A surface mode is a electromagnetic field distribution bounded at a surface. It decays exponentially with the distance from the surface on the both sides of the surface and propagates along the surface. Besides its prominent near-filed properties, it can connect structures along its propagation surface and results in far-field effects. Extraordinary transmission (EOT) and beaming are two examples and they are the subjects I am studying in this thesis. The first chapter gives a brief introduction about the thesis.

In the second chapter I prove the existence of the surface modes at a metal-dielectric surface or a photonic crystal surface with a surface layer. I also briefly review the EOT phenomenon and beaming phenomenon.

In the third chapter, I calculate the surface waves along a metal-dielectric interface with an indentation analytically. I verify the surface wave can be decomposed into two parts: the surface

plasmons and the residue quasicylindrical wave. I analyze the asymptotic behavior of the quasicylindrical wave. Based on the distance to the indentation, the interface is divided into several

regions and the surface wave behaves differently in every region. The complete description of the surface wave sets up a solid foundation to understand EOT and beaming.

In the fourth chapter, a new theory from first principles is developed to explain EOT through one-dimensional periodic subwavelength metallic slits. The theory has clear physical meaning; the terms corresponding to surface plasmons appear explicitly in the equations.So it explains

the importance of surface plasmons in EOT. I prove analytically that the surface plasmon resonance results in transmission dips not peaks, which is against the common explanation. I also study the transmission peaks and contribute them to the Fabry-P\'{e}rot interference between

the input and output surfaces. The theory can be extended to EOT through a two-dimensional periodic hole arrays. It can explain a lot of experimental results published recently, such as the transmission through randomized hole arrays, the strong influence of the hole shape on the transmission peaks.

Beaming is study in the last chapter. Since the principle of beaming has been well understood. I focus on the design of novel beaming devices. First I find a two-layer dielectric rod structure can give excellent beaming and enhanced transmission simultaneously of a Gaussian source. By repeating periodically this two-layer structure one can obtain excellent beaming and enhanced transmission for very long distances. Second I study the structure of a subwavelength metallic slit surrounded by periodic grooves. I developed an efficient method to determine the geometric parameters of the grooves that are

necessary to achieve oblique beaming at any angle between 0 and 70

degrees. Surprisingly the best beaming actually happens not at the

forward direction but an oblique direction. I also design a frequency

splitter based on the structure.