We present experiments dealing with a femtosecond laser-driven cluster-based plasma, where by analyzing the nonlinear phenomenon of satellites of spectral lines of Ar XVII, we revealed the nonlinear phenomenon of the generation of the second harmonic of the laser frequency. For performing this analysis we developed new results in the theory of satellites of spectral lines. From such lineshape analysis we found, in particular, that the efficiency of converting the short (40 fs) intense (3×10¹⁸ W/cm²) incident laser light into the second harmonic was 2%. This result is in the excellent agreement with the 2-Dimensional Particle-In-Cell (2D PIC) simulation that we also performed. There is also an order of magnitude agreement between the thresholds for the SHG found from the line shape analysis and from the 2D PIC simulations.