We study fully relativistic nonlinear 1D fluid equations
describing steady-state solutions for an electromagnetic
wave interacting with plasma in the self-induced transparency
regime. In addition to the well-known solution that corresponds
to the transmission of the electromagnetic wave into plasma,
another steady-state solution is shown to exist in a certain
range of the amplitude of the wave. The latter one satisfies
the same boundary conditions but corresponds to the full
reflection of the incident wave. The co-existence of the
two solutions indicates a rich structure of the interface
between the opaque and transparent phases in ultraintense
laser interactions with near-critical and overdense plasmas—in
particular, one may expect hysteresis-like behavior when
a current state of the system depends on its history.
Self-induced transparency in plasmas with sharp boundary