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The origin of the Redshift Spikes in the reflection spectrum of a Few-cycle Pulse in a Dense Medium

We give a detailed description about the reflected spectrum of a few-cycle pulse propagating through a resonant dense medium. An unexpected low-frequency spike appeared in the red edge of the spectrum. To figure out the origin of this redshift spike, we analysis the mechanisms responsible for the redshift of the reflected field. So far, the redshift has not been well studied for few-cycle pulses except a brief explanation made by the previous study [Kaloshan et al., Phys. Rev. Lett. 83 544 (1999).], which attributed the origin of the redshift to the so-called intrapulse four-wave mixing. However, we demonstrate numerically that the redshift consists of two separated spikes is actually produced by the Doppler effect of backpropagation waves, which is an analogue effect of dynamic nonlinear optical skin effect. Our study elucidates the underlying physics of the dynamic nonlinear optical effects responsible for the redshift spikes. Moreover, the dependency of the their frequency on the laser and medium parameters, such as medium density and input pulse area are also discussed.