The output of amplified spontaneous emission lasers

The output of amplified spontaneous emission (ASE) lasers such as X-ray lasers operated without mirrors is calculated exactly for Gaussian and Lorentzian small signal gain profiles by a simple Taylor series expansion. The accuracy of the 'Linford' formula commonly used as an approximation for the output of ASE lasers is evaluated by comparison to our exact solutions. The Linford formula is accurate to better than 10% for intensities produced by a Gaussian gain profile, but requires multiplication by a correction factor of 1/π, at gain length product greater than 5 for Lorentzian gain profiles.