Regression and Correlation-Based Modeling of Nonlinear Optical Response in Quantum Wells

This study investigates the nonlinear optical properties of quantum wells (QWs) by analyzing the energy eigenvalues and eigenfunctions of confined electrons. The nonlinear optical rectification (NOR) coefficient was numerically calculated under various structural parameters and external fields. To establish relationships between the system’s energy eigenvalues, dipole moment matrix elements, and NOR coefficient, regression and correlation analyses were conducted using IBM SPSS Statistics. Linear, quadratic, and cubic regression models were evaluated, with the cubic model demonstrating the best fit. Model accuracy was assessed using several evaluation metrics, including coefficient of determination (R²), mean absolute percentage error (MAPE), mean absolute error (MAE), mean square error (MSE), and root mean square error (RMSE) values for different external factors (temperature, pressure, electric field, barrier width, and barrier thickness). The results indicate that predictive modeling of the NOR coefficient enhances experimental efficiency by reducing cost and time while providing a reliable framework for understanding the optical behavior of QWs. This study offers a data-driven approach to optimizing nonlinear optical responses, contributing to advancements in optoelectronic applications.