Perfect Nonreciprocal Absorption Based on Metamaterial Slab

Abstract

In order to achieve nonreciprocal absorption, we design a metamaterial slab made of arrays of tilted metal layers. Through studying the extraordinary material dispersion, we derive the transfer matrix to calculate its transmittance and absorption. Given specific conditions and two opposite incidence directions, the slab can achieve total absorption for one direction and total transmittance for the other direction. The designed structure is demonstrated to be a perfect nonreciprocal absorber.

Appendix

In the coordinate system x’y’z’, the electric displace vector D ^'and electric filed vector E ^'satisfies

$$ {\mathbf{D}}^{\mathbf{\hbox{'}}}={\varepsilon}_0{\tilde{\varepsilon}}^{\hbox{'}}{\mathbf{E}}^{\mathbf{\hbox{'}}} $$

(27)

where

$$ {\tilde{\varepsilon}}^{\hbox{'}}=\left[\begin{array}{ccc}\hfill {\varepsilon}_{xx}\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill {\varepsilon}_{yy}\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill {\varepsilon}_{zz}\hfill \end{array}\right] $$

(28)

When the coordinate system x’y’z’ is rotated anticlockwise around y’ axis for an angle of φ, the basic vectors in the new coordinate system xyz and old coordinate system x’y’z’ have the following relation

$$ \left[\begin{array}{c}\hfill \hat{x}\hfill \\ {}\hfill \hat{y}\hfill \\ {}\hfill \hat{z}\hfill \end{array}\right]=\left[\begin{array}{ccc}\hfill \cos \varphi \hfill & \hfill 0\hfill & \hfill \sin \varphi \hfill \\ {}\hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ {}\hfill \hbox{-} \sin \varphi \hfill & \hfill 0\hfill & \hfill \cos \varphi \hfill \end{array}\right]\left[\begin{array}{c}\hfill {\hat{x}}^{'}\hfill \\ {}\hfill {\hat{y}}^{'}\hfill \\ {}\hfill {\hat{z}}^{'}\hfill \end{array}\right]=\mathrm{P}\left[\begin{array}{c}\hfill {\hat{x}}^{'}\hfill \\ {}\hfill {\hat{y}}^{'}\hfill \\ {}\hfill {\hat{z}}^{'}\hfill \end{array}\right] $$

(29)

where $\mathrm{P}=\left[\begin{array}{ccc}\hfill \cos \varphi \hfill & \hfill 0\hfill & \hfill \sin \varphi \hfill \\ {}\hfill 0\hfill & \hfill 1\hfill & \hfill 0\hfill \\ {}\hfill \hbox{-} \sin \varphi \hfill & \hfill 0\hfill & \hfill \cos \varphi \hfill \end{array}\right]$.

In the new coordinate system xyz, the electric displace vector D and electric filed vector E satisfies

$$ \mathbf{D}={\varepsilon}_0\tilde{\varepsilon}\mathbf{E} $$

$$ \tilde{\varepsilon}{=\mathrm{P}}^{\hbox{'}}{\tilde{\varepsilon}}^{\hbox{'}}\mathrm{P}=\left[\begin{array}{ccc}\hfill {\varepsilon}_{xx}\hfill & \hfill 0\hfill & \hfill {\varepsilon}_{xz}\hfill \\ {}\hfill 0\hfill & \hfill {\varepsilon}_{yy}\hfill & \hfill 0\hfill \\ {}\hfill {\varepsilon}_{zx}\hfill & \hfill 0\hfill & \hfill {\varepsilon}_{zz}\hfill \end{array}\right] $$

(30)

where

$$ \begin{array}{l}{\upvarepsilon}_{xx}={\upvarepsilon}_{xx}{ \cos}^2\upvarphi +{\upvarepsilon}_{yy}{ \sin}^2\upvarphi \\ {}{\upvarepsilon}_{xz}={\upvarepsilon}_{zx}=\left({\upvarepsilon}_{yy}-{\upvarepsilon}_{xx}\right) \sin \upvarphi \cos \upvarphi \\ {}{\upvarepsilon}_{zz}={\upvarepsilon}_{xx}{ \sin}^2\upvarphi +{\upvarepsilon}_{yy}{ \cos}^2\upvarphi \end{array} $$

(31)