The extraction of parameters in photovoltaic (PV) cells is essential for optimizing the performance of solar energy systems. Accurate parameter extraction ensures reliable performance under various environmental conditions. In this paper, we introduce the Newton-Raphson-Based Optimizer (NRBO), a novel metaheuristic algorithm designed to enhance the accuracy and convergence speed of the parameter extraction process. The NRBO leverages the Newton-Raphson Search Rule (NRSR) and the Trap Avoidance Operator (TAO) to efficiently navigate the search space, avoiding local optima and improving exploitation-exploration balance. The algorithm is applied to the parameter extraction of the RTC France PV cell using SDM and is compared to state-of-the-art algorithms, including the Grey Wolf Optimizer (GWO), Dandelion Optimizer (DO), Whale Optimization Algorithm (WOA), and Atomic Orbital Search (AOS). Performance metrics such as Root Mean Square Error (RMSE), Mean Absolute Error (MAE), coefficient of determination (R2), and execution time are used for evaluation. The simulations, conducted using MATLAB Simulink, demonstrate that NRBO outperforms its counterparts, providing superior accuracy and convergence efficiency. The results affirm that NRBO is a powerful tool for parameter extraction in PV cells, significantly improving the optimization process and offering a robust solution for real-world photovoltaic applications.