In the long-wavelength limit, we establish the analytical resonance relation for coated rotationally uniaxial anisotropic spheres. We examine ranges of permissible constitutive parameters in conjunction with feasible radial ratios for two cases, one with a metallic shell and the other with a metallic core. In general, for the metallic shell case, an increase in core dielectric anisotropy leads to a larger permissible region constituted by both the shell permittivity and the core tangential permittivity for supporting localized surface plasmonic resonance (LSPR). A reverse trend is observed for having shell dielectric anisotropy. Furthermore, it is shown that for both above-mentioned arrangements, an increase in the order of LSPR results in a smaller permissible region. The derived relation serves as a design map of permissible values of the structural and material parameters, so that considerable time can be saved for future designs of resonant structures with radial anisotropy.
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