A surface plasmon polariton analogue of a Wannier-Stark ladder

By using the finite-difference time-domain method we have investigated the propagation of a surface plasmon polariton on a metallic grating consisting of N equally spaced rectangular grooves, each with the same width but with varying depths. We find that the transmissivity of the surface plasmon polariton, and the power radiated into the vacuum, as functions of its frequency consist of N equally spaced dips and peaks, respectively, that have the form of a Wannier-Stark ladder. By using an analytical approach we show that the localized states with a constant difference in frequency qualitatively agree with the resonances obtained from solving the equations for symmetric modes associated with the crosswise plasmons, which identifies the coupling of the incident wave to localized modes confined within the groove as the major mechanism responsible for the existence of equally spaced resonances.