Tunable Broadband Optical Responses of Substrate-Supported Metal/Dielectric/Metal Nanospheres

Using the image charge theory and finite element methods, we present the first comprehensive study on the optical properties of substrate-supported, three-layer, metal/dielectric/metal nanospheres. By adopting dipolar and quadrupolar approximations of the quasistatic image charge theory, we derive analytical expressions for the polarization-dependent polarizabilities of a three-layer nanosphere near a substrate and use them to find the nanosphere's plasmon resonance wavelengths as functions of the geometric and material parameters of the nanosphere-substrate system. By calculating the resonance wavelength of substrate-supported gold/silica/gold nanosphere over a sufficiently large domain of the nanosphere's dimensions, we show that this wavelength can be tuned from visible to infrared regions by altering only the size of the nanosphere's core. We also show that the resonance position as well as the enhancement and confinement of the near-field can be dynamically tuned over broad ranges by changing the polarization of the excitation light. Of significance for the applicability of our results in practice is that we employ size-dependent permittivity of gold, which allows experimentalists to readily produce these substrate-supported nanospheres with desired optical responses. Upon comparing our analytical results with the results of numerical simulations, we reveal the range of the nanospheres' outer radii within which the dipolar and quadrupolar approximations adequately describe the nanosphere-substrate interaction. Since majority of the optical functions are realized with light polarized parallel to the substrate, our results allow one to readily engineer the broadband optical responses of substrate-supported metal/dielectric/metal nanospheres for applications in resonance-enhanced sensing, in light harvesting, and in biomedicine.