We demonstrate a new high-order harmonic generation mechanism reaching the `water window spectral region in experiments with multi-terawatt femtosecond lasers irradiating gas jets. A few hundred harmonic orders are resolved, giving uJ/sr pulses. Harm
onics are collectively emitted by an oscillating electron spike formed at the joint of the boundaries of a cavity and bow wave created by a relativistically self-focusing laser in underdense plasma. The spike sharpness and stability are explained by catastrophe theory. The mechanism is corroborated by particle-in-cell simulations.
Since the advent of chirped pulse amplification1 the peak power of lasers has grown dramatically and opened the new branch of high field science, delivering the focused irradiance, electric fields of which drive electrons into the relativistic regime
. In a plasma wake wave generated by such a laser, modulations of the electron density naturally and robustly take the shape of paraboloidal dense shells, separated by evacuated regions, moving almost at the speed of light. When we inject another counter-propagating laser pulse, it is partially reflected from the shells, acting as relativistic flying (semi-transparent) mirrors, producing an extremely time-compressed frequency-multiplied pulse which may be focused tightly to the diffraction limit. This is as if the counterstreaming laser pulse bounces off a relativistically swung tennis racket, turning the ball of the laser photons into another ball of coherent X-ray photons but with a form extremely relativistically compressed to attosecond and zeptosecond levels. Here we report the first demonstration of the frequency multiplication detected from the reflection of a weak laser pulse in the region of the wake wave generated by the driver pulse in helium plasma. This leads to the possibility of very strong pulse compression and extreme coherent light intensification. This Relativistic Tennis with photon beams is demonstrated leading to the possibility toward reaching enormous electromagnetic field intensification and finally approaching the Schwinger field, toward which the vacuum nonlinearly warps and eventually breaks, producing electron-positron pairs.
