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Relativistic High Harmonic Generation (ROM Harmonics)

Relativistic High Harmonic Generation (ROM) is a non-linear process setting in when a laser pulse with relativistic laser intensity interacts with a steep plasma surface (SHHG). A laser with relativistic intensity I_L > 10¹⁹ W/cm² drives electrons on the plasma boundary to relativistic oscillations, upon which the laser itself is reflected (plasma mirror). According to the relativistic doppler effect the reflected light is shifted in frequency proportional to the plasma mirrors velocity. This leads to the emission of an ultra-short light burst once per laser cycle. The resulting spectra is a frequency comb with even and odd orders (for incidence angle >0°) of the laser frequency - high harmonic spectra of the laser frequency. This mechanism is named Relativisitc Mirror Model (ROM). The SHHG are investigated as a novel brilliant and coherent ultrashort pulse source with high pulse intensity. In differentiation to gaseous HHG or laser driven HHG sources from plasma plums, the relativistic HHG process is not limited by the applied laser intensity and enables a high HHG pulse energy for a single driving laser pulse.

Content

1. Relativistic Mirror Model
2. Characteristics

Relativistic Mirror Model

Ultrashort laser pulses with high laser energy reach the relativistic intensity at > 1x10¹⁹ W/cm² and ionize the surface of a solid during the first laser cycles. A steep plasma boundary is created and the laser can be reflected when the electron densities reach the critical density (n_c). In the further interaction the laser pulse drives the plasma electrons at the plasma boundary to collective oscillations with the laser frequency (ω), reaching relativistic velocities β = v/c, where with c the speed of light. Due to the relativistic doppler effect, light is reflected from a moving source is shifted in frequency. This leads for the reflected laser pulse to the generation of new frequency content that could reach up to the maximum of the doppler shift. The forward movement of the electron density towards the laser occurs in a time duration less than a laser cycle T_L, and this leads to the emission of one pulse per driving laser cycle with an pulse duration of T < T_L/2. In detail, the ROM model includes plasma dynamics and the plasma mirror is described by the relativistic dynamics of the plasma current density.

Characteristics

The highest harmonic number, the cutoff frequency is N_max = 3γ³ with γ being the Lorentz factor of the electron oscillations at the boundary. The theoretical model predicts a scaling of the HHG intensity with the laser intensity I(N) ~n^-p, where p lies between 8/3 or higher. The efficiency of the process is predicted to reach 10^-6. Experiments demonstrated HHG reaching to photon energies in the keV range . The HHG divergence follows the laser divergence Θ(N) ~ Θ_L * C/N, with C > 1 . Plasma dynamics, as e.g. target denting, introduce spatial temporal couplings and alter divergence and spectral structure.