Second-harmonic generation by intense lasers in inhomogeneous plasmas

We study the second-harmonic generation by laser interaction with a cold inhomogeneous underdense plasma, using a perturbative approach to solve the coupled set of Maxwell fluid, and momentum equations. The laser field is assumed to be Gaussian with diffractive effects included. The solution of the second-order inhomogeneous wave equation is obtained from the Green's function formalism in the paraxial approximation. We show that the total power generated is proportional to the square of the laser intensity and independent of the plasma density in the low-density limit. Depending on the laser beam waist and on the plasma density profile, the second-harmonic generation can be highly efficient.