Numerical optimization of Mie scattering using the nonlinear conjugate gradient method

Abstract The Riccati–Bessel and Riccati–Hankel functions are fundamental to analyzing the optical scattering characteristics of spherical nanoparticles and are widely applied in Mie theory to describe the scattering of electromagnetic waves by spherical particles. However, in practical applications especially under high-order computation modes or extreme parameter ranges the numerical evaluation of these functions often encounters challenges such as reduced accuracy, slow convergence, and computational redundancy, limiting their scalability in complex scattering systems. To enhance computational efficiency within Mie theory, this study introduces the nonlinear conjugate gradient (NCG) method. By constructing an objective function based on the Mie coefficients, the scattering problem is reformulated as an unconstrained minimization task and solved through optimization. Using gold and silver nanoparticles as case studies, an optimization model aimed at minimizing scattering error is developed. Results demonstrate that the NCG method enables rapid convergence to the optimal solution while maintaining consistency in scattering and absorption coefficients. Moreover, it significantly reduces redundant evaluations of Riccati–Bessel and Riccati–Hankel functions during iterations, thereby improving computational efficiency in determining optimal particle parameters. This method effectively minimizes deviations in scattering efficiency and is applicable across a broad spectral range, offering a novel and effective pathway for extending the application of Mie theory in numerical optimization domains.