Rectangular waveguide and resonant cavity with semiconductor metamaterials

Abstract

Dispersion equations of bulk modes in a rectangular waveguide of semiconductor metamaterial are derived by a modified "Marcatili method". The existence conditions for bulk modes are discussed, and the Brillouin diagrams of different bulk modes and the lowest TM bulk mode in different waveguides are drawn. They demonstrate that different heights correspond to different guidance frequency ranges which have no superposition with each other and a waveguide with larger height possesses wider pass band of light. In addition, tendencies of degeneracy for different modes are observed. These properties are of particular relevance to devices requiring band-pass or single-mode propagation. Then a rectangular resonant cavity with different anisotropic parameters is designed and investigated, which is filled partially with a right-handed semiconductor metamaterial (RHSM) and partially with a left-handed semiconductor metamaterial (LHSM). The resonant mode solutions of the general case of the 3-D rectangular resonator cavity filled with non-dispersive RHSM and dispersive LHSM are explored by use of a graphical method. It is demonstrated that the resonant modes in such a resonator cavity are closely dependent on the spatial dispersion relation of the semiconductor metamaterial. The resonant cavity including three subcases of different combinations of real and imaginary propagation constants of the two regions is discussed. This novel 3-D semiconductor metamaterial brings a new method to construct rectangular resonant cavities and provides more design flexibility and tolerance.