Abstract-In this work, we consider a waveguide composed of two periodic, perfectly conducting, one-dimensional rough surfaces. 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, wide gaps can be obtained. It is even possible to obtain discrete modes for some frequency range and then the periodic waveguide acts as an unimodal filter. 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 whose optical response is similar to that of a one-dimensional photonic crystal.
The conditions to observe and excite electromagnetic surface modes at the interface between a two-dimensional (2D) photonic crystal (PC) and bulk metal are studied. It is shown that these modes can exist in the region where bandgaps of the PC overlap with the region below the plasma frequency of a metal in the dispersion diagram in both polarizations. The dispersion relation of these electromagnetic surface modes is determined numerically by considering a system of a thin metallic layer in contact with a finite PC of some periods. The reflectance is computed by using the finite-difference time-domain (FDTD) method. With this method, it is shown that these modes can be excited and observed even under normal incidence from a vacuum. For the studied system, the cell in contact with the metallic layer must be truncated in order to observe the interface mode. It is shown that we can select the frequency of the mode inside the bandgaps by properly choosing the truncation parameter.
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