Analysis on plasmonic modes within rectangular sub-wavelength holes on metallic nanofilms

The nanoscale rectangular sub-wavelength hole (RSH), functioned by plasmonic modes, is a key component in modern nanophotonics since it holds various unconventional optical phenomena and has many interesting applications. Yet to date, its analytic theory still has not been well-developed. Here we aim to present detailed analysis on the plasmonic modes within RSH by using full waveguide theory with real metal. We obtain the complete field expressions and derive out the dispersion equations of guided modes in metallic waveguide, based on which we achieve the resonant properties of RSH. Influences of size and shape of RSH on resonant properties are revealed, the results of which are verified by numerical simulations. This theory is helpful for understanding the unconventional optical phenomena based on RSH and for developing new optical devices.