X-ray absorption by matter has long been described by the famous Beer-Lambert law. Here, we show how this fundamental law needs to be modified for high-intensity coherent x-ray pulses, now available at x-ray free electron lasers, due to the onset of stimulated elastic forward scattering. We present an analytical expression for the modified polarization-dependent Beer-Lambert law for the case of resonant core-to-valence electronic transitions and incident transform limited x-ray pulses. Upon transmission through a solid, the resonant absorption and dichroic contrasts are found to vanish with increasing x-ray intensity, with the stimulation threshold lowered by orders of magnitude through a resonant superradiantlike effect. Our results have broad implications for the study of matter with x-ray lasers.

• Received 26 March 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.107402