Effect of chirp parameter on the second harmonic efficiency in relativistic super-Gaussian laser-plasma interaction

In this paper, a homogeneous, under-dense plasma channel was subjected to an interaction with a chirped super-Gaussian laser beam. We assume that the plasma already existed. The plasma electron velocity and density variance have been obtained in the relativistic regime. We derived the second harmonic efficiency that depends on normalized laser propagation distance in plasma by solving the wave equation under W–K–B (Wentzel–Kramers–Brillouin) approximation. The influence of different kinds of laser chirp parameters is examined on the second harmonic efficiency. The second harmonic efficiency has been plotted against the ratio of the plasma frequency to the initial laser frequency and normalized laser propagation distance in the plasma channel. The effects of positive and negative chirp parameters on second harmonic efficiency are compared with non-chirped laser pulses in the maximum value. The maximum value of second harmonic efficiency depends on the laser distance propagation and chirp parameter. Also, the positive chirp is more impressive than other kinds of chirping.