Based on the fundamental theory of heat transfer, the mathematical formulas that describing the transient temperature distributions of two-sided laser diode (LD) pumped Nd∶GGG (gadolinium gallium garnet) heat capacity slab laser were derived in this paper. By means of finite element analysis by ANSYS, transient temperature fields and stress distribution in the slab medium were simulated with various boundary conditions, while the beam distortions induced by thermal gradients were analyzed briefly. The obtained results could benefit to the primary designing of solid state heat capacity laser (SSHCL). Numerical analysis proved that under incomplete adiabatic boundary conditions, it would result in temperature gradients perpendicular to the optical axis. About 0.2 μm optical path differences would occur between the edge and optical axis of the slab. In addition, the thermal distributions in the slab during the subsequent cooling stage were mainly studied. The influences of different cooling methods such as air cooling, water cooling and mist cooling were discussed and cooling methods suitable for a SSHCL were briefly studied.

Approximate formulas of transient temperature and stress distributions in the slab of a two-side pumped heat capacity laser are attained by solving the heat diffusion equation. Based on the formulas, the distributions of temperature and stress during the pump period of a two-sided symmetrically laser diode array (LDA) pumped Nd:GGG slab laser with 5-kW average output power are numerically simulated. The results show that the temperature in the slab will averagely increase by more than 70 Celsius degrees after operating for 10 seconds; the stress and maximum of the temperature difference in the slab are about 30 MPa and 24 Celsius degrees, respectively. The thermal induced effects are discussed also.

The pumping configurations for realizing high average power solid state laser are summarized, including Nd:GGG crystal slab laser in heat capacity operating mode, Yb-doped slab lasers and thin-disk lasers etc., which provide a reference for designing high average power solid state lasers pumping modes.

The small-scale self-focusing of divergent beams is studied. Based on the nonlinear paraxial wave equation, the propagation equation of small-scale perturbation of divergent beams has been deduced with a coordinate transformation. The evolvement law of the growth critical frequency of small-scale perturbation, maximum growth frequency and relative B integral is obtained. The influence of the initial radius of divergent beams on small-scale self-focusing is discussed. It is found that for a given propagation distance, the fastest growing frequency, the maximum perturbation growth, and thus the B integral decrease with the decrease of the initial radius of divergent beams. For a given initial radius, as the propagation distance increases, the growth of the B-integral becomes slow and stops at last. Also, the expression for the distance at which the filaments are formed is obtained by local energy conservation, and it is shown that a small initial radius extends the filamentation distance.

研究了发散光束的小尺度自聚焦效应。从非线性傍轴波动方程出发,利用坐标变换,推导出发散光束小尺度扰动的传输方程,进而得到小尺度扰动增长的临界频率、最大增长频率和相应B积分值的变化规律。研究了发散光束初始曲率半径对小尺度自聚焦效应的影响。结果表明,对于一定的传输距离,随着发散光束初始曲率半径的减小,小尺度扰动的最大增长频率减小,相应的最大增益减小,即B积分值也减小。对于一定的初始曲率半径,随着传输距离的增大, B积分值增长变缓,并最终停止。利用局部能量守恒定律研究了发散光束的成丝距离,发现小的初始曲率半径可以延长成丝距离。

基于对称双侧激光二极管(LD)抽运Nd∶GGG(掺钕钆镓石榴石)激光晶体板条,从热传导基本方程出发,以废热等效于内热源模型为前提, 利用有限元分析软件ANSYS对Nd∶GGG板条在热容工作下的瞬态温度场及应力场进行了数值模拟,分析了在不同边界条件下温度和应力随时间和空间的变化特性及其热致变形。计算结果表明：在激光发射阶段,边界非绝热使得板条在垂直光轴方向产生温度梯度,由此产生的折射率梯度和应力梯度导致距离光轴最远的板条边缘和光轴处产生约0.2 μm的变形量。同时模拟了冷却阶段空气对流冷却、水循环冷却及喷雾冷却条件下的温度变化过程,研究了适用于热容板条固体激光器工作的冷却手段。

Approximate formulas of transient temperature and stress distributions in the slab of a two-side pumped heat capacity laser are attained by solving the heat diffusion equation. Based on the formulas, the distributions of temperature and stress during the pump period of a two-sided symmetrically laser diode array (LDA) pumped Nd:GGG slab laser with 5-kW average output power are numerically simulated. The results show that the temperature in the slab will averagely increase by more than 70 Celsius degrees after operating for 10 seconds; the stress and maximum of the temperature difference in the slab are about 30 MPa and 24 Celsius degrees, respectively. The thermal induced effects are discussed also.

总结了实现高平均功率固体激光器的抽运结构,包括Nd:GGG热容激光器、掺Yb激光器及薄片激光器等,为设计高平均功率激光器及抽运方式选择提供了参考依据。