  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.
