Theoretical study of the nonlinear response function describing optical second-harmonic generation in nonlocal metal optics

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Abstract
Optical second-harmonic generation from the bulk of centrosymmetric metals stems from non- local electronic transport effects. So far, the nonlinear bulk response has been described within the framework of magnetic dipole and electric quadrupole interactions. In the present work a nonlinear conductivity response function incorporating nonlocal effects in all orders is presented. Through a multipole expansion, contact with previous analysis is established. The nonlinear responses stemming from the electric and magnetic field of the fundamental wave, respectively, are separated and analyzed. Plasmon effects usually neglected in bulk studies are retained. It is demonstrated that the polarization selection rules on which several conclusions about the relative strength of magnetic and electric effects have been drawn previously are violated in a fully nonlocal treatment. The most general polarization selection rules for nonlocal second-harmonic generation in centrosymmetric metals are established.