There is growing interest in designing waveguide couplers with low reflections. Using impedance-tunable transformation optics, we propose a coordinate transformation technique in the design of compact three-dimensional waveguide couplers. To transmit electromagnetic waves between two coaxial waveguides with different inner and outer radii in the microwave range, a suitable impedance function is derived to reduce the impedance mismatch at the boundary, which make the fabrication process being simplified due to the reduced set of transformation media(dielectric response materials only). A larger refractive index is set to raise the coupling performance in the low frequency range. Next we apply impedance-tunable transformation optics to the design of dielectric waveguide couplers, where only the core region be contained in the transformed space; by selecting a tunable impedance function, waves can transmit efficiently through waveguides with quite different cross sections and background media. The proposed impedance-tunable three-dimensional waveguide couplers are confirmed by the 3-dimensional numerical simulation with good performances, which can have potential applications in fiber-to-chip coupling.
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