## 1 Introduction  
The word nanoantenna is widely used to denote a scattering device able to localize an optical field into a region smaller than its wavelength [1]. An example is a plasmonic-based nanoparticle. The collective oscillation of its surface electrons, i.e., the local surface plasmon resonance (LSPR), produces a local, subwavelength field enhancement in its vicinity. Noble metals like silver (Ag) and gold (Au) exhibit LSPR resonances in optical regime. They are used in a variety of optoelectronics devices for bio sensing, imaging properties, and surface-enhanced Raman spectroscopy wireless communication [2; 3; 4; 5; 6].  
A variety of different configurations of gold and silver nano-structures, e.g., nanorods, nano-bowties, nanowires, nanoparticles, and nano-cubes have been investigated alone and in combination with dielectrics across the UV-Visible band [5; 7; 8]. Tuning of the LSPR frequency and/or wavelength of these nanoantennas has been obtained by variations in their size, shape, and material properties [9]. The dielectric constant of the medium in which the metallic nanoparticles are embedded also has a significant impact on their resonance wavelengths [10]. Related experimentally observed LSPR frequency tuning and shifts have been reported. For example, a red shift in the LSPR resonance wavelength of Ag nanoparticles was reported by [PERSON] et al. [11], when the thickness of their undercoated SiO\({}_{2}\) layers was increased. In the same study, a blue shift was also reported when the thickness of an overcoated SiO\({}_{2}\) layer was increased. The blue shift was attributed to the increase in the effective dielectric constant of the SiO\({}_{2}\) medium when the layer's thickness was increased. Bulk permittivity values were recovered only when that layer became thick. However, when the coating layer was very thin, it was found that the combination of the permittivity values of the air and dielectric yielded the effective dielectric constant.  
This article presents the concept of material quantity based (MQB) and nano size-dependent (NSD) optical losses to explain the frequency blue shift observed in fabricated core-shell (Ag-coated SiO\({}_{2}\)) nanoparticles. Increase in the size of the plasmonic nanostructures under investigation means increasing the amount of lossy materials in the system. Consequently, the LSPR frequency should be red-shifted [12; 13]. However, NSD losses mostly occur because of the presence of a larger number of defects that occur in the outer surface of the structure during its nanofabrication. The NSD optical losses are more likely to vanish beyond a certain size limit (\(\geq\)100 nm) because of smaller surface to volume ratios. In the case of larger particles, the volume effects dominate all other surface issues. Our experiments have identified a blue shift in the LSPRs of the Ag-coated SiO\({}_{2}\) nanoparticles. The measured data indicates that an increase in the effective dielectric constant of the SiO\({}_{2}\) region is not the only feature responsible for the blue shift. Furthermore, additional size-dependent effects in the nano-regime are necessary to explain the observed blue shifts of the LSPR frequencies.  
The Ag-coated SiO\({}_{2}\) nanoparticles were synthesized with different Ag shell thicknesses by a wet chemical method. Photoluminescence spectroscopy analyses revealed a blue shift in the LSPR wavelengths. The fabricated nanoparticles were then simulated with the full-wave vector finite element method (FEM) frequency domain solver in CST (Computer Simulation Technology) Microwave Studio. The NSD optical losses were incorporated in the numerical simulations through a lossy Drude model of the Ag layer with a size-dependent collision frequency of the charge carriers. The simulation and experimental analyses demonstrate the existence of higher order resonance modes in all samples. The measured results and their simulated values are in reasonable agreement.