In the literature one finds several conflicting accounts of the phase difference of stimulated and spontaneous emission, as well as absorption, with respect to an existing (triggering) electromagnetic field. One of these approaches proposes that stimulated emission and absorption occur in phase and out of phase with their driving field, respectively, whereas spontaneous emission occurs under an arbitrary phase difference with respect to an existing field. It has served as a basis for explaining quantum-mechanically the laser linewidth, its narrowing by a factor of 2 around the laser threshold, as well as its broadening due to amplitude–phase coupling, resulting in Henry’s $\alpha$-factor. Assuming the validity of Maxwell’s equations, all three processes would, thus, violate the law of energy conservation. In semi-classical approaches, we investigate stimulated emission in a Fabry–Perot resonator, analyze the Lorentz oscillator model, apply the Kramers–Kronig relations to the complex susceptibility, understand the summation of quantized electric fields, and quantitatively interpret emission and absorption in the amplitude–phase diagram. In all cases, we derive that the phase of stimulated emission is 90° in lead of the driving field, and the phase of absorption lags 90° behind the transmitted field. Also spontaneous emission must obey energy conservation, hence it occurs with 90° phase in lead of an existing field. These semi-classical findings agree with recent experimental investigations regarding the interaction of attosecond pulses with an atom, thereby questioning the physical explanation of the laser linewidth and its narrowing or broadening.

中文翻译：

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光子发射和吸收的相态

在文献中，人们发现了相对于现有的（触发）电磁场，受激发射和自发发射以及吸收的相位差有几个相互矛盾的解释。这些方法之一提出，受激发射和吸收分别与它们的驱动场同相和异相地发生，而自发发射在相对于现有场的任意相位差下发生。它已成为量子力学解释激光线宽，在激光阈值附近变窄2倍以及由于振幅-相位耦合而变宽的基础，从而导致了亨利（Henry）$\alpha$-因素。假设麦克斯韦方程组的有效性，那么这三个过程都将违反能量守恒定律。在半经典方法中，我们研究了Fabry-Perot谐振器中的受激发射，分析了Lorentz振荡器模型，将Kramers-Kronig关系应用于复杂的磁化率，了解了量化电场的总和，并定量地解释了电磁场中的发射和吸收。幅相图。在所有情况下，我们得出的结果是，受激发射的相位在驱动场的前面是90°，而吸收的相位则在透射场后面滞后90°。另外，自发发射必须遵守能量守恒，因此，它以90°相位在现有电场的铅中发生。