Waveguide tapering using Conformal transformation optics for ideal transmission

In this paper, conformal transformation optics (TO) is employed to guide the electromagnetic wave between two waveguides with different cross-sections. Owing to the properties of conformal mapping, an all-dielectric medium is obtained. The conformal transformation is derived by solving the Laplace equation. The tapering equation is obtained by conducting an optimization to achieve maximum less-than-unity refractive index while maintaining the uniformity of the refractive index at the input and output boundaries. The functionality of the proposed idea is confirmed by a simulation in COMSOL.