The relativistic mirror (RM) is an interesting subject which introduced in the nonlinear
regime of the laser–plasma interaction. Reflection of counter-propagating probe pulse from
relativistic flying mirror has some excellent features, such as frequency up-shifting and compressing
by a factor of 4γ2. In the high-intensity laser–plasma interaction, sometimes a
sequence of RMs creates. For example, electron density cusps generate in the nonlinear
laser wakefield generation or flying electron sheaths create in the blown-out regime of the
laser foil interaction. Under these circumstances, the second counter-propagated seed
(probe) pulse can be reflected back and forth between two or more successive RMs. This
structure may be used as a relativistic cavity (RECA). Amplification and threshold conditions
for the gain medium and pumping rate in the RECA are obtained, and it is shown that amplification
can be started from background simultaneous emission (without seed pulse). A new
feature of RECA is it’s bidirectional (two frequencies) characteristic. Thereupon, the gain process
can be implemented on the two different transitions in this bidirectional gain structure.
In the RECA, driver pulse may be assembled as a pumping operation, and background plasma
medium with high degree ionized substances is a good candidate for gain medium in the UV
or X-ray regions. In this paper, we propose a new all-optical cavity for the generation of the
ultrashort laser pulse in the UV or X-ray regions.