| Summary: | The optical transmission properties of squarely-modulated metallic gratings has been widely investigated. This study used rigorous-coupled wave analysis (RCWA) to re-examine in detail the band structure of a laminated metal film with squarely-modulated metallic gratings located at the top. The top structure was shown to modify the long-range surface plasmon polariton modes (LRSPP) at both interfaces of the thin metal film. When the thickness of the intact metal film was altered, the coupling between the two interfaces presented intriguing behavior. If the thickness of the metallic film was 30nm, the field achieved strong coupling similar to that of a two-level system. When the thickness was decreased to 10nm, the band branch possessing negative group velocity was dominant. Our results also verify that the first-order Fourier expansion of the gratings determined the energy position of bands at k||=0, whereas the second-order term caused band gap opening. Introducing an asymmetrical component to the grating profile intensified the opening effect at k||=0 due to an increase in the amplitude of the second-order Fourier component.
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