Unified treatments for localized surface plasmon resonance and propagating surface plasmon polariton based on resonance modes in metal nanowire

The understanding on surface plasmon polaritons (SPPs), which contain propagating surface plasmon polaritons (PSPP) and localized surface plasmon resonance (LSPR), are of significant. In this study, we approximately solve Maxwell’s Equations to obtain the properties of PSPP and LSPR supported in Ag nanowire and Au nanorod. The propagation length and the transmitted spectra are analyzed with the obtained formula and agree well with other researchers’ work. We find that both PSPP and LSPR result from the same mechanism, i.e., the propagating modes together with their constructive interference effects. Therefore, we unify the two phenomena. This work provides an alternative way to describe the phenomenon of SPP modes and is helpful to the applications which employ SPP. •The understanding on surface plasmon polaritons (SPPs), which contain propagating SPPs (PSPPs) and localized surface plasmon resonance (LSPR), are of significant.•We approximately solve Maxwell’s Equations to obtain the properties of PSPP and LSPR supported in Ag nanowire and Au nanorod.•The propagation length and the transmitted spectra are analyzed with the obtained formula and agree well with other researchers’ work.•Both PSPP and LSPR result from the same mechanism, i.e., thepropagating modes together with their constructive interference effects.•We unify the two phenomena.•This work provides an alternative way to describe the phenomenon of SPP modes.