Theoretical analysis of compact cylindrical microlenses for terahertz photoconductive antennas in the photomixer regime

A terahertz photoconductive antenna placed on the back side of a semiconductor slab with and without a compact cylindrical semiconductor microlens on the front side is studied theoretically. The antenna is operated as a photomixer giving narrowband radiation at 1 THz. Radiation patterns and emitted powers are found to oscillate with slab thickness as a consequence of multiple-reflection interference. It is further shown that an antireflection layer on the lens may eliminate these oscillations to a large extent. In the absence of a lens, most of the radiation is trapped inside the semiconductor slab, and the radiation pattern is far from that of a pencil-beam. Both light trapping and radiation patterns are shown to be significantly improved by a very compact lens with a size smaller than a cubic wavelength. The improvements on outcoupling of radiation in a predominantly forward direction versus lens radius and height are mapped out. The calculated outcoupling efficiency of the antenna-lens system takes into account the Purcell effect and radiation trapped in the semiconductor slab. The antenna-lens system is modeled rigorously by using the Green’s function volume integral equation method in a form that exploits cylindrical symmetry.