arXiv 1807.109922018-07physics.optics

标量势与矢量势等效的近场光学单极化率理论

Theory of Single Susceptibility for Near-field Optics Equally Associated with Scalar and Vector Potentials

Itsuki Banno

备注：: 34pages, 1figure with a supplemental document (9 pages). arXiv admin note: text overlap with arXiv:1807.10991

摘要：

发展了一种非局部响应理论来描述纳米结构附近辐射纵向和横向电场的多电子系统，这些电场从根本上简化为标量势和矢量势（SP和VP）。SP和VP入射的共存将这种近场光学系统与普通光学系统区分开来，在普通光学系统中，只有VP（在库仑规范下）入射远离光源而存在。这一事实是同等对待SP和VP作为近场光学系统中的响应的原因的动机。在半经典处理中，线性和非线性单重性以Heisenberg算子的形式由物质的作用量积分关于SP和VP的泛函导数导出。这些单一的可解释性将SP和VP（作为原因）与感应电荷和电流密度（作为结果）联系起来，并保证电荷守恒和规范不变性;这个理论没有规范固定。在非微扰系统中，要使基态有界，必须考虑量子多电子效应（交换关联效应）。这是通过采用密度泛函理论的基本思想来完成的，而不是通常的SP和VP的不平等处理，也就是说，将SP改造成电子电荷之间的库仑相互作用。将现有的线性响应理论应用于有限近场光学系统中的非金属材料，发现用与介电常数相关的电场并不是描述响应的合适量，而是用与单一极化率相关的SP和VP来描述响应。

英文摘要：

A nonlocal response theory was developed to describe a many-electron system within the neighborhood of a nanostructure radiating the longitudinal and transverse electric fields, which are fundamentally reduced to the scalar and vector potentials (SP and VP). The coexistence of the SP and VP incidences distinguishes such a near-field optical system from the ordinary optical system, in which only the VP (under the Coulomb gauge) incidence survives far from the light source. This fact is the motivation for equal treatment of the SP and VP as the cause of the response in the near-field optical system. In the semiclassical treatment, the linear and nonlinear single susceptibilities are derived in the form of Heisenberg operators by the functional derivatives of the action integral of the matter with respect to the SP and VP. These single susceptibilities relate the SP and VP (as the cause) to the induced charge and current densities (as the result), and guarantee charge conservation and gauge invariance; this theory is free from gauge-fixing. It is necessary to consider the quantum many-electron effect (exchange-correlation effect) to make the ground state bounded in the non-perturbed system. This is done by employing the fundamental idea of density functional theory, instead of the ordinary unequal treatment of the SP and VP, that is, remaking the SP into a Coulomb interaction between electron charges. Applying the present linear response theory to the non-metallic material in a limited near-field optical system reveals that the electric field with the associated permittivity is not suitable quantity to describe the response, instead, the SP and VP with associate single susceptibility are essential.

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摘要：

英文摘要：

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