探索非线性光学材料中谐波产生的基于因果性与基于量子力学的求和规则的等价性
Exploring the equivalence of causality-based and quantum mechanics-based sum rules for harmonic generation in nonlinear optical materials
AI总结：
本文从因果性积分求和规则出发，为二次谐波产生磁化率推导出一组新的离散求和规则，并证明其与独立量子力学分析结果等价，进而探讨其对确定非线性光学材料响应基本极限的意义。
摘要：
Kramers-Kronig关系和各种振子强度求和规则对材料的物理响应构成了强约束。在本工作中，受线性光学中f-求和规则与Thomas-Reiche-Kuhn求和规则之间已确立的等价性的启发，我们探索了非线性光学过程背景下基于因果性的求和规则与基于量子力学的求和规则之间的联系。具体而言，通过考虑二次谐波产生磁化率的态求和表达式，我们为该磁化率的虚部推导出一个新的表示基，并利用它从基于因果性的积分求和规则推导出一组新的跃迁偶极矩必须满足的离散求和规则。与Thomas-Reiche-Kuhn求和规则的情形一样，我们也证明这些结果可以通过独立的量子力学分析以另一种方式导出。最后，我们考虑了所推导的求和规则对二能级和三能级系统二次谐波产生磁化率的影响，并更广泛地讨论了利用这些结果来确定非线性光学材料响应基本极限这一目标可能具有的意义和面临的挑战。
英文摘要：
The Kramers-Kronig relations and various oscillator strength sum rules represent strong constraints on the physical response of materials. In this work, taking inspiration from the well-established equivalence between $f-$sum rules and Thomas--Reiche--Kuhn sum rules in linear optics, we explore the connection between causality-based and quantum-mechanics-based sum rules in the context of nonlinear optical processes. Specifically, by considering the sum-over-states expression for the second harmonic generation susceptibility, we deduce a new representation basis for the imaginary part of this susceptibility and we use it to derive, from causality-based integral sum rules, a new set of discrete sum rules that the transition dipole moments must satisfy. As in the case of the Thomas--Reiche--Kuhn sum rules, we also show that these results can alternatively be derived through an independent quantum mechanical analysis. Finally, we consider the implications of the derived sum rules for the second-harmonic-generation susceptibility of two- and three-level systems and, more broadly, we discuss the possible significance and challenges of using these results for the goal of identifying fundamental limits to the response of nonlinear optical materials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
