\begin{array}{ll} \vec{n}\cdot(\vec{D}_2-\vec{D}_1)=\sigma~~&~~\vec{n}\times(\vec{E}_2-\vec{E}_1)=0\\ \vec{n}\cdot(\vec{B}_2-\vec{B}_1)=0~~&~~\vec{n}\times(\vec{H}_2-\vec{H}_1)=\vec{K} \end{array} \\ \vec{E}(\vec{x},t)=\vec{\cal E}(x,y){e}^{i(kz-\omega t)} \\ \vec{B}(\vec{x},t)=\vec{\cal{B}}(x,y){e}^{i(kz-\omega t)}
                            

            \begin{array}{ll} \vec{n}\cdot(\vec{D}_2-\vec{D}_1)=\sigma~~&~~\vec{n}\times(\vec{E}_2-\vec{E}_1)=0\\ \vec{n}\cdot(\vec{B}_2-\vec{B}_1)=0~~&~~\vec{n}\times(\vec{H}_2-\vec{H}_1)=\vec{K} \end{array} \\
            \vec{E}(\vec{x},t)=\vec{\cal E}(x,y){e}^{i(kz-\omega t)} \\ 
            \vec{B}(\vec{x},t)=\vec{\cal{B}}(x,y){e}^{i(kz-\omega t)} \\
            \begin{array}{ll} \displaystyle {\cal B}_x=\frac{i}{\varepsilon\mu\omega^2-k^2}\left(k\frac{\partial {\cal B}_z}{\partial x}-\varepsilon\mu\omega\frac{\partial {\cal E}_z}{\partial y}\right)~~&~~ \displaystyle {\cal B}_y=\frac{i}{\varepsilon\mu\omega^2-k^2}\left(k\frac{\partial {\cal B}_z}{\partial y}+\varepsilon\mu\omega\frac{\partial {\cal E}_z}{\partial x}\right)\\ \displaystyle {\cal E}_x=\frac{i}{\varepsilon\mu\omega^2-k^2}\left(k\frac{\partial {\cal E}_z}{\partial x}+\varepsilon\mu\omega\frac{\partial {\cal B}_z}{\partial y}\right)~~&~~ \displaystyle {\cal E}_y=\frac{i}{\varepsilon\mu\omega^2-k^2}\left(k\frac{\partial {\cal E}_z}{\partial y}-\varepsilon\mu\omega\frac{\partial {\cal B}_z}{\partial x}\right) \end{array}
        

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