Second harmonic generation from hemispherical metal nanoparticle covered by dielectric layer

Abstract

Using hydrodynamic theory of electron gas motion in metals, we obtain hyperpolarizability of the metal hemisphere in the framework of the quasistatic approach. For a silver hemisphere placed on a glass substrate and covered with TiO2 shell, we demonstrate analytically that conduction electrons in the vicinity of the hemisphere sharp edge dominate the nonlinear optical response of the nanoparticle. The developed theory is verified by numerical simulation in COMSOL. Numerical analysis reveals that rounding of the sharp edge affects the linear polarizability and first hyperpolarizability of the hemisphere differently. We also discuss dependence of the hyperpolarizability on the dielectric shell thickness and show that both lacking of the inversion symmetry and presence of the glass–air-TiO2 interface essentially contribute to the polarizability of the hemisphere at the frequency of the second harmonic.