Doppler effects in the propagation of a few-cycle pulse through a dense medium.

This numerical study demonstrates that Doppler redshift exists in the reflected spectrum of a few-cycle pulse, propagating through a dense medium. It manifests itself in two different forms, a sharp low-frequency spike (LFS) located at the red edge of the reflected spectrum and a relatively broader redshift near the carrier frequency. With the variation of the laser and medium parameters, the dominant reflection mechanism changes between bulk generation of backwards propagation waves and nonlinear reflection near the front face. This leads to the manifestation of Doppler effect changing accordingly between the two different forms. This study unifies the physical mechanism behind the LFS and dynamic nonlinear optical skin effect, which enriches the theoretical explanation of the spectral redshift of few-cycle pulse propagation beyond the intrapulse four-wave mixing.