纵-横场耦合与个体-集体激发的综合微观理论
Comprehensive Microscopic Theory for Coupling of Longitudinal--Transverse Fields and Individual--Collective Excitations
摘要：
等离子体激元是由于库仑相互作用引起的电子的集体激发。等离子体激元和单粒子激发（SPE）都是块体金属系统的本征态，它们相互正交。然而，在诸如纳米结构的非对称系统中，等离子体激元和SPE相干地相互作用。已经充分讨论了在这样的系统中，等离子体激元和SPE分别可以与横向（T）电场耦合，并且它们通过纵向（L）场彼此耦合。然而，在以往的研究中一直缺少一个环节：T场介导的等离子体激元和SPE之间的相干耦合。在这里，我们开发了一个理论框架来描述等离子体激元和SPE之间的自洽关系，通过L和T场。的激发描述的电荷和电流密度的本构方程与非局部磁化率，其中密度包括L和T组件。由密度产生的电磁场用麦克斯韦方程组中的格林函数描述。T场由两种密度产生，而L分量仅归因于电荷密度。我们引入了一个四矢量表示，结合库仑规范中的矢量和标量势，其中的T和L场是明确分开的。自洽方程矩阵的特征值作为系统激励的极点。所开发的配方能够接近未知的机制，增强等离子体激元和热载流子产生的辐射场之间的相干耦合。
英文摘要：
A plasmon is a collective excitation of electrons due to the Coulomb interaction. Both plasmons and single-particle excitations (SPEs) are eigenstates of bulk metallic systems and they are orthogonal to each other. However, in non-translationally symmetric systems such as nanostructures, plasmons and SPEs coherently interact. It has been well discussed that the plasmons and SPEs, respectively, can couple with transverse (T) electric field in such systems, and also that they are coupled with each other via longitudinal (L) field. However, there has been a missing link in the previous studies: the coherent coupling between the plasmons and SPEs mediated by the T field. Herein, we develop a theoretical framework to describe the self-consistent relationship between plasmons and SPEs through both the L and T fields. The excitations are described in terms of the charge and current densities in a constitutive equation with a nonlocal susceptibility, where the densities include the L and T components. The electromagnetic fields originating from the densities are described in terms of the Green's function in the Maxwell equations. The T field is generated from both densities, whereas the L component is attributed to the charge density only. We introduce a four-vector representation incorporating the vector and scalar potentials in the Coulomb gauge, in which the T and L fields are separated explicitly. The eigenvalues of the matrix for the self-consistent equations appear as the poles of the system excitations. The developed formulation enables to approach unknown mechanisms for enhancement of the coherent coupling between plasmons and the hot carriers generated by radiative fields.
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