Surface plasmon sorting and engineered dispersion curves using multilayer doped semiconductors

A method to engineer complex shapes into the dispersion curves (DCs) of surface plasmon (SP) in flat multilayer structures composed of doped semiconductors is shown analytically and numerically. It is shown that the shapes of SP DCs in multilayer structures can be engineered by controlling not only the free electron density in each layer, as has been well described in past literature on the subject, but also by controlling the spatial profiles of the electromagnetic fields associated with surface plasmons. It is the ability to impart complex shapes in the SP DCs that is new and described in this paper—and not just raising or lowering the surface plasmon energies as a function of free electron concentration. DCs with stair-step or dove-tail shapes are possible. In this work, a method to design structures that support SPs with DCs of arbitrary shapes is described. An analytical description of the design methodology is developed, and the resulting structures are numerically modeled using continuous wave excitation and time-dependent pulsed excitation. Time domain studies of the creation and decay in which the SPs are performed, along with spatial sorting of the SPs, yield results in agreement with the predictions of the analytic model.