laser中Kramers-Kronig关系的泵浦-探测模型
Pump-probe model for the Kramers-Kronig relations in a laser
摘要：
本文从理论上研究了激光运转中Kramers-Kronig（KK）关系的泵浦-探测模型。激光增益介质在稳定状态下变得饱和，并且激光场经历等于腔损耗的平坦增益。激光方程的解表明，激射频率在允许的带宽上经历线性色散。然而，在该频带之外，激光停止，使得色散是不饱和增益介质的色散。因此，组合的轮廓是非分析性的，并且不能用KK关系来解释。为了解释这种情况，仔细考虑KK关系的物理基础及其与因果关系的联系是很重要的。我们的结论是，KK关系预计将仅适用于一个独立的探头施加到介质，这是在激励下的泵产生的增益以及激光模式。吸收/增益和色散曲线，然后分析，并满足KK关系。具体地，这些是在存在泵的情况下的探针吸收/增益和色散的所谓的Mollow-Ezekiel光谱的变体，除了在这种情况下介质被反转。
英文摘要：
In this paper, we study theoretically a pump-probe model for the Kramers-Kronig (KK) relations during laser operation. A laser gain medium at steady state becomes saturated and the lasing field experiences a flat gain equal to the cavity loss. A solution of the laser equations reveals that the lasing frequency experiences a dispersion that is linear over the allowed bandwidth. However, outside this band, the lasing stops, so that the dispersion is that of the unsaturated gain medium. The combined profile is therefore non-analytical, and cannot be explained in terms of the KK relations. In order to interpret this situation, it is important to consider carefully the physical basis of the KK relations and its connection to causality. We conclude that the KK relation is expected to apply only to an independent probe applied to the medium, which is under excitation by the pump producing the gain as well as the lasing mode. The absorption/gain and dispersion profiles are then analytical, and satisfy the KK-relations. Specifically, these are variants of the so-called Mollow-Ezekiel spectra of probe absorption/gain and dispersion in the presence of a pump, with the exception that in this case the medium is inverted.
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