Effect of a periodic magnetic field on phase matching condition in second harmonic generation at interactions of laser-plasma

In this paper, the process of second harmonic generation (SHG) is studied in underdense plasma in the presence of a periodic magnetic field. It is shown that the difference of momentums of photon of second harmonic and two photons of main wave can be provided by momentum of everyone of Fourier components of periodic magnetic field so that momentum of nth Fourier component can be chosen by . It is also proven that the highest efficiency of second harmonic generation will be provided by the first Fourier component of periodic magnetic field . It is revealed that periodic magnetic field can produce longitudinal waves at and as well.