时变粒子的偶极极化率
Dipole polarizability of time-varying particles
摘要：
时间平移下的不变性（或平稳性）可能是研究电磁现象时最重要的假设之一。打破这一假设有望开辟新的可能性，并导致超越传统的限制。然而，要探索时变电磁结构领域，我们首先需要从非平稳性的角度考虑基本原理和概念。在这里，我们重新审视其中一个关键概念：小粒子的极化率，假设它的性质随时间变化。我们描述了创造的诱导偶极矩的外部领域中的非平稳，因果关系的方式，并引入一个复值函数，称为时间复极化率，阐明了非平稳赫兹偶极子下的时间谐波照明。这种方法可以扩展到任何亚波长粒子表现出电响应。此外，我们还利用阻尼系数和固有频率随时间变化的运动方程研究了振荡电子极化率的经典模型。接下来，我们从理论上推导出对应于时变介质（包括自由或束缚电子，或偶极元原子）的有效介电常数，并明确显示与传统的宏观德鲁德-洛伦兹模型的差异。本文将有望铺平道路，更好地了解非平稳散射的小颗粒和均匀化的时变材料，超材料和超表面。
英文摘要：
Invariance under time translation (or stationarity) is probably one of the most important assumptions made when investigating electromagnetic phenomena. Breaking this assumption is expected to open up novel possibilities and result in exceeding conventional limitations. However, to explore the field of time-varying electromagnetic structures, we primarily need to contemplate the fundamental principles and concepts from a nonstationarity perspective. Here, we revisit one of those key concepts: The polarizability of a small particle, assuming that its properties vary in time. We describe the creation of induced dipole moment by external fields in a nonstationary, causal way, and introduce a complex-valued function, called temporal complex polarizability, for elucidating a nonstationary Hertzian dipole under time-harmonic illumination. This approach can be extended to any subwavelength particle exhibiting electric response. In addition, we also study the classical model of the polarizability of an oscillating electron using the equation of motion whose damping coefficient and natural frequency are changing in time. Next, we theoretically derive the effective permittivity corresponding to time-varying media (comprising free or bound electrons, or dipolar meta-atoms) and explicitly show the differences with the conventional macroscopic Drude-Lorentz model. This paper will hopefully pave the road towards better understanding of nonstationary scattering from small particles and homogenization of time-varying materials, metamaterials, and metasurfaces.
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