Terahertz Emission From Annular Microstrip Antennas

One of the most promising proposed sources of terahertz (THz) electromagnetic radiation is superconductor-based devices. These superconductors work by utilizing the intrinsic Josephson junctions (IJJs) present in single crystals of the superconductor Bi₂Sr₂CaCu₂O_8+δ (BSCCO). To exploit the Josephson effect, a groove is inscribed in a crystal of BSCCO, producing a mesa about 1 μm thick of any shape, the geometry of which determines the emission spectrum. Alternatively, much more efficient stand alone mesa structures can be built in the desired geometry. The mesa or mesa cavity effectively functions as a microstrip antenna, which can be analyzed using standard antenna theory.
In this project, we study the one and two-dimensional wave functions of a thin annular antenna, with inner and outer radii ρ₁ and ρ₂, respectively. This involves constructing the wave functions from products of Bessel functions of the radial coordinate and trigonometric functions of the angular coordinate, finding expressions for the energy eigenvalues, and producing contour plots of the emitting wave functions. We then employ the Love equivalence principles to integrate the emission phase factor around the circumference and produce plots of the emission power patterns.