Plasmonic properties of composition graded spherical nanoparticles in quasi-static approximation

During the operation of a localized surface plasmon resonance (LSPR) sensor made in the form of a core-shell nanoparticle with the shell acting as a sensing layer, the target molecules penetrate into the shell due to intrinsic diffusion or reaction mechanisms. As a result, these molecules or various reactants are nonuniformly distributed in the shell layer. Such sensing particles are termed composition graded plasmonic particles, and their LSPR characteristics may be quite different from those of the uniform core-shell particles. Here, under the quasi-static assumption, a perturbation theory is developed to predict the LSPR properties of composition graded plasmonic particles. The effects of the composition gradient on the LSPR properties due to a metal hydride, a dielectric, and an effective medium are either numerically calculated or analytically derived. Our results show that various configurations of the composition gradient can tune the location and the amplitude of the LSPR peak. The results are important for understanding the sensing performance of composition graded plasmonic particles, and the perturbative treatment presented here can also be used for other composition graded structures.