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Transformation optics for perfect two-dimensional non-magnetic all-mode waveguide couplers

Here, we demonstrate that transformation optics can be used to produce 2-D non-magnetic waveguide couplers with no reflections. Our approach consists of using a scaling function for reflection suppression and introducing an auxiliary function in the transformation optics formulation to achieve a non-magnetic medium for coupling the TM polarization. To demonstrate the potential of this method, two non-magnetic waveguide couplers are designed. The first one satisfies the Brewster angle condition for any arbitrary incidence angle (TMn modes), extending the performance of couplers previously reported in the literature that only operate for TEM (TM0 mode), i.e. waves with normal incidence. Our method can be applied to match any given dielectric constant. Our results demonstrate that for a given mode (angle), we achieve a perfect match to a defined dielectric constant. The second design removes the dependence of the reflectionless condition to the incident angle at the boundary. Hence, this coupler works for all incident angles (TMn modes). It is used to compress all the modes into a region with a higher predefined refractive index.