Absorption coefficient along a propagated ultra-short laser pulse in the air based on Kramers–Kronig relations

In this manuscript, some effects such as nonlinear Kerr, stimulated Raman, and plasma generation effects lead to obtaining the nonlinear refraction index of the air along an intense ultra-short laser pulse based on one-dimensional propagation analysis. The variations in the pulse frequency by the self-phase modulation effect are investigated for achieving the functionality of the refractive index to the frequency. The mentioned functionality allows implementing Kramers–Kronig relations to measure the absorption coefficient. Results indicate that the front of the laser pulse faces a high rate of the energy loss whereas the back of the pulse experiences a gain. The implementation of Kramers–Kronig relations for a theoretical calculation of absorption coefficient variation along a laser pulse propagating in the air in which we have simultaneously taken into account the three above-mentioned effects distinguishes our work from other studies.