Design of a hybrid plasmonic electro-optical modulator based on n doped silicon and barium titanate

In this paper, a numerical solution for a hybrid plasmonic modulator is presented with a six-layer structure consisting of an air superstrate, a gold layer, a barium titanate layer, a n type silicon layer, a gold layer and an Al2O3 nanolattice substrate. Regarding the suggested structure, the parameters related to the phase and the absorption modulation are investigated at different thicknesses. Here, the Pockels effect and the free carrier dispersion effect are considered simultaneously. The dispersion equation of this structure is analytically obtained and numerically solved by the Nelder-Mead method. The minimum {\pi} shift length is predicted to be equal to 6.91{\mu}m and the maximum calculated figure of merit is 10.74. Furthermore, according to our results, it is understood that this modulator has a high ability to be utilized in optical communication systems. Also, it could be integrated to the microelectronic systems and it is compatible with CMOS technology.