We present a theory of frequency comb generation in high-Q ring microresonators with quadratic nonlinearity and normal dispersion and demonstrate that the naturally large difference of the repetition rates at the fundamental and second-harmonic frequencies supports a family of bright soliton frequency combs provided the parametric gain is moderated by tuning the index-matching parameter to exceed the repetition rate difference by a significant factor. This factor equals the sideband number associated with the high-order phase-matched sum-frequency process. The theoretical framework, i.e., the dressed-resonator method, to study the frequency conversion and comb generation is formulated by including the sum-frequency nonlinearity into the definition of the resonator spectrum. The Rabi splitting of the dressed frequencies leads to four distinct parametric down conversion conditions (signal-idler-pump photon energy conservation laws). The parametric instability tongues associated with the generation of the sparse, i.e., Turing-pattern-like, frequency combs with varying repetition rates are analyzed in detail. The sum-frequency matched sideband exhibits optical Pockels nonlinearity and strongly modified dispersion, which limit the soliton bandwidth and also play a distinct role in Turing comb generation. Our methodology and data highlight the analogy between the driven multimode resonators and the photon-atom interaction.

中文翻译：

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χ(2)微谐振器中的亮孤子频率梳和装饰态

我们提出了在具有二次非线性和法向色散的高 Q 环形微谐振器中产生频率梳的理论，并证明了基频和二次谐波频率处重复率的自然大差异支持了一系列明亮的孤子频率梳，提供参数通过调整索引匹配参数以超过重复率差异一个重要因素来调节增益。该因子等于与高阶相位匹配和频过程相关的边带数。通过将和频非线性纳入谐振器频谱的定义，制定了研究频率转换和梳状生成的理论框架，即修整谐振器方法。修整频率的 Rabi 分裂导致四个不同的参数下转换条件（信号-惰轮-泵浦光子能量守恒定律）。详细分析了与具有不同重复率的稀疏（即类似图灵模式）频率梳的生成相关的参数不稳定性舌。和频匹配边带表现出光学普克尔斯非线性和强修正色散，这限制了孤子带宽，并且在图灵梳生成中也发挥了独特的作用。我们的方法和数据突出了驱动多模谐振器与光子-原子相互作用之间的类比。详细分析了具有不同重复率的频率梳。和频匹配边带表现出光学普克尔斯非线性和强修正色散，这限制了孤子带宽，并且在图灵梳生成中也发挥了独特的作用。我们的方法和数据突出了驱动多模谐振器与光子-原子相互作用之间的类比。详细分析了具有不同重复率的频率梳。和频匹配边带表现出光学普克尔斯非线性和强修正色散，这限制了孤子带宽，并且在图灵梳生成中也发挥了独特的作用。我们的方法和数据突出了驱动多模谐振器与光子-原子相互作用之间的类比。