活动时间：2024-09-08 15:55
活动地点：2号学院楼2202报告厅
主讲人：Andrei Vladimirov
主讲人中文简介：
A. G. Vladimirov德国魏尔斯特拉斯研究所教授，是光电子器件中非线性动力学研究领域的国际顶尖专家。 已在顶尖的同行评审国际期刊上发表了 114 篇原创性研究成果，其中包括近10篇论文发表在《Phys. Rev. Lett.》，此外还撰写了四部著作。他的研究得到了欧盟第七框架计划、德国研究基金会、国际科学基金会、INTAS 和俄罗斯政府联邦计划的支持。 他曾在许多著名的国际会议（包括著名的索尔维研讨会）上发表全会演讲和特邀演讲，并受邀担任多个著名学术机构的客座教授。他还是许多国际会议组织委员会的成员，曾被授予圣彼得堡国立大学 275 周年纪念荣誉奖章和爱尔兰科学基金会颁发的 E.T.S. 沃尔顿奖。
A.G. Vladimirov 教授在光电设备数学建模领域的研究成果广泛应用于科学和技术领域。通过与全球著名机构合作开展的大量工作，他在多个关键领域取得了重大进展，其中包括锁模激光器、光学微腔、耦合激光阵列、用于光学相干断层扫描的扫频激光器，以及光的时间和空间局部结构的动态和相互作用研究。
活动内容摘要：
In this study, we develop a mathematical framework for describing dispersive nonlinear optical cavities using neutral delay differential equations (NDDEs). We investigate a Kerr cavity with coherent injection for the generation of optical frequency combs, deriving a NDDE model that generalizes the Ikeda map and is equivalent to a delay differential-algebraic equations system. In the absence of losses and injection, the model displays conservative behaviour. It is noteworthy that the NDDE model is able to overcome certain limitations of the Lugiato-Lefever equation (LLE), and can be reduced to the LLE in the mean-field limit. It is demonstrated that temporal cavity solitons exist within the neutral DDE framework, both in the vicinity of the LLE limit and beyond it. In the latter scenario, solitons are subject to significant perturbations due to Cherenkov radiation, which ultimately results in their decay. We establish analytical conditions that ensure the stability of the model by preventing spurious instabilities. Furthermore, we extend the NDDE model to incorporate higher-order derivative terms, accounting for higher-order dispersion effects. By introducing spectral filtering, we demonstrate that the model can be converted into a regular DDE. Finally, we discuss the application of the NDDE model to analyze the dynamics of a Kerr cavity under pulsed injection.
主持人：孙春友