Design of polarization-sensitive IR photothermoelectric detectors
To achieve a high polarization-sensitive photoresponses, two main aspects including a high optical anisotropy and a high photon-to-electron conversion efficiency are considered in our proposed IR PTE detectors. As shown in Fig. 1a, the structure of our proposed mid-IR PTE detector is made up of an IR perfect plasmonic absorber and a 1D tellurium nanoribbon (Te NR). The perfect plasmonic absorber is made from an array of rectangular gold (Au) microstructure, a dielectric spacer (Al2O3), and an optical thick Au backplate. To investigate the optical properties of the perfect plasmonic absorber, full-wave electromagnetic simulations were performed. The structural parameters of the perfect plasmonic absorbers are obtained using global optimization (See Supplementary Fig. 1 and Table 1). The optical absorption peak of the perfect plasmonic absorber can be well designed at a specific wavelength in the IR regime. Both the electric field and absorption density distributions are simulated with polarization angle of 0° and 90°, respectively. As shown in Fig. 1b, for incident light with a polarization angle of 0°, the electric field on the Au nanostructures is near zero (Fig. 1b). For the incident light with a polarization angle of 90°, the maximum normalized electric field can reach up to 20 showing a dipole resonance mode (Fig. 1b, the top right)18, 19. The maximum absorption density can reach up to 10 and the main absorption of light is located at the Au microstructure (Fig. 1b, the bottom right). In addition, the polarization angle dependent absorption at 8.0 µm of the perfect plasmonic absorber is plotted in Fig. 1c. The absorption (Abs.) as a function of the polarization angle can be well fitted by a sine function as:
$$\text{A}\text{b}\text{s}.=\frac{{\text{A}\text{b}\text{s}.}_{90}}{2}+\frac{{\text{A}\text{b}\text{s}.}_{90}}{2}\times \text{sin}\left(2{\theta }-90\right)$$
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where, Abs.90 denotes the peak absorption intensity for a polarization angle of 90°, and θ denotes the polarization angle. Here, the Abs. is about 0% and 98% for the incident light with a polarization angle of 0° and 90°, respectively. This indicates a large optical anisotropy of the designed perfect plasmonic absorber, which is crucial for achieving a high polarization-sensitive PTE response. Furthermore, we experimentally demonstrated the polarization angle resolved absorption of the designed perfect plasmonic absorber. Here, three typical perfect plasmonic absorber (R1, R2 and R3) are designed and their polarization angle resolved absorption spectra are measured (Supplementary Fig. 2). The experimentally measured absorption spectra agree very well with the simulation results. Next, we focus on the photothermal heating effect of the perfect plasmonic absorber20. Figure 1d plots the simulated absorption (blue) and calculated temperature increase ∆T (red) as a function of the wavelength with a polarization angle of 90°. The maximum ∆T at the resonance wavelength of 8.0 µm is about 5.85 K corresponding to an absorption of 98%. The absorption spectrum and ∆T display the same trend. Moreover, the simulated temperature distribution (Supplementary Fig. 3a) is in line with the absorption density distribution (Fig. 1b, the bottom right). These results indicate a linear relation between them. Apparently, ∆T exhibits a polarization angle dependent and a linear relation to the laser power, which are verified by the simulation results (Supplementary Fig. 3b).
Apart from the large optical anisotropy used for supporting a large PR, the thermoelectric material with large Seebeck effect is also desirable to achieve a high responsivity. Benefiting from the high tolerance for selection of thermoelectric materials for the as-proposed PTE mechanism, we select Te nanoribbon as the active material owing to its advantages in thermoelectric material, such as ultralow thermal conductivity (2.16 W/m•K) due to its heavy atom mass21, a high Seebeck coefficient (413 µV/K) boosted by the quantum confinement effect induced sharp shapes of the density of states at band edges22, 23, and a good electrical conductivity owing to its narrow-bandgap24. Here, the Te NRs are synthesized using a hydrothermal method 25, 26 and characterized using Raman spectrum (Supplementary Fig. 4a and b). The electrical transport behavior indicates a p-type semiconductor with a hole mobility of 993 cm2/V•s for Te NR based field effect transistor (Supplementary Fig. 4c and d). Finally, we consider the PTE response of a typical device with perfect plasmonic absorber integrated with Te NR under a global IR illumination at room-temperature. With consideration of the heat conductance, radiation, and convection, the temperature distribution of the device in a large scale was simulated as shown in Supplementary Fig. 5. Particularly, the temperature source as input is set according to the results of both photothermal simulations and experimental measurement. Figure 1e shows the temperature distribution surrounding the device indicating a large temperature gradient localized in the Au microstructure array. As shown in Fig. 1f, with an incident laser power of 30 mW, a large temperature gradient is built up (Fig. 1f, the blue line) along the Te NR direction, and the corresponding potential distribution is also plotted (Fig. 1f, the red line). The photovoltage response of about 1.30 mV is achieved, which is calculated by Vph = ‒SΔT, where S is the Seebeck coefficient and set to be 413 µV/K, and Vph is the photovoltage.
Local absorption of the metamaterials with finite-size effect
As shown in Supplementary Fig. 2, the experimental measured polarization angle resolved absorption spectra show almost same results with the full wave simulation, which is based on an infinite extended metamaterials obtained by periodically exploiting the elementary unit cell through Floquet’s theorem27, 28. However, from the aspect of practical device fabrication, the finiteness of the array size and the boundary effects of the nano/micro-structure array should be considered29. Here, to investigate the finite-size effect of the perfect plasmonic absorber, we first prepared the perfect plasmonic absorbers with different array edge lengths (Fig. 2a) and measured their absorption spectra (Fig. 2b) under a polarization angle of 90°. The absorption peaks for different array are all located at 8.0 µm, but the absorption peak intensity increases from 39–96% when the edge length of the Au microstructure array increases from 10 to 50 µm. This result arises from the symmetry broken at the array boundaries with a consideration of the dipole resonance of our plasmonic absorber27. On the other hand, the dipole resonance mode of each microstructure will vary with its location within the array, resulting in a nonuniform absorption density distribution28. Therefore, to further investigate this effect, we measured the absorption mapping under different polarization angles of a typical perfect plasmonic absorber array with a finite-size of 30×30 µm2 (Fig. 2c). Figure 2d shows the absorption distribution of the perfect plasmonic absorber array with finite size for the IR light with a resonance wavelength of 8.0 µm and a polarization angle of 90°. As can be seen in Fig. 2d, for a finite-size array of the perfect plasmonic absorber, the maximum absorption is localized at the centra. The peak absorption intensity decreases from about 90% for central position to 30% for edge position, which is consistent with previous analysis and results28. In addition, the same trend of the absorption distribution is observed under a polarization angle of 45° (Supplementary Fig. 6b). While no same trend is observed for the polarization angle of 0° because the absorption intensity is near zero (Supplementary Fig. 6a). Although the finite size affects the total absorption of a perfect plasmonic absorber array, the localization of the absorption distribution can introduce a large temperature gradient within the array, which can be utilized to further boost the PTE response in our device. Therefore, as illustrated in Fig. 1a and Fig. 1e, one electrode is set at the centra of the Au microstructure array, and the other electrode is outside of the array.
Ultrahigh polarization sensitive photoresponses
As discussed above, the proposed PTE detector is properly designed to achieve an ultra-high polarization sensitivity by considering a high optical anisotropic ratio to support a high PR, and a large temperature gradient and a high Seebeck coefficient to support a high PTE responsivity, simultaneously. To experimentally demonstrate this, we fabricated a device as shown in Fig. 3a accordingly. In this device, the GND port indicates the ground terminal of one electrode, and ports 1 to 3 are used as the other electrode with different channel lengths. Firstly, the Ids-Vds curves for three ports show linear behaviors indicating a good ohmic contact between the Au electrode and Te NRs owing to their matched work functions (Supplementary Fig. 7a). Good ohmic contact in our device is also important for achieving a high responsivity because the barrier between electrode and thermoelectric material suppresses the PTE responses30. Then, under a global IR light illumination with a wavelength of 8.0 µm, the polarization resolved zero-bias photovoltage responses were measured for three ports (P1, P2, and P3). As shown in Fig. 3b, all three ports show polarization resolved photovoltage (Vph) responses, which can be well fitted by:
$${V}_{\text{p}\text{h}}=\frac{\text{A}}{2}+\frac{\text{A}}{2}\times \text{sin}\left(2{\theta }-90\right)$$
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where, A denotes the maximum photovoltage at a polarization angle of 90°, and θ denotes the polarization angle. This indicates that the PR of three ports in our device is infinite (∞) according to the fitting lines. In addition, the maximum photovoltage increases slightly with the increase of the channel length, verifying again that the dominating temperature gradient is localized within the Au microstructure array. To further verify this, simulation on the temperature distribution in such device with different ports is carried out. As shown in Supplementary Fig. 8, for different ports with different channel length, the maximum temperature difference (ΔT) changes slightly and the temperature falls sharply from the centra to the edge of the Au microstructure array due to the finite-size effect. Consequently, the responsivity decreases with the increase of the channel length (Supplementary Fig. 7b). The photovoltage responsivity changes from to 410 to 225 V/W, and the photocurrent responsivity calculated using the device resistance obtained from the Ids-Vds curves in Supplementary Fig. 7a changes from 28.6 to 8.56 mA/W when port changes from P1 to P3. Moreover, the polarization resolved photovoltage responses of P1 were also measured with different incident light powers as shown in Fig. 3c. Here, the laser beam size is measured using our device with a short channel (20 µm) and the laser power density can be fitted well by using Gaussian distribution with two axis radii (1/e2 intensity) as 173 and 173 µm (Supplementary Fig. 9). Considering the small size (channel length: 20–40 µm) of our devices, the peak intensity is used for calculating the light power at device (PDevice) by31:
$${P}_{\text{D}\text{e}\text{v}\text{i}\text{c}\text{e}}=\frac{2{P}_{0}S}{\pi {r}_{1}{r}_{2}}$$
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where, P0 is the total power of the incident light, S is the device area, and r1 and r2 are two axis radii of the Gaussian beam. When the power of the incident light at device increases from 2.76 to 25.6 µW, all the polarization resolved photovoltage responses can be fitted well using Eq. (2), and the maximum photovoltage A increases from 1.13 to 10.6 mV correspondingly. For different incident light powers, the device shows stable and repeatable photovoltage responses according to the photo-switching test (Supplementary Fig. 10). Figure 3d plots the maximum photovoltages as a function of the incident light power showing a linear relation. By fitting the measured data, we can achieve a high responsivity of 410 V/W. Meanwhile, the transient photovoltage response shows a rise time of 176 µs and a decay time of 71 µs, indicating a -3dB bandwidth of 5.7 kHz of our device (Supplementary Fig. 11). Moreover, the detector also exhibits a low dark noise spectrum down to 17 nV Hz− 1/2 at high frequency range (over 5 kHz) corresponding to a noise-equivalent power of 0.04 nW Hz− 1/2, and a specific detectivity of 1.2×107 Jones at room-temperature (Supplementary Fig. 12). Furthermore, the photoresponse of the device at low temperatures is also measured and shown in Supplementary Fig. 13. Coming from the efficient heat dissipation or high thermal conductivity at lower temperatures, the device exhibits a lower photovoltage response, which further certifies the PTE response mechanism of our proposed devices. Thanks to the configuration flexibility of the perfect plasmonic absorber, the proposed PTE detectors can also realize a bipolar response with a PR = ‒1 (Supplementary Fig. 14). Comparing with the Te nanosheet based device, the Te NR based detector with same device architecture exhibits a higher responsivity (380 V/W), indicating that 1D Te NRs are more suitable than 2D Te nanosheets for PTE type detectors owing to its higher aspect ratio.
To further evaluate the polarization sensitivity of our proposed devices reasonably and accurately, a new FoM of the polarization angle sensitivity (PAS) is proposed by considering both the responsivity and the PR. As shown in Fig. 3c, the photovoltage is a function of polarization angle and can be expressed by Eq. (2). Therefore, the polarization sensitivity of photovoltage can be obtained by calculating the first-order derivative of photovoltage Vph versus polarization angle θ:
$$\frac{d{V}_{\text{p}\text{h}}}{d\theta }=\text{A}\times \text{cos}\left(2{\theta }-90\right)$$
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Therefore, the peak polarization sensitivity of photovoltage is localized at θ = 45°. The polarization sensitivity of photovoltage as a function of the incident light power is plotted in Fig. 3d and is fitted linearly, showing a peak PAS of 7.1 V/W•degree. More generally, both the responsivity (R) and polarization ratio (PR) are given in most of previous reports. In this case, the A in Eq. (4) can be replaced by R and PR. In addition, the R is proportional to Vph. As a result, the PAS can be calculated using:
$$\text{P}\text{A}\text{S}=R\times \frac{\text{P}\text{R}-1}{\text{P}\text{R}}\times \text{cos}\left(2{\theta }-90\right)$$
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Based on this equation, the PAS as a function of both R and PR is mapped and shown in Fig. 3e. As can be seen in Fig. 3e, the PAS increases when R rises, and PR undergoes polarity transition from 1 to ‒1 with polarity transition. In addition, considering the polarization-dependent photoresponses described with Eq. (5), the PASs of the recent mid-/long-wave IR photodetectors reported in previous works are calculated and shown in Fig. 3e7, 8, 16, 31–34. Comparing with other recent polarization-sensitive IR photodetectors, our proposed detectors exhibit a high responsivity and a large PR, as well as a high PAS. In addition, the specific polarization angle detectivity (PAD) can also be calculated using the specific detectivity (D*) of the detectors considering its proportional relation to R.
$$\text{P}\text{A}\text{D}={D}^{*}\times \frac{\text{P}\text{R}-1}{\text{P}\text{R}}\times \text{cos}\left(2{\theta }-90\right)$$
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As listed in Supplementary Table 2, the PADs are calculated for the mid-/long-wave polarization-sensitive photodetectors in both previous works and our work7, 8, 16, 31–34. Our devices exhibit a high PAS of 7.1 V/W•degree (13.2 V/W•degree), which is one order of magnitude higher than those reported in previous studies, and a higher PAD of 2.1×105 Jones/degree (3.8×105) for PR=∞ (PR=‒1), indicating an ultrahigh polarization sensitivity.
Full linear polarimetry detection
Although the polarization-sensitive photodetectors with a large PR have been achieved, based on either artificial nanostructures or natural semiconductors. Simultaneous detection of light intensity, polarization angle and degree of linear polarization remains challenging. There are two main challenges for realizing the full linear polarimetry detection. The mechanism of most of existing polarization-sensitive photodetectors is based on the scalar anisotropic absorption, and hence their polarization angle resolved photoresponse signals overlap twice as the angle of linear polarized light changes from 0° to 180°6, 32. Therefore, it is difficult to unambiguously detect the angle of linear polarized light in a single device. On the other hand, the detection of light intensity needs a polarization-insensitive photoresponse, which is more unrealistic for the previously reported detectors, although the polarization angle detection could be achieved by using the twist two-dimensional heterostructures or bulk photovoltaic effect in metasurface-mediated graphene detectors6, 31, 35. Here, leveraging on the configuration flexibility of the proposed perfect plasmonic absorber mediated photothermoelectric response, we design a suitable device with three ports for full linear polarimetry detection. As shown in Fig. 4a, three output ports (P0, P1, and P2) are connected to same ground terminal (GND) through three Te NRs and perfect plasmonic absorber arrays with different morphologies and orientations. In detail, a polarization-insensitive perfect plasmonic absorber is designed with an Au micro-disk array as illustrated in Supplementary Fig. 1 (right) and is used in port P0 for the light intensity detection. The corresponding simulated electric field and absorption distribution at designed resonance wavelength of 8.0 µm are shown in Supplementary Fig. 15a and b. More importantly, the experimentally measured polarization angle dependent absorption spectra show a polarization-insensitive absorption, which is the same as the simulated results (Supplementary Fig. 15c and d). In addition, two polarization-sensitive perfect plasmonic absorber arrays with a relative orientation angle of 120° are used for ports P1 and P2 to extract the polarization angle θ. Figure 4b shows the two-dimensional plot of experimental measured photovoltages of P1 and P2 under different incident light powers. The (P1, P2) pairs plotted with colored dots based on the polarization angle moves counterclockwise along a closed elliptical curve for a fixed incident light power. As the incident light power increases, the closed elliptical curve shifts towards the upper right, as shown in Fig. 4b. All (P1, P2) pairs are localized at the first quadrant owing to the unipolar responses of the designed devices. Apparently, there are some intersection points between the elliptical cures for different incident light powers. Therefore, it is necessary to distinguish these points with the port P0, which is polarization insensitive and can help to extract the accurate polarization angle. Based on the polarization angle sensitive photovoltage as described by Eq. (2), the analytical expressions of the polarization angle θ dependent photovoltage response for three ports can be written as:
$$\left(\begin{array}{c}{\text{P}}_{0}\\ {\text{P}}_{1}\\ {\text{P}}_{2}\end{array}\right)=\left(\begin{array}{c}\frac{{\text{A}}_{0}}{2}\\ \frac{{\text{A}}_{1}}{2}\\ \frac{{\text{A}}_{2}}{2}\end{array}\right)+\left(\begin{array}{c}\frac{{\text{A}}_{0}}{2}\\ \frac{{\text{A}}_{1}}{2}\times \text{sin}\left(2\left({\theta }+30\right)-90\right)\\ \frac{{\text{A}}_{2}}{2}\times \text{sin}\left(2\left({\theta }-30\right)-90\right)\end{array}\right)$$
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where A0,1,2 refers to the maximum photovoltage outputs under a fixed incident power of port P0, P1, and P2, respectively. The θ denotes the polarization angle of the incident light referring to the horizontal axis as illustrated in Fig. 4a. Moreover, considering the linear relation between the incident light power and photovoltage output of port P0 (inset in Fig. 4b), the incident light power intensity P can be obtained from the output of port P0 directly.
Beyond the light intensity, the polarization angle θ can be extracted using port P1 and P2 as:
$${\theta }=\left\{\begin{array}{c}-\frac{1}{2}{\text{tan}}^{-1}\left(-\frac{1}{\sqrt{3}}\frac{{\text{P}}_{1}^{{\prime }}-{\text{P}}_{2}^{{\prime }}}{{\text{P}}_{1}^{{\prime }}+{\text{P}}_{2}^{{\prime }}}\right) \text{w}\text{h}\text{e}\text{n}{ \text{P}}_{1}^{{\prime }}+{\text{P}}_{2}^{{\prime }}<0\\ -\frac{1}{2}{\text{tan}}^{-1}\left(-\frac{1}{\sqrt{3}}\frac{{\text{P}}_{1}^{{\prime }}-{\text{P}}_{2}^{{\prime }}}{{\text{P}}_{1}^{{\prime }}+{\text{P}}_{2}^{{\prime }}}\right)+90 \text{w}\text{h}\text{e}\text{n}{ \text{P}}_{1}^{{\prime }}+{\text{P}}_{2}^{{\prime }}>0\end{array}\right.$$
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Here, both \({\text{P}}_{1}^{{\prime }}\) and \({\text{P}}_{2}^{{\prime }}\) are normalized photovoltage outputs using equation of \({\text{P}}_{1}^{{\prime }}=\frac{2{\text{P}}_{1}}{{\text{A}}_{1}}-1\) and \({\text{P}}_{2}^{{\prime }}=\frac{2{\text{P}}_{2}}{{\text{A}}_{2}}-1\), respectively. In addition, both A1 and A2 can be easily obtained by using the incident light power P measured by port P0 and corresponding responsivity (R1 and R2) for port P1 and P2. To date, the full linear polarimetry detection including both the intensity and polarization angle of the incident linear polarized light is realized by using our properly designed three-ports device.
However, the incident light is not always ideal linear polarized owing to its complex reflection, refraction, and scattering environments. Therefore, the degree of linear polarization (DoLP) is also another important figure of merit of the linear polarized light36, 37. As discussed above, the port P0 is polarization-insensitive, and hence the light intensity P represents the total intensity of the incident light. For example, the outputs of both P1 and P2 for a non-ideal linear polarized light must deviate the closed elliptical curve of the ideal linear polarized light with a power intensity P. Despite this, the polarization angle θ can also be obtained by finding the intersection point between the closed elliptical curve and the straight line connecting the (P1, P2) and the center of the ellipse. Then, the DoLP can be obtained according to the relation between it and outputs of P1 or P2. To figure out the relation between DoLP of incident light and the photovoltage outputs of port P1 or P2, we use a quarter-wave plate to generate the non-ideal linear polarized light. Figure 4c shows the simulated absorption of the polarization-sensitive perfect plasmonic absorber as a function of linear polarization angle and quarter-wave plate (QWP) angle. Simultaneously, the photovoltage output of P1 under a fixed light power intensity as a function of linear polarization angle and QWP angle are experimentally measured and shown in Fig. 4d. As can be seen, the experimentally measured Vph shows same dependency on the linear polarization angle and QWP angle as the absorption of the perfect plasmonic absorber. More importantly, the photovoltage responses of P1 are monotonically increasing (decreasing) with the DoLP increases from 0 to 1 for θ = 90° (θ = 0°), indicating the ability to detect the DoLP of the incident light (Supplementary Fig. 16).
Application demonstrations in polarization coded communication and optical strain measurement
Finally, to demonstrate the practical usage of our polarization-sensitive IR photodetectors with infinite PR and ultrahigh polarization sensitivity, their applications in polarization coded communication and optical strain measurement are carried out. As shown in Fig. 5a, a mid-IR laser was used as the light source, and the input message was converted into American Standard Code for Information Interchange (ASCII) codes by changing the polarization angle (0° for “0” and 90° for “1”). Subsequently, the message was transferred and encoded by the polarization-sensitive photodetector with a finite PR. At last, the signals output from the photodetector were transmitted to a terminal computer through a source-measure unit (SMU). Figure 5b shows the input ASCII signals of the letter “Mid-IR” encoding by the polarization angle. Figure 5c shows the received signals by our detector. The received signal exhibits perfect square waves and matches well with the original input information, indicating a high quality of reproduction and high speed of information transmission. These results indicate that our proposed polarization-sensitive IR photodetectors with infinite PR have great potential in application of secure optical communication38, 39.
In addition to the infinite PR of our polarization-sensitive IR photodetectors, the ultrahigh polarization sensitivity supported by the high responsivity and large PR simultaneously could also offer great potential in optical strain measurement. Residual stress is an important factor of optical components that has a significant impact on their usage40. As a non-destructive measurement method to detect the strain in the optical components, the optical strain measurement based on the photoelasticity has widely been applied in the industry of glass manufacturing and photovoltaic panel manufacturing41. Here, taking advantages of our polarization-sensitive IR photodetectors with ultrahigh polarization sensitivity, we apply it into the optical strain measurement system to evaluate the strain in a polystyrene (PS) film. As shown in Fig. 5d, the IR light from a laser source with a polarization angle of 45° transmitted through the PS film with two lenses and then was focused on the detector. The x-y position of the PS film without or with strain is controlled by two stepping motors and the photovoltage outputs from the detector are recorded using an oscilloscope simultaneously. Firstly, under fixed light power and polarization angle, the photovoltage distribution for both PS film without and with strain were measured and shown in Fig. 5e (left: without strain, right: with strain). Comparing with the Vph mapping for the PS film without strain, the Vph for compressed PS film shows a non-uniform distribution, and a higher Vph is localized at the center of the film. Then, to investigate the strain distribution in the compressed PS film, the simulation of the strain distribution is carried out using a finite element method. The model used for the simulation is shown on the left panel of Fig. 5f. According to the practical deformation as shown in Fig. 5f, two forces along x and z directions are loaded to the boundary of PS film with a lateral size of 0.5×1 cm2 and a thickness of 0.5 mm. As shown on the right panel of Fig. 5f, the simulated first principal strain shows a non-uniform distribution with a maximum negative strain of ‒0.4% at the center of the PS film. Comparing the Vph mapping shown in right of Fig. 5e with the simulated local strain shown in right of Fig. 5f, they show same distribution profile, indicating the ability to test the local strain in the PS film of our polarization-sensitive IR photodetector. To further confirm that the Vph variation is caused by the local strain, a PS film with local positive strain induced by pre-embossing method is also used to measured (Supplementary Fig. 17a). As shown in Supplementary Fig. 17b, the measured Vph mapping shows a same distribution as the pre-embossed pattern of the NTU letters. In addition, the Vph is smaller for the positive strained area than that of the area without strain. This indicates that the positive and negative strain in PS film will generates opposite change of the dielectric constant.