激光输出功率随耦合率及放大率的变化规律

Variation of laser output power with coupling ratio and magnification

建立了涵盖稳定腔和非稳腔的激光有源理论模型和激光开式谐振腔的边界条件。根据定态薛定谔方程与亥姆霍兹方程的等价性,采用量子力学方法求解谐振腔的亥姆霍兹波动方程,得到满足方程、边界条件、矩阵光学、稳定条件的本征解和本征方程。根据本征方程推导出横模数目随耦合率变化的规律,进而推导出激光输出功率随耦合率变化公式,以及激光输出功率随放大率的变化规律。该理论模型能够从稳定腔自然过渡到非稳腔,在小耦合率情况下退化到与传统公式基本一致的形式,又能在大耦合率情形下与实验结果符合得很好。

A novel laser model with active gain medium and open-resonator boundary condition was developed, which is ap- plicable to both stable and unstable resonators. Based on the equivalency between the Schr6dinger equation and Helmholtz equa- tion, quantum mechanics method was used to solve the Helmholtz equation of resonators, and the eigen equation and eigen solu- tion were obtained, which fully satisfy the wave equations, boundary condtions, matrix optics, and stability criterion. Based on the eigen equation, the relationship between transverse mode number and output coupling ratio was derived. Futhermore, the re- lationship of the output power and output coupling ratio to magnification was deduced. This model not only can regress into the exact form of the traditional formula in case of small output couplings, but also consists with the curve-fittings of experimental da- ta very well in case of large output couplings.