Curvature sensing plays an important role in mechanical bending angle measurement, human posture detection, bridge and road construction, structural deformation, and other mechanical engineering and structural health monitoring fields^[1–4]. Compared with electrical curvature sensors, the optical curvature sensor has the advantages of small size, anti-electromagnetic interference, corrosion resistance, high sensitivity, and low maintenance cost, so it has been widely used in bending measurement^[5]. Common optical curvature sensors include curvature sensing fiber and other technologies^[6–9]. But there are still some problems unsolved, such as a small detection range, poor sensitivity, and linearity^[10].

One-dimensional photonic crystals (1D-PCs) have been the focus of optoelectronics research because of their high reflection, wide bandgap, and simple structure^[11–20]. In addition, the reflection and transmission spectra of 1D-PCs change with the angle of incident light. Using this interesting property, if flexible 1D-PC films can be realized, the reflection and transmission spectra will change with the curvature. In this paper, we report a curvature sensor based on flexible 1D-PC films. The curvature sensor exhibits a maximum sensitivity of 0.26nm/m−1 and a wide measuring range of 33–133m−1, nearly 10 times larger than the fiber-based curvature sensors^[21]. And the shift of the transmission peak varies approximately linearly with the curvature in the entire measurement range. This work provides a feasible scheme for the construction of a curvature sensor.

The structure diagram of 1D-PC is shown in Fig. 1(a), which consists of periodic low-refractive index (nL) materials and high-refractive index (nH) materials alternately stacked. When the number of cycles gradually increases, the photonic bandgap will gradually form in the reflection spectrum, and the larger the number of cycles, the more obvious the photonic bandgap will be, as shown in Fig. 1(b). If a defect layer is introduced into the periodic structure, generally doubling the thickness of the intermediate layer, a defect peak will be introduced into the photonic bandgap^[22,23]. One of the important characteristics of 1D-PC films is that their spectrum changes with the incident angle. Regarding Fig. 1(c), it presents the transmission spectrum of a defective 1D-PC film with a simulated central wavelength of 1500 nm. This film consists of 5 periods, and the low refractive index layer has a thickness of 246 nm, while the high refractive index layer measures 168 nm. As the angle of light increases gradually, its transmission peak gradually blue shifts, and the peak gradually decreases.

In addition, the spectra of 1D-PC films with different periodic thicknesses vary in different amplitudes with angles. Figure 1(d) shows the variation of the transmission spectrum of the defect 1D-PC films with the center wavelength of 1500 nm and 1800 nm as the incident angle changes. As for the defect 1D-PC thin film with a simulated central wavelength of 1800 nm, it comprises 5 periods and possesses a low refractive index layer with a thickness of 296 nm, along with a high refractive index layer that is 202 nm thick. When the incident angle changes from 0° to 60°, the transmission peak of the defective 1D-PC films with a central wavelength of 1500 nm is shifted by 202 nm, while the transmission peak of the defective 1D-PC films with a central wavelength of 1800 nm is shifted by 246 nm. The larger the periodic thickness is, the larger the offset is. These properties make curvature sensors based on flexible 1D-PC films possible. Assuming that the bending radius of the circular 1D-PC film is r, its transmission spectrum can be written as T=∫0xTxS2rx−x2dx,(1)where Tx is the transmission spectrum at x, x is the position of 1D-PC film, and S is the total area of the 1D-PC film. The above calculation formula can be interpreted as follows: the total transmission spectrum of the curved 1D-PC film is the integral of the spectra of each small area with different angles. Since the curvature change will lead to the change of the included angle between each film and the incident light, the total transmission spectrum will inevitably change so that the curvature sensing can be realized.

The transmission spectrum of a 1D-PC film with different bending radii can be calculated by using Eq. (1). Figure 1(e) shows the change of transmission peak of defective 1D-PC films with a central wavelength of 1500 nm with the bending radius. As the curvature increases, the transmission peak gradually blue shifts. When the curvature changes from 33m−1 to 133m−1, the defect peak shifts by 29 nm, and the sensitivity is 0.29nm/m−1. Due to the increase of periodic thickness, the transmission peak increases with the angular offset, so the increase of periodic thickness leads to the improvement of sensitivity of the defective one-dimensional photonic crystal curvature sensor. Figure 1(f) shows the change of transmission peak of the defective one-dimensional photonic crystal with a central wavelength of 1800 nm along with the bending radius. When the curvature changes from 33m−1 to 133m−1, the defect peak shifts by 36 nm, and the sensitivity is 0.36nm/m−1. The increase of periodic thickness improves the sensitivity of the curvature sensor. Moreover, a detailed analysis of the curvature change response in the flexible 1D-PC films with different period numbers is provided in the Supplementary Material, Figs. S3 and S4.

In this paper, 1D-PC films are prepared by a spin coating method. The selected materials are As30S70 and PVA as high and low refractive index materials. As a chalcogenide glass, As30S70 has high transmittance and a refractive index in the near-infrared range. Meanwhile, PVA is a water-soluble polymer with good light transmittance [Supplementary Material, Fig. S5(a)] and flexibility. The solvents of the two materials have no mutual influence on the materials, so As30S70 and PVA are a group of ideal materials for constructing high-performance flexible 1D-PC films. Additionally, both As30S70 and PVA exhibit low coefficients of thermal expansion (CTE), with As30S70 having a CTE of 24 ppm/°C and PVA having a CTE of 21 ppm/°C (ppm, parts per million)^[24,25]. The compatibility of these materials is advantageous for their seamless integration into the fabrication process of flexible 1D-PC films. Their low CTE values further contribute to the films’ thermal stability and resistance to temperature-induced deformations. At the wavelength of 1550 nm, the refractive indices of As30S70 and PVA are about 2.2 and 1.5, respectively, so the refractive index contrast of these two materials can be up to 0.7. The reflectivity simulations are conducted with different periodic layers according to the above theoretical thickness. When the thicknesses of PVA/As30S70 are 245/167 nm and 298/204 nm in the model, the transmission peaks are at 1500 nm and 1800 nm when the light is incident normally, respectively.

Based on the simulation results, we alternately fabricated As30S70 and PVA thin films to form periodic structures through spin-coating. During the preparation of As30S70 layers, when 100% n-propylamine or 100% n-butylamine (BA) is used as a solvent, nano-scale pores appear in the As30S70 films [see Supplementary Material, Fig. S6(a)], which greatly affect the stability and reflectivity of the 1D-PC films. The dissolution mechanism of As30S70 in n-propylamine, n-butylamine, and ethylenediamine (EDA) is different. In n-propylamine or n-butylamine, the dissolution of As30S70 results in the formation of alkyl ammonium arsenic sulfide (AAAS) salts, which lead to the formation of pores during spin-coating^[26,27]. However, this problem does not appear when ethylenediamine is used as the solvent. Since the ethylenediamine molecule contains two N atoms, it chelates two arsenic centers^[27], avoiding the formation of AAAS salts, and its dissolution mechanism is shown in Fig. 2(a). Therefore, adding a small amount of ethylenediamine as a mixed solvent to n-propylamine can effectively prevent the generation of pores. However, excessive ethylenediamine will cause poor wettability for As30S70 solution on the surface of the PVA film, affecting the film quality^[28]. Here we use 95% n-propylamine and 5% ethylenediamine as the mixed solvent, effectively avoiding the generation of pores and ensuring wettability.

Moreover, the relative humidity in the environment during spin-coating also significantly impacts the quality of the films. Unstable relative humidity can lead to large differences in the thickness of the PVA films during the fabrication (see Supplementary Material, Fig. S7 and Table S3). Also, the spin-coating of the As30S70 layers should be executed at low relative humidity, or the film will absorb water and atomize. After spin-coating, the film is heated for uniform forming and drying, as shown in Figs. 2(b) and 2(c). At last, when the 1D-PC film is fabricated and dried, it can be easily peeled off from the substrate with tape to obtain a flexible 1D-PC film, as shown in Figs. 2(d) and 2(e).

The reflectance of the 1D-PC films gradually increases with the number of layers, as shown in Fig. 3(a), which is highly consistent with the theoretical calculation results illustrated in Fig. 1(b). It can be seen that the reflectance spectrum does not change much when the number of film layers is larger than 13 and remains essentially constant when the number of film layers is larger than 18. It is worth noting that, as the number of layers increases, the photonic bandgap’s center gradually blue-shifts because the thickness of the previous spin-coated film decreases with each heating step. The scanning electron microscope (SEM) image of the cross-section of the near-infrared 1D-PC film is shown in Fig. 3(b), which clearly shows the morphology of the As30S70 and PVA films. The clear dividing line between the PVA and As30S70 indicates that there is no residual stress in each layer, and the alternate spin-coating does not affect the integrity between layers.

The comparison of transmittance, reflectance, and simulated reflectance of the 1D-PC film with 18 layers is shown in Fig. 3(c). The actual photonic bandgap reflection spectrum is consistent with the simulation results, and the photonic bandgap formed in the near-infrared band has an extremely wide bandwidth of more than 450 nm, which is more than 3 times that of all-polymer-based 1D-PC films^[11,29]. Meanwhile, the experimental reflectance in Fig. 3(c) is as high as 98.1%, which is nearly 5% higher than the highest for the near-infrared flexible 1D-PC film^[30]. Changing the incident angle, the near-infrared photonic bandgap reflection that is basically consistent with the simulation results (Supplementary Material, Fig. S1) can be obtained, as shown in Fig. 3(d). In order to test the repeatability of this approach, different samples were prepared under the same experimental conditions. It can be seen that the reflectance spectra of different samples are substantially identical in Fig. 3(e), which proves that the process has good repeatability (for details, see Supplementary Material, Fig. S2, Table S1, and Table S2). The near-infrared 1D-PC films can be easily peeled off with tape after drying, and there is almost no discrepancy between the reflectance of the films before and after the transfer, as shown in Fig. 3(f). The inset of Fig. 3(f) shows excellent mechanical properties and good flexibility of the films, potential for various flexible infrared devices. Furthermore, we placed the 1D-PC film in different ambient humidity for a while to test the effect of environmental moisture on the PVA in the film. The results show that the ambient humidity has a negligible effect on the photonic bandgap properties of the 1D-PC film, proving that the film has excellent robustness [see Supplementary Material, Fig. S5(b)]. The reason for the robustness is that the PVA thin layers in the 1D-PC film are covered by As30S70 layers, effectively preventing PVA from absorbing moisture in the environment.

By doubling the middle layer of the 1D-PC film, the defect peak can be introduced into the photonic bandgap (for details, see Supplementary Material, Fig. S8). After the experimental investigation, the total number of layers is 10, and the thickness of the fifth layer (from top to bottom, the material is PVA) is doubled. Figures 4(a) and 4(b) show the variation of the transmission spectrum of the defect 1D-PC film with the center wavelength of 1500 nm and 1800 nm, respectively, with the incident light angle. When the incident light angle increases from 5° to 60°, the transmission peaks shift by 213 nm and 257 nm, which is consistent with the above simulation calculation. And the larger the period, the larger the shift is. Figure 4(c) is a schematic diagram of measuring the transmission spectrum of defective 1D-PC film as a function of curvature. Standard dies of different diameters are used to plastic the film, thus changing the curvature of the film. Incident light is filtered through the film and into the spectrometer for analysis. It can be seen that the transmission peaks blue-shift significantly with the increasing of the films’ curvature from 33m−1 to 133m−1 in Figs. 4(d) and 4(e). The shift of the peak position is plotted in Fig. 4(f), and a linear relationship between the shift of the peak and the film’s curvature is inferred from the results. The results present that the fabricated defective 1D-PC films have a wide measuring range within 33–133m−1 for curvature sensing, nearly 10 times larger than that of the fiber-based curvature sensors^[21,31–33]. And the curvature sensitivities of the initial transmission peak at 1500 nm and 1800 nm are 0.23nm/m−1 and 0.26nm/m−1, respectively. Obviously, the 1800-nm-curvature sensor has a higher sensitivity than the 1500-nm-curvature sensor, which is consistent with the simulation results illustrated in Figs. 1(e) and 1(f). With the same incident angle variation, the films with an initial transmission peak at 1800 nm exhibit a greater transmission peak shift than those with a transmission peak at 1500 nm, so they show a higher sensitivity to variations in the incident angle and exhibit a higher sensitivity in curvature measurement. In addition, the sensitivity of the prepared 1D-PC film curvature sensor is slightly lower than that calculated by theory, which is mainly caused by two reasons: one is that there is a certain gap between the actual period thickness and the theory, and the other is that the incident light has a divergence angle. However, this does not affect the reliability of the experimental results.

In conclusion, we propose a curvature sensor based on 1D-PC films. By taking advantage of the property of the one-dimensional photonic crystal transmission spectrum changing with the incident angle, the flexible 1D-PC films are realized for curvature sensing. High-performance near-infrared flexible 1D-PC films with a dense chalcogenide glass layer and polymer layer were fabricated by solution processing. Among them, chalcogenide glass is used as a high refractive index layer, and water-soluble polymer PVA is used as a low refractive index layer, which makes the refractive index of the two materials in 1D-PC thin films have significant differences, and the prepared 1D-PC film has good flexibility and robustness. In order to obtain a narrow transmission peak in a wide photonic bandgap, a defect layer is introduced into the periodic structure. The curvature sensitivity of 1D-PC films with initial transmission peaks at 1500 nm and 1800 nm is 0.23nm/m−1 and 0.26nm/m−1, respectively. And the shift of the transmission peak varies approximately linearly with the curvature in the entire measurement range. This flexible thin-film-based curvature sensor opens up new possibilities for optical curvature sensing and measurement.