Modal study of refractive effects on x ray laser coherence

The role of smoothly varying transverse gain and refraction profiles on x-ray laser coherence is analyzed by modally expanding the laser electric field within the paraxial approximation. Comparison with a square transverse profile reveals that smoothly varying profiles generally lead to a greatly reduced number of guided modes and a consequent improvement in transverse coherence length. However, the refractive defocussing responsible for enhanced coherence can also significantly degrade the coherent power of x-ray lasers based on amplified spontaneous emission. An optimal value to Fresnel number is indicated, below which the coherent power rapidly decreases as refractive defocussing is increased. Further improvement in the coherence length without degradation of coherent power may require multipass architectures with spatial filtering instead of relying on increased refraction through narrowing of the laser.