Abstract
The dispersion equations of bulk modes and surface modes in a rectangular waveguide of semiconductor metamaterial are derived by a modified “Marcatili's method". The cutoff frequencies of the lowest TM bulk mode are discussed, and the Brillouin diagrams of different bulk modes are drawn. They demonstrate that different heights correspond to different guidance frequency ranges which have no superposition with each other and a waveguide with a larger height possesses a wider passband of light. In addition, tendencies of degeneracy for different modes are observed. Finally, the existence of surface modes is verified by a graphical method.
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