A high-quality optical microcavity can enhance optical nonlinear effects by resonant recirculation, which provides a reliable platform for nonlinear optics research. When a soliton microcomb and a probe optical field are coexisting in a micro-resonator, a concomitant microcomb (CMC) induced by cross-phase modulation (XPM) will be formed synchronously. Here, we characterize the CMC comprehensively in a micro-resonator through theory, numerical simulation, and experimental verification. It is found that the CMCs spectra are modulated due to resonant radiation (RR) resulting from the interaction of dispersion and XPM effects. The group velocity dispersion induces symmetric RRs on the CMC, which leads to a symmetric spectral envelope and a dual-peak pulse in frequency and temporal domains, respectively, while the group velocity mismatch breaks the symmetry of RRs and leads to asymmetric spectral and temporal profiles. When the group velocity is linearly varying with frequency, two RR frequencies are hyperbolically distributed about the pump, and the probe light acts as one of the asymptotic lines. Our results enrich the CMC dynamics and guide microcomb design and applications such as spectral extension and dark pulse generation.

中文翻译：

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交叉相位调制引起的伴随微梳的双曲线共振辐射

高质量的光学微腔可以通过共振再循环增强光学非线性效应，为非线性光学研究提供可靠的平台。当孤子微梳和探测光场共存于微谐振腔中时，将同步形成由交叉相位调制（XPM）引起的伴随微梳（CMC）。在这里，我们通过理论、数值模拟和实验验证来全面表征微谐振器中的 CMC。研究发现，CMC 光谱由于色散和 XPM 效应相互作用产生的共振辐射 (RR) 而受到调制。群速度色散在 CMC 上引起对称的 RR，这分别导致频域和时域中的对称光谱包络​​和双峰脉冲，而群速度失配破坏了 RR 的对称性并导致不对称的光谱和时间分布。当群速度随频率线性变化时，两个 RR 频率围绕泵呈双曲线分布，探测光作为渐近线之一。我们的结果丰富了 CMC 动力学并指导微梳设计和应用，例如光谱扩展和暗脉冲生成。