Observation and theory of X-ray mirages

The advent of X-ray lasers allowed the realization of compact coherent soft X-ray sources, thus opening the way to a wide range of applications. Here we report the observation of unexpected concentric rings in the far-field beam profile at the output of a two-stage plasma-based X-ray laser, which can be considered as the first manifestation of a mirage phenomenon in X-rays. We have developed a method of solving the Maxwell-Bloch equations for this problem, and find that the experimentally observed phenomenon is due to the emergence of X-ray mirages in the plasma amplifier, appearing as phase-matched coherent virtual point sources. The obtained results bring a new insight into the physical nature of amplification of X-ray radiation in laser-induced plasma amplifiers and open additional opportunities for X-ray plasma diagnostics and extreme ultraviolet lithography.