Discovering Ag@TiO₂ core-shell nanoparticles capable of precisely adjusting the localized surface plasmon resonance (LSPR) peak within the near-infrared biological window is crucial for improving cancer diagnosis and treatment. Conventional diagnostic approaches are restricted by high expenses, intricate procedures, and potential risks. Despite the benefits of near-infrared bioluminescence imaging technology, current methods have limitations. While Ag nanoparticles exhibit advantageous LSPR properties, their stability and biocompatibility are sub-optimal, and the problems can be addressed via core-shell formation. Previous Ag@TiO₂ core-shell nanospheroids feature LSPR wavelengths beyond the near-infrared biological window, thus making them unsuitable for biological imaging. Therefore, investigating the light scattering properties of non-spherical Ag@TiO₂ core-shell nanoparticles (such as rotary nanospheroids and nanorods) and optimizing their size parameters are essential for advancing near-infrared bioluminescence imaging technology, especially in the field of cancer diagnosis.

We employ the finite element method (FEM) for electromagnetic field analysis, integrating a refractive index size modification model for metal nanoparticles to simulate light scattering properties of Ag@TiO₂ core-shell nanoparticles, including nanospheroids and nanorods. Meanwhile, a geometric model is built by inputting incident light, particle parameters, and environmental conditions, followed by setting material properties, boundary conditions, mesh division, calculations, and post-processing of results. To validate FEM accuracy, we conduct comparisons with the Mie theory and T-matrix method, demonstrating high agreement. Furthermore, the influence of metal nanoparticle size on the refractive index is considered, with a specific complex refractive index formula utilized for computation. This approach not only ensures precision and reliability but also provides an effective avenue for exploring the light scattering behavior of Ag@TiO₂ core-shell nanoparticles with diverse shapes and dimensions.

We investigate metal@TiO₂ core-shell nanoparticles and yield the following novel findings. The first is core material selection. By carrying out simulation and comparison of volume scattering coefficients of Ag@TiO₂, Au@TiO₂, Cu@TiO₂ core-shell nanospheroids and nanorods (Fig. 4), it is determined that Ag-core nanoparticles demonstrate the most pronounced light scattering properties at resonance wavelengths. The volume scattering coefficient of Ag@TiO₂ nanospheroids peaks at 804 nm, providing a basis for future investigations. The second is the influence of size parameters. An analysis of the scattering properties of Ag@TiO₂ core-shell nanoparticles under varying core lengths, aspect ratios, and shell thicknesses is conducted. With the increasing core length, the resonance wavelength initially shifts toward shorter wavelengths before transitioning to longer wavelengths, accompanied by a scattering coefficient increase. Additionally, a rise in the core aspect ratio leads to a red shift in the resonance wavelength and a decrease in the scattering coefficient, while a shell thickness increase brings about a similar red shift in the resonance wavelength and a scattering coefficient decrease (Figs. 5?7). The manipulation of these size parameters enables precise tuning of the resonance wavelength within the visible to near-infrared spectrum, which is consistent with practical application demands. Meanwhile, we investigate environmental and orientation effects to assess their influence on light scattering properties. It is observed that an increase in the environmental refractive index leads to a red shift in the resonance wavelength and an increase in the scattering coefficient (Fig. 8). Furthermore, alterations in particle orientation result in the appearance of longitudinal and transverse LSPR modes in the scattered light spectrum. The wavelength of the longitudinal LSPR mode can be adjusted from the visible to near-infrared range, exhibiting high intensity and enhanced versatility (Fig. 9). In the field of biological imaging optimization, the size parameters of Ag@TiO₂ core-shell nanoparticles are fine-tuned for two commonly utilized laser wavelengths of 800 nm and 980 nm. This optimization strategy aims to achieve maximum volume scattering coefficients, thereby determining the optimal core lengths and aspect ratios (Fig. 10). The tailored Ag@TiO₂ core-shell nanoparticles are identified as promising contrast agents for biological imaging applications.

We find that Ag@TiO₂ core-shell nanoparticles outperform their counterparts with Au and Cu cores in terms of light scattering properties, especially at the commonly employed 800 nm and 980 nm wavelengths for biological imaging. By adjusting the core length, aspect ratio, and shell thickness, the resonance scattering peak position can be precisely controlled, covering the visible to near-infrared spectrum to meet diverse application requirements. An increase in the environmental refractive index leads to a red shift and reduced intensity of the scattering peaks. Although particle orientation does not change the scattering peak position, it can control the appearance of L-LSPR and T-LSPR modes, with L-LSPR providing a wider wavelength tuning range. At 800 nm, optimized Ag@TiO₂ core-shell nanoparticles exhibit optimal light scattering performance, with the maximum volume scattering coefficient reached at a core length of 106 nm and an aspect ratio of 2.8. At 980 nm, both the optimal size parameters and scattering coefficients have been improved. Therefore, optimized Ag@TiO₂ core-shell nanoparticles are ideal contrast agents for biological imaging.