Second-order susceptibilities of small metallic particles are calculated by the quantum size effect, in which the wave functions of conduction electrons are constrained in a small sphere. The electric-quadrupole term, which plays an essential role in the second-harmonic generation in metals, varies inversely with different powers of the radius. The magnitude of the quadrupole susceptibility is enhanced by the quantum size effect as the particle size diminishes below 10 nm, and approaches the results evaluated from the free-electron-gas model as the particle radius goes to infinity. The enhancement of the second-harmonic reflectivity generated from small metallic particles, as calculated in this work, is in general agreement with experimental results.
All Science Journal Classification (ASJC) codes