Diffraction analysis of periodic structures using a transmission-line formulation: Principles and applications

Using a linear combination of properly chosen spatial harmonics, we present a solution to Maxwell's equations which lends itself to the diffraction analysis of periodic structures. The proposed formulation is in a one-to-one correspondence with the well-known formulation governing the wave propagation along a multi-conductor transmission line. Like other modal methods, this approach can be applied to the modal analysis of a wide class of structures such as 2D and 3D photonic crystals and photonic crystal slabs involving defects. Moreover, using this method, the incidence of a plane or Gaussian wave can also be analyzed so that one is able to predict the existence of the surface plasmons and negative refraction.