The design of an optical waveguide coupler has several challenges, such as reflection losses at the interfaces of the coupler, material complexity for optical applications, and the coupling between arbitrary materials at the input and the output of the coupler. In this paper, for the first time to the best of our knowledge, we propose a solution to overcome the above difficulties. For this purpose, we introduce an auxiliary transformation function and an impedance scaling function. The auxiliary function specifies the matched dielectric materials at the input and output interfaces of the coupler, and the scaling function suppresses the reflections and makes the material nonmagnetic for transverse magnetic (TM) polarization. As a result, an optical waveguide coupler is designed that can ideally couple two waveguides with arbitrary dielectric materials and arbitrary cross sections using a nonmagnetic material. Validation of the design method is done by using COMSOL Multiphysics.