Photonic crystal integrated in a waveguide with periodic roughness

In this work we consider a waveguide composed of two periodic, perfectly conducting, one-dimensional rough surface. This periodic system has a band structure similar in some aspects to a one-dimensional photonic crystal. However our system has some additional interesting features. We calculate the band structure and the reflectivity of a corresponding finite waveguide. We found that the variation of the roughness amplitude and the relative phases allow to control at a certain degree the band structure of the system. Particularly, broad bandgaps can be obtained. The system considered constitutes itself a photonic crystal whose band structure corresponds in many ways to a conventional photonic crystal but using just a single material. The key properties of this system are that it really constitutes a waveguide which has integrated a dispositive that acts as a photonic crystal.