Mode calculations in unstable resonators with flowing saturable gain. 1:hermite-gaussian expansion

We present a procedure for calculating the three-dimensional mode pattern, the output beam characteristics, and the power output of an oscillating high-power laser taking into account a nonuniform, transversely flowing, saturable gain medium; index inhomogeneities inside the laser resonator; and arbitrary mirror distortion and misalignment. The laser is divided into a number of axial segments. The saturated gain-and-index variation. across each short segment is lumped into a complex gain profile across the midplane of that segment. The circulating optical wave within the resonator is propagated from midplane to midplane in free-space fashion and is multiplied by the lumped complex gain profile upon passing through each midplane. After each complete round trip of the optical wave inside the resonator, the saturated gain profiles are recalculated based upon the circulating fields in the cavity. The procedure when applied to typical unstable-resonator flowing-gain lasers shows convergence to a single distorted steady-state mode of oscillation. Typical near-field and far-field results are presented. Several empirical rules of thumb for finite truncated Hermite-Gaussian expansions, including an approximate sampling theorem, have been developed as part of the calculations.