Relativistic Doppler effect: universal spectra and zeptosecond pulses

Abstract

We report on a numerical observation of the train of zeptosecond pulses produced by reflection of a relativistically intense femtosecond laser pulse from the oscillating boundary of an overdense plasma because of the Doppler effect. These pulses promise to become a unique experimental and technological tool since their length is of the order of the Bohr radius and the intensity is extremely high $\propto 10^{19}$ W/cm${}^2$. We present the physical mechanism, analytical theory, and direct particle-in-cell simulations. We show that the harmonic spectrum is universal: the intensity of $n$th harmonic scales as $1/n^p$ for $n<4{\gamma }^2$, where $\gamma$ is the largest $\gamma$--factor of the electron fluid boundary, $p=3$ and $p=5/2$ for the broadband and quasimonochromatic laser pulses respectively.

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