Quasinormal Mode Expansion Theory for Mesoscale Plasmonic Nanoresonators: An Analytical Treatment of Nonclassical Electromagnetic Boundary Condition
Can Tao, Ying Zhong, Haitao Liu
Abstract
Nonclassical quantum effects will significantly affect the optical response of plasmonic nanoresonators with mesoscale feature sizes between about 2 and 20 nm, and can be fully described by the nonclassical electromagnetic boundary condition (NEBC) expressed with the surface-response Feibelman d parameters. In this Letter, a quasinormal mode (QNM) expansion theory under the NEBC is proposed. By adopting the easily solved classical QNMs under the classical electromagnetic boundary condition as a complete set of basis functions, rigorous expansions of the nonclassical source-free QNMs and source-excited electromagnetic field under the nonperturbative NEBC are provided. With the obtained nonclassical QNMs as basis functions, expansions of the nonclassical source-excited field and Green's function tensor are further obtained. These expansions have a fully analytical dependence on the NEBC and classical QNMs, thus transparently unveiling their impact on the nonclassical QNMs and source-excited electromagnetic field. For instance, a new expression of mode volume is proposed for analyzing the nonclassically corrected Purcell factor. The proposed theory is physically intuitive and computationally efficient which is enabled by the dominance of a small set of classical QNMs, thus providing an efficient tool for understanding and designing mesoscale plasmonic nanoresonators.