An augmented surface impedance theory for acoustically actuated magneto-electro-elastic nanospheres with terahertz nanoantenna applications

Abstract

A precise analytical treatment for predicting the behavior of nano-sized magneto-electro-elastic (MEE) antennas and resonators under incident acoustic waves requires careful consideration of multiphysics surface/interface effects, including magnetization, polarization, and elasticity. To date, no analytical solutions have incorporated all three phenomena simultaneously. By addressing these surface effects, this work presents a rigorous mathematical analysis of a nano-sized spherically isotropic embedded MEE spherical shell subjected to incident acoustic waves. The set of coupled spectral constitutive relations relevant to the bulk of the MEE spherical shell is distinguished from those pertinent to its free inner surface and matrix-shell interface. The surrounding matrix may consist of an isotropic dielectric or metallic material. Conventional electrodynamics theories are insufficient to address this problem, as they do not adequately account for MEE effects at the surface or interface. To overcome this limitation, the study employs the equivalent impedance matrix (EIM) method combined with surface/interface elasticity to model the surface/interface MEE behaviors rigorously. For metallic matrices, a plasmonics-based mathematical framework is utilized, with the optical properties described by the plasma model to accurately capture metallic behavior. The spectral EIM method, combined with vector and tensor spherical harmonics forming a Schauder basis for square-integrable vector fields and second-rank symmetric tensor fields on the unit sphere, is shown to be a pivotal tool for solving the fully coupled elastodynamics and Maxwell’s equations. This approach is particularly effective in capturing significant MEE surface/interface effects. This methodology enables a detailed exploration of surface/interface characteristic lengths, facilitating the examination of size-dependent effects on electromagnetic radiated power and fundamental resonance frequency. The findings provide valuable insights into the behavior of acoustically actuated nanospherical antennas, nanosensors, and nanoresonators based on MEE nanospheres. Moreover, these results have significant implications for the design and optimization of nanoscale devices in advanced technological applications.