Transmission-type photonic doping for high-efficiency epsilon-near-zero supercoupling

General concept

We begin the discussion with the general ENZ supercoupling model, which consists of an arbitrary-shaped ENZ channel with the area Ap connecting two rectangular waveguide ports with the widths of a1 and a27,8. The EM waves are excited from Port 1, squeezed through the ENZ channel, and received at Port 2. As demonstrated theoretically, the reflection coefficient can be described as7

$$\rho=\frac{({a}_{1}-{a}_{2})+i{k}_{0}{\mu }_{{{{{{\rm{r}}}}}},{{{{{\rm{p}}}}}}}{A}_{{{{{{\rm{p}}}}}}}}{({a}_{1}+{a}_{2})-i{k}_{0}{\mu…

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