反馈调谐CO_2激光器的静态与动态行为

Stability and dynamical behavior of a CO_2 laser with feedback control of the detuning

建立了反馈调谐CO_2激光器的物理数学模型.稳态分析结果表明,只有当反馈系数大于某一临界值之后,才能出现激光器泵浦速率与激光输出之间的光学双稳性.线性稳定性分析的结果表明,系统失稳的必要条件是失谐量的Debye弛豫速率(反馈系统的带宽)必须超过布居反转的衰减速率.只有当激光泵浦落在某一范围内时,才出现不稳性.数值分析的结果证明了系统输出倍的周期分岔混沌行为.线性稳定性分析预言的Hopf分岔频率与数值分析的结果符合得很好.

The physical and mathematical models of CO2 laser with feedback control of detuning has been set up. The analysis of steady state shows that the optical Disability between the pump rate and the output intensity of the laser will appear when the feedback coefficient exceeds the critical value. Eesults of linearized stability analysis indicate that the necessary condition of the dynamical instability is that the Debye-relaxation rate of the detuning (bandwith of the feedback circuit) must exceed the decay rate of the population inversion. The instability appears only when the laser pump falls into a proper region. The behaviours of the period-doubling bifurcation and chaos have been proved by the result of numerical calculation. Th frequency of the Hopf bifurcation predicated by the stability analysis is consistent with that given by the numerical calculation.