Simple ABCD matrix treatment for transversely varying saturable gain

We have developed an ABCD matrix that, for the first time to our knowledge, accurately describes the transformation of a Gaussian beam by a medium wit h transversely varying saturable gain. In contrast with the conventional AB CD matrix, the newly developed matrix is shown to be in excellent agreement with a full beam propagation code over a wide parameter range. Accurate tr eatment of transversely varying saturable gain in laser resonators is impor tant for the optimization of end-pumped lasers, particularly for efficient diode-pumped solid-state and Kerr-lens mode-locked systems. (C) 2001 Optica l Society of America.