Nonlinear electromagnetic response of a uniform electron gas

The linear electromagnetic response of a uniform electron gas to a longitudinal electric field is determined, within the self-consistent-field theory, by the linear polarizability and the Lindhard dielectric function. Using the same approach we derive analytical expressions for the second- and third-order nonlinear polarizabilities of the three-, two- and one-dimensional homogeneous electron gases with the parabolic electron energy dispersion. The results are valid both for degenerate (Fermi) and non-degenerate (Boltzmann) electron gases. A resonant enhancement of the second and third harmonics generation due to a combination of the single-particle and collective (plasma) resonances is predicted.