Siegman A E, Sziklas E A
Appl Opt. 1974 Dec 1;13(12):2775-91. doi: 10.1364/AO.13.002775.
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.
我们提出了一种计算振荡高功率激光器三维模式图案、输出光束特性和功率输出的程序，该程序考虑了不均匀、横向流动的可饱和增益介质；激光谐振腔内的折射率不均匀性；以及任意的镜面畸变和失准。将激光器划分为多个轴向段。将每个短段上的饱和增益和折射率变化集中为该段中平面上的复增益分布。谐振腔内的循环光波以自由空间方式从中平面传播到中平面，并在通过每个中平面时乘以集中的复增益分布。在光波在谐振腔内完成每一次完整往返后，基于腔内的循环场重新计算饱和增益分布。当该程序应用于典型的非稳腔流动增益激光器时，会收敛到单一的畸变稳态振荡模式。给出了典型的近场和远场结果。作为计算的一部分，已经制定了几条关于有限截断厄米-高斯展开的经验法则，包括一个近似采样定理。
