Design of an Efficient GeSn Based Grating Coupler to excite Plasmon Waves in $\mathbf{3}-\mathbf{20}\ \boldsymbol{\mu}\mathbf{m}$ MIR Range in GeSn/SiGeSn Structure on Si Platform

We describe in this paper the design of a GeSn alloy based planar grating to efficiently excite surface plasmon waves in a heavily doped GeSn layer replacing the usual metal conductor. The $\text{Ge}_{1-\mathrm{x}}\text{Sn}_{\mathrm{x}}$ layer is grown on $\text{Si}_{1-\mathrm{y}-\mathrm{z}}\text{Ge}_{\mathrm{y}}\text{Sn}_{\mathrm{z}}$ layer which may be grown on Si platform. The composition $x,\ y$ and $z$ are chosen to give rise to tensile, compressive and no strain in GeSn layer. The plasma frequency, real and imaginary parts of permittivity, etc., are calculated by using the modified Drude model developed by us. The optimized grating period and height for efficient coupling are calculated analytically.