Port analysis using s-matrix for 2d metasurface waveguide coupler in Mid-IR application

We present an intuitive method of port analysis based on an S-matrix formalism for the design of a 2D metasurface coupler integrated with strip waveguide in SOI for 3.8 µm wavelength. The metasurface design has been achieved using Lumerical by systematically optimizing the radius of circularly shaped unit cells and the period between them. The effective coupling efficiency achieved for the designed 2D metasurface integrated with waveguide is ∼98% in the in-plane waveguide for the out-of-plane surface illumination. The achieved bandwidth of the structure is 1 µm. The S-parameters of the optimized design are calculated and the 3-port analysis of the device is carried out using Interconnect by Lumerical. The suggested method is general and can be applied to any multi-port devices with some simple changes made in the layout of the design. Gain is the performance metric in our case and it is defined as the ratio of power transmitted at the output port to that of power in the input port. The gain of all the three ports are calculated. We believe our design is a good alternative for conventionally employed grating couplers and inverse tapers.