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Effective Medium Analysis of Stacked-Nanoparticles Array’s Optical Responses

Metallic nanoparticle-based material is currently implemented in many photonics-based applications such as biosensors, imaging, and color filter due to its remarkable properties called localized surface plasmon or LSP. Numerical methods are commonly used to calculate the optical responses arising from the nanostructure. However, a faster calculation can be provided by analytical methods. In this paper, we used an analytical calculation based on dipolar approximation and the transfer matrix method to calculate the optical responses of stacked-nanoparticles array on a dielectric substrate. Gold (Au) and silver (Ag) nanoparticles embedded inside a dielectric medium are considered. To validate the results, the analytical model was benchmarked to a finite element method (FEM) calculation. We found that the absolute difference of the absorbance peak of the analytical model to FEM calculation is less than 2 nm with the volume fraction of ~20% and it becomes better with a lower volume fraction. The field distribution analysis shows that lower volume fraction structures lead to weaker near-field coupling, therefore concluding that the analytical model is suitable only for sparse structure. Experimental data also can be replicated from the spectral profile showing opportunities to use the analytical model in the application design stage.