Polarizability of a Hemispherical Metal Nanoparticle Located on a Dielectric Substrate

The frequency dependence of the dipole polarizability has been determined in the quadrupole approximation for a metal hemisphere located on a dielectric substrate in the case where light is normally incident on the substrate. Formulas for the effective relaxation time and for the invisibility and surface plasmon resonance frequencies are obtained. The evolution of plasmon resonances with a change in the hemisphere radius is studied. The origin of two resonances in the imaginary part of the polarizability and the difference of the maxima in the imaginary part of the polarizability of the hemispheres made of different metals are discussed. The character and position of the resonances in the imaginary part of the polarizability of aluminum islands are explained. Recommendations regarding the creation of an invisibility frequency band near the metal nanoisland are given. (author).