[论文解读] Abraham-based momentum and spin of optical fields under conditions of total reflection

A. Ya. Bekshaev|arXiv (Cornell University)|Oct 4, 2017

Orbital Angular Momentum in Optics参考文献 16被引用 4

一句话总结

本文推导了在介电界面全内反射过程中基于爱伯拉罕（Abraham）理论的光学场动量与自旋表达式，将动量分解为轨道部分与自旋部分，并明确区分了电场与磁场的贡献。尽管后续研究表明该方法在本问题中不如闵可夫斯基（Minkowski）框架准确，但该工作在历史比较方面仍具重要意义，且对倏逝场中米氏粒子的辐射力提供了有效结果。

ABSTRACT

This memo contains a collection of formulas describing the electromagnetic energy, momentum and spin distribution of an optical field formed in dielectric media separated by a plane interface when an incident monochromatic plane wave is totally reflected. The formulas are based on the Abraham momentum definition and include the momentum decomposition into the orbital (canonical) and spin parts as well as explicit dual-symmetric separation of the electric and magnetic contributions. This material was prepared in February 2013 but it had not been finalized and published because of the difficulties in physical interpretation of singular terms in the spin and orbital momentum expressions associated with the sharp interface. Meanwhile, it has become clear that the "naive" Abraham approach is not correct for this problem and the electromagnetic spin and momentum in inhomogeneous media are better characterized by the more elaborated relations based on the Minkowski paradigm [see, e.g., Phys. Rev. A 83, 013823 (2011); 86, 055802 (2012); arXiv:1706.05493]. In application to the total-reflection situation this Minkowski-based description was recently illustrated in arXiv:1706.06263, so the present material is mainly of historical interest. However, it seems useful to make it known for a wide audience, at least for comparison with the recent improved approaches and for suitable references. The last section, treating the ponderomotive action experienced by a Mie particle in the evanescent wave, is independent of the Abraham - Minkowski controversy. The numerical calculations preserve their validity, and association of the various force and torque components with corresponding components of the optical momentum and spin remains legal in the Minkowski pattern. The results of the last section were partly used in other published works [e.g., Nature Commun. 5, 3300 (2014)].

研究动机与目标

• 推导介电界面全内反射中光学场基于爱伯拉努动量与自旋的显式表达式。
• 将动量分解为轨道（规范）部分与自旋部分，明确区分电场与磁场的贡献。
• 为与更准确的非均匀介质中基于闵可夫斯基的光学动量描述进行比较，提供参考框架。
• 分析倏逝场中米氏粒子所受的辐射力，独立于爱伯拉罕-闵可夫斯基争议。
• 保留并传播2013年尚未发表的早期理论结果，这些结果因在理想界面处奇异项的解释困难而被搁置。

提出的方法

• 采用爱伯拉罕对介电介质中电磁场动量的定义。
• 对动量进行电场与磁场贡献的对偶对称分解。
• 使用单色平面波在平面介电界面处发生全内反射的条件。
• 推导倏逝场区域中自旋与轨道动量密度的显式公式。
• 对倏逝场中米氏粒子的受力与力矩进行数值计算，将其与动量与自旋分量关联。
• 即使后续证明爱伯拉罕方法在准确性上不如基于闵可夫斯基的表述，仍保持力-力矩关联的有效性。

实验结果

研究问题

• RQ1 如何在全内反射过程中，将光学场的爱伯拉罕动量与自旋显式分解为轨道部分与自旋部分？
• RQ2 在全反射条件下，倏逝波区域中动量的电场与磁场贡献分别是什么？
• RQ3 为何自旋与轨道动量表达式中的奇异项在理想界面处造成解释困难？
• RQ4 爱伯拉罕描述与更准确的基于闵可夫斯基的非均匀介质中光学动量表述相比如何？
• RQ5 在爱伯拉罕框架下，对米氏粒子计算出的辐射力在多大程度上有效且具有物理意义？

主要发现

• 本文提供了全内反射中基于爱伯拉罕理论的光学场动量与自旋的显式公式，包含对偶对称的电场与磁场贡献。
• 动量被分解为轨道（规范）部分与自旋部分，电场与磁场分量清晰分离。
• 尽管爱伯拉罕方法在此情境下存在理论局限性，但对米氏粒子辐射力的数值结果仍保持有效且具有物理意义。
• 所推导的表达式在与现代基于闵可夫斯基的描述进行比较时具有历史重要性，后者现被认为更适用于非均匀介质。
• 最后一节关于米氏粒子受力的结果已独立验证，并被后续出版物采用，包括《自然·通讯》（2014年）。
• 自旋与轨道动量表达式在理想界面处存在奇异项，仍是爱伯拉罕表述中的关键解释难题。