Resonant modes of multi-layer structures which contain the regions of negative epsilon material (such as a metal in the visible range) are analyzed. Existence of two separate classes of resonant modes is demonstrated. One is related to the excitation of the surface mode at the interface of the regions with opposite signs of the dielectric constant and involve energy transport by evanescent modes throughout the whole structure. The second class involves propagating modes (which form the resonant standing wave) in some regions and the evanescent waves in other layers with ε＜0. It is shown that the resonant transmission is related to the existence of quasi-stationary leaky modes having a finite life-time and characterized by large wave amplitude in the trapping region. It is shown that both types of resonances can coexist in multi-layer structures. It is also shown that the interaction of the symmetric and anti-symmetric surface eigen-modes widens the resonant transmission region.
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