  We develop a theoretical framework, based on a multipole, quasi-static
approach, for the prediction of the localized surface plasmon resonances in
Fanoshells formed via geometrical symmetry-breaking in multilayer nanoshells
consisting of a metallic core, a dielectric inner shell, and a metallic outer
shell. By tuning the core and shell offsets of a gold-silica-gold multilayer
nanoshell, we show that the theoretical model is in good agreement with
electrodynamic simulations. The dipolar resonances are more suppressed when the
core and the outer shell are concurrently offset, and less suppressed when
either the core, the inner shell, or the outer shell is offset. We attribute
the former to coupling constants arising from dual symmetry-breaking, and the
latter to coupling constants due to single symmetry-breaking. Using three
performance parameters, we propose the outer shell offset as the optimal
Fanoshell for sensing applications. This study systematically investigates all
types of offset-based, symmetry-broken, metal-dielectric-metal multilayer
nanoshells within the Rayleigh regime.
