In this tutorial, the physical origins and mathematical analyses of laser linewidths are reviewed. The semi-classical model is based on an equation for the light-mode amplitude that includes random source terms, one term for each process that affects the amplitude (stimulated and spontaneous emission, stimulated absorption, and facet and material loss). Although the source terms are classical, their assigned strengths are consistent with the laws of quantum optics. Analysis of this equation shows that the laser linewidth is proportional to the sum of the (positive) source strengths for all gain and loss processes. Three-level and semiconductor lasers have broader linewidths than comparable four-level lasers, because stimulated absorption and the stimulated emission that compensates it both contribute to the linewidth.

中文翻译：

---

激光线宽：教程

在本教程中，回顾了激光线宽的物理起源和数学分析。半经典模型基于光模式振幅方程，其中包括随机源项，每个影响振幅的过程（受激和自发发射、受激吸收以及小平面和材料损失）对应一个项。尽管源项是经典的，但它们的指定强度符合量子光学定律。对该方程的分析表明，对于所有增益和损耗过程，激光线宽与（正）源强度的总和成正比。三能级和半导体激光器比类似的四能级激光器具有更宽的线宽，因为受激吸收和补偿它的受激发射都对线宽有贡献。