Surface plasmon modes for periodic lattices of plasmonic hole waveguides

This study investigates surface plasmon modes for periodic lattices of plasmonic hole waveguides. The interface matching method is proposed to solve the apparently nonlinear eigenvalue problem, with the proper use of the interface condition. It is shown that surface plasmon modes occur for both TE and TM polarizations, and as the off-plane wave number increases, surface plasmon modes for the two polarizations begin to interchange their characteristics. The basic pictures of off-plane surface plasmon modes are explained on a unified basis by examining different types of the interface conditions for TM and TE modes and employing variational arguments based on the Rayleigh quotients for the wave equations. In particular, there exists a TM optical branch which intersects the light line and eventually joins into the surface branches. These features are illustrated by the evolution of surface plasmon mode patterns. For plasmonic hole waveguide structures, the optical branch may exhibit negative group velocities over the whole branch, and the net power flow through the unit cell along the waveguides is shown to direct in the opposite direction of the wave vector.