Retrieval of Two-Dimensional Size Distribution and Concentration of SiO2@Au Core–Shell Nanospheres by Extinction Spectroscopy

The optical properties of SiO2@Au core–shell nanospheres are related to the core radius, shell thickness, and particle number concentration. However, simultaneously retrieving their joint distribution of core radius and shell thickness, together with particle number concentration from extinction spectra, is challenging because of parameter coupling and ill-posedness. In this work, we address issues in retrieving this two-dimensional size distribution and concentration of SiO2@Au core–shell nanospheres from extinction spectra. A standardized inversion strategy applicable to structural configurations is established through physical mechanism verification, the optimization of inversion parameters, and robustness evaluation. The results show that the optimal inversion parameters depend on particle structure. For small-core/thin-shell nanospheres, the optimal wavelength range is 200–400 nm with a wavelength interval of 5 nm. For the three structural categories, the optimal wavelength range extends over 200–1200 nm with a wavelength interval of 10 nm. In simulated tests with random noise levels ranging from 0.01% to 1%, the relative errors in the retrieved mean core radius and shell thickness are below 2% for all systems, indicating stable recovery of the mean structural parameters under the specified noise conditions. These numerical results provide a theoretical proof of concept; experimental validation with real SiO2@Au nanoparticles remains necessary before practical application.