The [001]-oriented Pr³⁺ doped Pb(Mg_1/3Nb_2/3)O₃-0.30PbTiO₃ (Pr-PMN-PT) thin films with a composition near the morphotropic phase boundary (MPB) were synthesized by a sol–gel method. The crystal structure was characterized using X-ray diffraction. It was found that a single perovskite phase was achieved in Pr-PMN-PT thin films annealed at 650 °C for 3 min. The dielectric constant (ε_r) value was 2400 in 2.5% Pr-PMN-PT thin films at room temperature, 110% higher than that of pure PMN-PT samples. Through 2.5% Pr³⁺ doping, remanent polarization (P_r) and coercive field (E_c) values increased from 11.5 μC/cm² and 35 kV/cm to 17.3 μC/cm² and 63.5 kV/cm, respectively, in PMN-PT thin films. The leakage current densities of pure and 2.5% Pr-PMN-PT thin films were on the order of 1.24 × 10⁻⁴ A/cm² and 5.8 × 10⁻⁵ A/cm², respectively, at 100 kV/cm. A high pyroelectric coefficient (p_y) with a value of 167 μC/m²K was obtained in 2.5% Pr-PMN-PT thin films on Si substrate, which makes this material suitable for application in infrared detectors.

Subwavelength grating structure has excellent filtering characteristics, and its traditional design method needs a lot of computational costs. This work proposed a design method of two-dimensional subwavelength grating filter based on a series feedback neural network, which can realize forward simulation and backward design. It was programed in Python to study the filtering characteristics of two-dimensional subwavelength grating in the range of 0.4–0.7 µm. The shape, height, period, duty cycle, and waveguide layer height of two-dimensional subwavelength grating were taken into consideration. The dataset, containing 46,080 groups of data, was generated through numerical simulation of rigorous coupled-wave analysis (RCWA). The optimal network was five layers, 128 × 512 × 512 × 128 × 61 nodes, and 64 batch size. The loss function of the series feedback neural network is as low as 0.024. Meanwhile, it solves the problem of non-convergence of the network reverse design due to the non-uniqueness of data. The series feedback neural network can give the geometrical structure parameters of two-dimensional subwavelength grating within 1.12 s, and the correlation between the design results and the theoretical spectrum is greater than 0.65, which belongs to a strong correlation. This study provides a new method for the design of two-dimensional subwavelength grating, which is quicker and more accurate compared with the traditional method.