摘要： Under the combined effect of relativistic and ponderomotive nonlinearity, resonant second harmonic generation of an intense Hermite–Gaussian (H–Gaussian) laser beam in a plasma having upward density ramp profile has been theoretically investigated. Under WKB approximation and with the use of the moment theory approach the coupled differential equations are derived which govern the spot size of the H–Gaussian laser beam. The ponderomotive force creates the density gradient in the background plasma electrons which is responsible for the excitation of the electron plasma wave. The large-amplitude electron plasma wave interacts with the fundamental beam which produces coherent radiations with double the frequency of the incident beam. In addition, the Gouy phase shift is observed for the H–Gaussian laser beam in plasma under the effect of density transition. The analysis shows the vital role of the different modes of the H–Gaussian laser beam and density ramp on the efficiency of generated harmonics and self-phase shift of laser beams in plasma.