metasurface technology is becoming a hot development direction because it is easy to integrate with the large area array detectors and does not need complex optical system. In addition, the development of the compact polarization camera is limited mainly by the bandwidth, extinction ratio and circular dichroism of the circularly polarizing dichroism waveplate (CPDW).
Phase change material GST, with good stability, high-speed and wide operating temperature range, is a good candidate for reconfigurable metasurface [9–14]. Researchers can effectively adjust the Fano resonance [15], intensity of circular dichroism [16,17] and chiroptical response [18] by controlling the phase transition of GST. In the past ten years, CPDW based on the metasurface have developed rapidly [19–32]. The imaging idea is divided into the off-axis diffraction focusing type [33] and the coaxial absorption [26,34] or transmission [35] type. The transmission type CPDW can be mainly divided into the three-dimensional chiral metamaterials [35–38] that are difficult to manufacture accurately, two-dimensional bilayer chiral metasurface [39,40] and single-layer chiral metasurface [41,42]. At present, the single-layer metasurface with the advantages of easy processing is faced with the embarrassment of small bandwidth and low extinction ratio, and the maximum extinction ratio near 1550 nm wavelength reported in the experiment is still less than 10:1 [41]. However, the maximum extinction ratio of the double-layer metasurface at the same working wavelength can reach 35:1, and the circular dichroism can exceed 80% [39]. The study of the bilayer metasurfaces may be more urgent based on the application perspective. In addition, the phase-change materials of lower losses operating at the visible regime such as Sb2S3 and Sb2Se3 might find more applications [43].
In this paper, we have designed a dynamically reconfigurable metasurface grating, which consists of the glass substrate and the phase change material GST (amorphous and crystalline state). The grating can be converted from the 0° to 90° polarizer in the different physical states. A double-layer metasurface consisting of this dynamic grating and a large broadband plasmonic quarter-wave plate can achieve the circular polarization dichroism. We can expect to achieve the fully polarized detection with the ultra-high spatial resolution using only three elements (0, 45-degree polarizer and CPDW). In addition, if we use the six-image-element technique, the ultra-large bandwidth full Stokes large-image-element can be obtained. We believe that the super polarization pixel designed by us may be easy to integrate with infrared detector, which can extend our detection dimension from intensity to polarization.
2. Structure and simulation
Figure 1(a) shows the 3D structure of the full Stokes large-image-element based on the metasurface. The device consists of the silica substrate, the silver grating submerged in the silica support layer, and a polarization grating composed of the phase change material GST. The phase-change properties of the germanium antimony telluride (GST) reversible transitions between amorphous and crystalline states with markedly different optical properties. The specific refractive index parameters in the two physical phases are derived from the Refs. [44], and the refractive index at 1500 nm wavelength is 2.4-0.02*j in the amorphous state and 5.2-0.1*j in the crystalline state. The index parameter of the silver comes from the literature [45]. The index parameters of the SiO2 is 1.46. P0 is the 0 and 90-degree polarizer in the crystalline and amorphous state, respectively. P1 is the 45 and 135-degree polarizer in the crystalline and amorphous state, respectively. P2 is the left and right circular polarizer in the crystalline and amorphous state, respectively. Figure 1(b) shows the front view of the supper image element. The full wave numerical simulations model is based on commercial software COMSOL Multiphysics, which is used to calculate the intensity and phase information of the transmission mode of the metasurface. 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 x and y directions, and the S-parameters of the transmitted light are extracted to get the corresponding amplitude and phase information.
Fig. 1. (a): 3D structure of the full Stokes large-image-element based on the metasurface. Figure 1(b): Front view of the large-image-element. Light is emitted upward from the silica medium. The TE mode corresponds to x-polarized light. P0 is called type I gratings in the amorphous state and type II gratings in the crystalline state, respectively. P1 is obtained by rotating P0 45 degrees counterclockwise. The a2 is 170 nm, h2 = 600 nm, p2 = 870 nm, hs = 750 nm, a1 = 575 nm, h1 = 530 nm, p1 = 870 nm
The design tunability of the device by scaling up or down the dimensions is very important to follow. The effects of different structural parameters on the performance of the linear polarizer grating in the wavelength range of 1.3–1.8 $\mathrm{\mu }$ m is investigated. Figure 2(a-c) show the transmission of the type I grating depending on the structural parameter. Figure 2(a) shows the transmission peak and transmission valley both redshift in the TE and TM incidence mode, and the transmission valley in the case of the TM incidence mode can redshift for a range of 120 nm. Figure 2(b) shows the transmission valleys are almost independent on the grating height. As shown in Fig. 2(c), the redshift phenomenon both occur in two polarization forms of the incidence mode. Meanwhile, an almost perfect band stop effect about 100 nm bandwidth (1500 nm- 1600 nm) is found in the case of the TE incidence. Figure 2(d-f) show the transmission of the type II grating. A full band low transmission effect can be observed in the TM incident mode, which does not change with the geometric parameters. In the case of the TE incidence mode, the full width at half maximum (FWHM) of the transmission peaks are large, and all transmission peaks redshift with the geometric parameters. Obviously, the type II grating may have more advantages in broadband polarization imaging. Finally, an optimal linear polarizer whose width, thickness and period are 575 nm, 530 nm and 870 nm, respectively, is achieved.
Fig. 2. Transmission depending on the structural geometric parameters. The solid line corresponds to the TE mode and the dotted line corresponds to the TM mode. When one parameter is studied, other parameters remain unchanged. When one of the parameters is scanned, the remaining parameters remain unchanged
Figure 3(a) shows the transmission and extinction ratio spectrum of the type I grating. The extinction ratio peak is very narrow, and the maximum extinction ratio (${I_{TM}}/{I_{TE}}$) is about 80 at the 1550 nm wavelength. Figure 3(b,d) shows the distribution of the field vector and electric field intensity of the grating in X-Z section for the operation wavelength of 1550 nm. The electric field is localized in the center of the device, and the magnetic field vector rotates clockwise in the case of the TM incidence, as shown in Fig. 3(b). Meanwhile, as seen in Fig. 3(d), the electric field is mainly concentrated in the red ring, and the electric field vector on the ring rotates clockwise in the case of TE incidence. It is concluded that the grating can be equivalent to a magnetic dipole and electric dipole for the TE and TM incidence mode, respectively. It is seen from Fig. 3(c) that the multipole expansion is used to analyze the resonance mode of the grating, and the detailed calculation method can be consulted in the literature [46]. The metasurface is not only controlled by the dark magnetic dipole but also partially controlled by the bright electric quadrupole in the case of the TE incidence, and the Fano resonance with the mutually coupled excitation of the dark and bright mode explains the asymmetric TE transmission spectral pattern at 1550 nm wavelength in Fig. 3(a). The grating at 1450 nm ∼1800nm operation bandwidth is manipulated by a weak non-dispersive electric dipole in the case of the TM incidence. As shown in Fig. 3(e), the average transmittance of the type-II grating for the TE and TM incidence mode are 0.45 and 0.03, respectively. The average extinction ratio is 12 at the 1300 nm ∼ 1680 nm wavelength range. Figure 3(f) shows the free charge distribution in the X-Z section at the 1550 nm TE incidence mode, and the free charge comes from the divergence of the electric displacement vector. Two oppositely oriented electric dipoles maintaining a displacement constitute a typical electric quadrupole moment. Figure 3(g) shows the multipole expansion for the type- II grating. The grating is mainly controlled by the electric quadrupole at the 1550 nm wavelength in the case of the TE incident mode, which is consistent with the Fig. 3 (f). The dark electric quadrupole mode can’t be directly excited by the incident TE mode, whose spectrum shows a transmission peak that does not hinder the incident light. In the contrast, the grating is controlled by the electric dipole in the case of the TM mode, and the bright electric dipole mode is strongly coupled with the incident light to suppress the transmission intensity.
Fig. 3. The transmission and extinction ratio spectrum, The electromagnetic field and free charge distribution, Multipole expansion. Figure 3(a): the transmission and extinction ratio spectrum of the type- I grating, ER=${I_{TM}}/{I_{TE}}$. Figure 3(b): the distribution of the magnetic field vector and electric field intensity of the grating in the X-Z section at 1550 nm TM mode. Figure 3(c): the multipole expansion of type- I grating. Figure 3(d): the distribution of the electric field vector and electric field intensity of the grating in the X-Z section at 1550 nm TE mode. Figure 3(e): the transmission and extinction ratio spectrum of the type- II grating, ER=${I_{TE}}/{I_{TM}}$. Figure 3(f): the free charge distribution in X-Z section at 1550 nm TE mode. Figure 3(g): the multipole expansion of type- II grating.
In classical optics, a combination of the quarter-wave plate and the -45(+45)-degree polarizer has a significant extinction effect on the right (left) circularly polarized light [47]. This idea is applied to propose a bilayer metasurface constructing the circular dichroic device. The silver grating is the nanometer sized counterpart of the quarter wave plate in traditional optics, and the ± 45-degree linear polarizer is obtained by rotating the GST grating with two physical states by 45 degrees. Figure 4(a) shows the transmission spectrum and phase difference spectrum of the thick silver grating quarter waveplate. The silver grating controlled by the Fabry-Perot (FP) cavity resonances and Gap-Surface Plasmon Polaritons (G-SPPs) can be a large bandwidth phase retarder, which has been reported in some literatures [48,49]. The device maintains that the transmission of the TE mode is equal to one of the TM mode and the phase difference is between 80 and 100 degrees at the range of 1380 nm ∼ 1660 nm. Figure 4(b) shows the effects of the space layer hs on the performance of the circular dichroic device. The extinction ratio is almost constant 13 in the form of crystal. However, the extinction ratio index shows a cosine line in the amorphous state, and the maximum value is 50. The circular dichroic device must satisfy the requirement where the extinction ratio (${I_{bigger}}/{I_{smaller}}$) is not less than 10 for an acceptable the full stokes imaging quality. Figure 4(c) shows that the transmission spectrum and extinction spectrum of the right circular polarizer. The transmittance of the right circularly polarized light is about 0.7 for the operation bandwidth of 1525 nm ∼ 1575 nm, and the average extinction ratio is 22. The second largest extinction ratio peak at the 1375 nm wavelength is due to the sinking of the transmittance of TM mode in Fig. 3(a). Figure 4(d) shows that the transmission spectrum and extinction spectrum of the left circular polarizer. The operation bandwidth in the form of crystal is 1320 nm ∼ 1660 nm. The transmittance of the left circularly polarized light is about 0.5, and the average extinction ratio is 12 for the circular polarizer. It is worth noting that a right circular polarizer with the same operating bandwidth (340 nm) can be obtained if the metasurface in the crystal form is mirror transformed symmetrically in the YZ plane.
Fig. 4. Transmission spectrum and Phase difference spectrum of the plasmonic quarter waveplate. Figure 4(b): The extinction ratio depending on the space layer hs. Figure 4(c,d): Transmission spectrum and extinction spectrum of the circularly polarizing dichroism waveplate in two forms of amorphous and crystal, respectively. The right circular polarizing waveplate (RCPW) for the amorph, The left circular polarizing waveplate (LCPW) for the crystal.
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 two different form of the grating. In this section, we demonstrate the Full-Stokes Imaging Polarimetry using the nanoparticles dimensions of Sec.2. It is assumed that the Jones matrix of the transmission type optical element is the ${T_{extinctio}}$ = $\left[ {\begin{array}{ll} {a\ast {e^{i\ast \theta }}}&{a\ast {e^{i\ast ({\theta + \pi /2} )}}}\\ {b\ast {e^{i\ast \varphi }}}&{b\ast {e^{i\ast ({\varphi - \pi /2} )}}} \end{array}} \right]$. Here, a and b are real numbers, and $\mathrm{\theta \;\ and\;\ \varphi }$ are angles. In addition, ${T_{extinction}}$*$\left[ {\begin{array}{c} 1\\ i \end{array}} \right]$*$\frac{{\sqrt 2 }}{2}$ =$\frac{{\sqrt 2 }}{2}$ * $\left[ {\begin{array}{c} 0\\ {2b\ast {e^{i\ast \varphi }}} \end{array}} \right]$, which indicates the efficiency of the transmitted light can be zero when b is zero. ${T_{extinction}}$*$\left[ {\begin{array}{c} 1\\ { - i} \end{array}} \right]$*$\frac{{\sqrt 2 }}{2}$ =$\frac{{\sqrt 2 }}{2}$ *$\left[ {\begin{array}{c} {2a\ast {e^{i\ast \theta }}}\\ 0 \end{array}} \right]$, which indicates the device can depress the transmission of left circularly polarized light when a is very low. Figure 5(a) shows the Jones matrix information of the right circular polarizer. ${T_{yx}}$ and ${T_{yy}}$ are very close and both larger than 0.53, and ${T_{xx}}$ and ${T_{xy}}\; $ are both equal to 0.065 at 1550 nm operation wavelength. The phase difference arg(${T_{xy}}$)- arg(${T_{xx}}$) and arg(${T_{yy}}$)- arg(${T_{yx}}$) are $\mathrm{\pi }/2$ and $- \mathrm{\pi }/2$, respectively. It is obvious that the optical element corresponding to Fig. 5(a) can suppress the transmission of the left circularly polarized light. As shown in Fig. 5(b), ${T_{yx}}$ and ${T_{yy}}\; $ are both equal to 0.12, ${T_{xx}}$ and ${T_{xy}}\; $ are both 0.5 at 1550 nm wavelength, and the phase difference for the right circular polarizer is the same as one for the left circular polarizer. The Jones matrix in Fig. 5(b) can satisfy the function of the left circular polarizer.
Fig. 5. The Jones matrix of the right circular polarizer. Figure 5(b): The Jones matrix of the left circular polarizer. Figure 5(c): Results of theory and numerical solution of the Stokes parameters for the 1550 nm circularly polarized light. Figure 5(d): The error for degree of linear polarizations (DOLP) and degree of circular polarizations (DOCP) for different polarized light.
Due to the ohmic loss of the metasurface and unequal transmittance of two different form of the linear grating, the derivation formula of the corresponding Stokes vector is not simply determined by the difference of orthogonal pixel intensity, but requires the efficiency compensation. The Jones matrix of two different form of the linear grating can be expressed as $\left[ {\begin{array}{cc} {{p_1}}&0\\ 0&0 \end{array}} \right]$, $\left[ {\begin{array}{cc} 0&0\\ 0&{{p_2}} \end{array}} \right]$, respectively. In addition, The Jones matrix of the left and right circular polarizer both meet the ${T_{extinction}}$ format, and ${a_L}$, ${a_R}$, ${b_L}$ and ${b_R}$ correspond to their respective the circular dichroic device. The components of the Stokes parameter are defined as:
In fact, besides the pixel numbers, the number of period is also important for the spatial resolution. Particularly, in realistic devices, the number of period is limited. We use 2D and 3D models to simulate finite period line gratings. For the two-dimensional model, the number of periods of the grating in the x direction is limited, and the two sides are truncated by the scattering boundary conditions, but the dimension of the grating in the y direction is infinite. For the 3D model, the numbers of periods of the grating in the x and y directions are both limited. It is worth noting that the upper limit of the period number of the grating only depends on the computing power of the server, and the complexity of the circularly polarized metasurface structure limits the display of 3D optical simulation. Figure 6(a) shows the relationship between the extinction ratio and period number of the type I gratings in the case of 1550 nm wavelength. When the number of period is about 40, the two-dimensional model is close to the limit value, and when the number of period is small, the calculation trend of three-dimensional and two-dimensional models is consistent. Figure 6(b) shows that the curve of the 2D model and the linear fitting trend of the 3D model intersect with the limit values when the number of cycles is about 25 and 50 respectively.
Fig. 6. (a): Relation between period number and extinction ratio for the type I grating. Figure 6(b): Relation between period number and extinction ratio for the type II grating. Limit is the extinction ratio at 1550 nm wavelength in Fig. 3 (a) and (e). Figure 6(c): Six pixels full Stokes imaging scheme. All GST material is in the in the crystalline state. Figure 6(d): The error for degree of linear polarizations (DOLP) and degree of circular polarizations (DOCP) of the circularly polarized light in the 1350 nm to 1650 nm band.
We note that when the GST material is in the crystalline state, the extinction ratio of the left circular polarizer named P2 is greater than 10 over a large bandwidth (1320 nm ∼ 1660 nm). if we abandon the high spatial resolution scheme of three pixels and use the conventional full polarization detection scheme of six pixels, a high bandwidth full Stokes metasurface in the NIR band in Fig. 6(c) is designed. The 0-degree polarizer is rotated counterclockwise by 45 degrees, 90 degrees and 135 degrees to obtain 45 degrees, 90 degrees and 135-degrees polarizers respectively. The left circular polarizer can be transformed by mirroring the Y-Z section to obtain the right circular polarizer with different chirality. Figure 6(d) shows the error for degree of linear polarizations (DOLP) and degree of circular polarizations (DOCP) of the circularly polarized light at the 1350 nm to 1650 nm band. All errors are smaller than 0.1 at the bandwidth of 1440 nm to 1650 nm, which suggests that the full Stokes focal plane detector composed of this metasurface may be able to probe massive amounts of polarization information. Table 1 shows some recent Full-stokes polarimetric techniques. The proposed structure uses reconfigurable dynamic regulation technology to complete Full-Stokes polarization measurement with only three small pixels, which may greatly improve the spatial resolution of the infrared polarization focal plane detector. The Operation bandwidth in Table 1 corresponds to the cases where the extinction ratio is greater than 10. Under the premise of the circular dichroism greater than 0.5, the microstructure we designed has the maximum bandwidth.
Table 1. Full-Stokes polarimetric imaging techniques
4. Conclusion
We have designed a dynamically reconfigurable metasurface grating, which consists of the glass substrate and the phase change material GST (amorphous and crystalline state). In addition, the double-layer metasurface consisting of this dynamic grating and the plasmonic quarter-wave sheet enables realize the extraction of the left and right circularly polarized light separately. As a result, we can realize the full polarization detection with the ultra-high spatial resolution by using only three elements of full Stokes large image element, which can be widely used in photonic communication, satellite remote sensing, bio-optical imaging and sensing, etc.
Funding
the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB43010000).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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