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In this study, by using the Corning 1737 glass as a substrate and an e-beam system, the optical properties of the deposit MgF2 and Nb2O5 single-layer film were investigated in terms of extinction coefficients (k values) and refractive indices (n values). The equation d = λ /(4 n) was used to calculate the thickness (d) of 1/4 wavelength (λ) for each layer of MgF2 and Nb2O5 layer in the MgF2–Nb2O5 bilayer films of the designed distributed Bragg reflectors (DBRs) with a reflective wavelength at blue light (∼ 450 nm). Each pair of MgF2–Nb2O5 bilayer film was defined as a period, and the glass substrates were used to deposit the films with two, four, and six periods for the fabrication of the DBRs. The field emission scanning electron microscope equipped with a focused ion beam was used to measure the thickness of each MgF2–Nb2O5 layer in the DBRs with different periods. The measured maximum reflective ratios were compared with Sheppard's approximate equation, which calculates only the maximum reflective ratio at a specific wavelength. We would show that the measured results of the fabricated DBRs matched the results simulated using Sheppard's approximate equation. [ABSTRACT FROM AUTHOR]

The Ta2O5 and SiO2 single-layer films were deposited on the glass substrates to measure their refractive properties under different optical wavelengths. After that, the Ta2O5 and SiO2 films were used as high and low refractive index materials to design the blue distributed Bragg reflectors (DBRs) with different periods. The approximate formula proposed by Sheppard was used to calculate the maximum reflectance ratio of the bi-layer SiO–Ta2O5 DBRs with two, four, six, and eight periods. The COMSOL Multiphysics software was used to simulate the reflective spectra of the SiO2–Ta2O5 DBRs with different stacking orders and periods by incorporating the refractive indexes of the Ta2O5 and SiO2 films at a wavelength of 550 nm. The SiO2–Ta2O5 DBRs with different periods were fabricated by depositing the Ta2O5 and SiO2 films on glass substrates, and their reflective properties were measured. We compared the measured reflective spectra of the fabricated SiO2–Ta2O5 DBRs with the simulated reflective spectra to show the effect of the different stacking orders. [ABSTRACT FROM AUTHOR]

Early prediction of students' learning performance and analysis of student behavior in a virtual learning environment (VLE) are crucial to minimize the high failure rate in online courses during the COVID-19 pandemic. Nevertheless, traditional machine learning models fail to predict student performance in the early weeks due to the lack of students' activities' data in a week-wise timely manner (i.e., spatiotemporal feature issues). Furthermore, the imbalanced data distribution in the VLE impacts the prediction model performance. Thus, there are severe challenges in handling spatiotemporal features, imbalanced data sets, and a lack of explainability for enhancing the confidence of the prediction system. Therefore, an intelligent framework for explainable student performance prediction (ESPP) is proposed in this study in order to provide the interpretability of the prediction results. First, this framework utilized a time-series weekly student activity data set and dealt with the VLE imbalanced data distribution using a hybrid data sampling method. Then, a combination of convolutional neural network (CNN) and long short-term memory (LSTM) was employed to extract the spatiotemporal features and develop the early prediction deep learning (DL) model. Finally, the DL model was explained by visualizing and analyzing typical predictions, students' activities' maps, and feature importance. The numerical results of cross-validation showed that the proposed new DL model (i.e., the combined CNN-LSTM and ConvLSTM), in the early prediction cases, performed better than the baseline models of LSTM, support vector machine (SVM), and logistic regression (LR) models. [ABSTRACT FROM AUTHOR]