Abstract
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.
Highlights
We propose a three-dimensional coordinate transformation scheme for the design of waveguide couplers using impedance-tunable transformation optics
To couple waves efficiently between WG1 and WG2 in the +z direction, tapers are embedded within a transformation medium, Fig. 1(b) shows the coordinate transformation between the transformed space (ρ′, θ′, z′) and the original space (ρ, θ, z)
The inevitable imperfect performance due to the geometric optics limit can be improved through setting large refractive index coefficient p, the cost is that the relative permittivity of the transformation medium is not 1 and extreme larger parameters of p will increase the difficulty of realization of designed transformation medium
Summary
We propose a three-dimensional coordinate transformation scheme for the design of waveguide couplers using impedance-tunable transformation optics. We study the dielectric waveguide coupler design for coupling light efficiently from large size waveguide of low index to small size waveguide of high index, by setting appropriate impedance function the EM waves can be efficiently transmitted between different cross sections and background media. C d (i.e. coaxial waveguides with equal ratios between outer and inner radii), one can obtain k = 1, which is the standard transformation (the non-tunable impedance case for k = 1).
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