“…Metamaterial-dielectric waveguides have been studied in recent years 1 , 2 with a variety of applications in optical devices, such as switches, 3 sensors, 4 , 5 modulators, 6 , 7 waveguide polarizer, 8 and nonlinear nanophotonics 9 . There are different metamaterial waveguide structures including but not limited to slab, cylindrical, and elliptical waveguides 2 , 10 …”