Surface plasmon polaritons from plasmonic nanocavity have aroused great interest due to their applications in various fields, in which on-demand design is hindered by the lack of theoretical frameworks. Herein, based on its wave nature, we developed a wavefunction theory to explicitly describe individual surface plasmon polaritons and the resultant near-field and far-field behaviors, which serves as an efficient platform for high-throughput on-demand design of nanocavities. We found an applicative wavefunction form and proposed a two-body interaction function and a "shell" model for many-body interactions in surface plasmon polaritons' coupling. The wavefunction of individual surface plasmon polaritons and resultant near-field and far-field behaviors can be given explicitly and precisely. The theory provides a fundamental and quantitative understanding of surface plasmon polaritons and enables highly efficient on-demand design of plasmonic metamaterials and devices, leading to further methodological applications in numerous aspects.
Keywords: Electric near-field; Extraordinary optical transmittance; On-demand design; Surface plasmon polariton; Wavefunction theory.