While significant progress has been achieved in the generation of electromagnetic radiation in the terahertz range, compact and efficient emitters are still missing. Oscillations of terahertz plasmons in semiconductor structures have the potential for the design of compact terahertz generators.

We develop a semi-analytical theory of semiconductor plasmon structures, starting with simple model structures (those embedded in a uniform dielectric and supporting no dc currents) and progressing to more complicated, practical, ones (those comprising realistic interfaces and supporting dc currents). The main analytical and numerical techniques developed are based on the expansion of electromagnetic field into eigenmodes and matching them at the discontinuities of the structure.

For passive structures (i.e. without a current) we compare our results to other models and with full wave simulations, showing that our technique allows us to represent key features of the resonances of typical structures, unlike other models.

For active structures we employ a perturbative approach, show limitations of the analytical theory, and demonstrate two qualitatively different cases of oscillating structures (difference is due to different characteristics of waveguiding structure).
In both cases there is possibility of creation of terahertz generators, as long as correct design strategy is employed.