We investigate the threshold of χ⁽²⁾ frequency comb generation in lithium niobate whispering gallery microresonators theoretically and experimentally. When generating a frequency comb via second-harmonic excitation, also commonly known as second-harmonic generation, the threshold for the onset of cascaded second-order processes leading to a comb is found to be ∼85 µW. The second-harmonic generation efficiency up to this value is in excellent agreement with a previously known theoretical framework. This framework is extended here, showing that the onset of cascaded χ⁽²⁾ processes and the maximum of the second-harmonic generation efficiency coincide. The model introduced here allows us to determine the frequency comb generation threshold analytically. Furthermore, we observe that the frequency distance between the comb lines is a function of the pump power. It changes from four free spectral ranges at the oscillation threshold to one free spectral range at 590 µW.

中文翻译：

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χ（2）光学微谐振器中通过二次谐波激发的频率梳产生阈值

我们在理论和实验上研究了铌酸锂耳语画廊微谐振器中χ ^（2）频率梳产生的阈值。当生成经由二次谐波激励的频率梳，通常也被称为二次谐波产生，对于级联二阶过程导致梳的发作阈值被发现是〜85 μ W的二次谐波产生的效率达到这个值与先前已知的理论框架极为吻合。这里扩展了这个框架，表明了级联χ ^{（2）的出现}过程和二次谐波产生效率的最大值一致。这里介绍的模型使我们能够解析地确定频率梳的产生阈值。此外，我们观察到梳齿线之间的频率距离是泵浦功率的函数。它从振荡阈值的四个自由光谱范围变为590 µW的一个自由光谱范围。