Formation of the spatial coherence of amplified spontaneous emission. 2. Randomly inhomogeneous medium

An investigation is reported of the spatial coherence of amplified spontaneous emission (ASE) in a laboratory x-ray laser. Refraction by a regular defocusing square-law profile of the permittivity $\bar{\epsilon}$ and scattering by its fluctuations $\tilde{\epsilon}$ are taken into account. The scattering of the ASE by the fluctuations $\tilde{\epsilon}$ reduces the transverse coherence length $L_c$ and the coherent ASE power. When the laser length $z$ is increased, $L_c$ tends to a constant value which can be much less than the width of the ASE beam. Under linear amplification conditions and in the absence of refraction, the angular divergence of the ASE also reaches a constant level when $z$ is increased. At this level the divergence may be considerably greater than the values due to the geometry of and the diffraction by the laser aperture. When the refraction length is less than the characteristic length for the scattering on the fluctuations $\tilde{\epsilon}$, the influence of $\tilde{\epsilon}$ on the ASE is of “latent” nature: a considerable fall of $L_c$ at the laser exit and in the far-field zone is accompanied by a relatively small reduction in the ASE flux density in the paraxial region of the beam.