Lindsey Yue edited section_Reflection_Coefficients_The_reflection__.tex  almost 8 years ago

Commit id: 8525195622583f799a85cb48b9d8cbf6acb6b155

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\mathbf{E}_{c1} \times \mathbf{\hat{n}} = \mathbf{E}_{c2} \times \mathbf{\hat{n}}  \end{equation}  %  \begin{equation} \begin{equation}\label{eq:hboundary}  \mathbf{H}_{c1} \times \mathbf{\hat{n}} = \mathbf{H}_{c2} \times \mathbf{\hat{n}}  \end{equation}  % 

\mathbf{E}_{c} = \mathbf{E}_{0} e^{-2 \pi i \left( \mathbf{w}' \cdot \mathbf{r} - i \mathbf{w}'' \cdot \mathbf{r} \right)}, \quad \mathbf{E}_{0} = E_{\parallel} \mathbf{\hat{e}}_{\parallel} + E_{\perp} \mathbf{\hat{e}}_{\perp}  \end{equation}  %  Considering incident, reflected, and transmitted electric fields at a point on the boundary, Eqs. \label{eq:eboundary} and \label{eq:hboundary} become:  %  \begin{equation}  \mathbf{E}_{c\mathrm{i}} \times \mathbf{\hat{n}} + \mathbf{E}_{c\mathrm{r}} \times \mathbf{\hat{n}} = \mathbf{E}_{c\mathrm{t}} \times \mathbf{\hat{n}}  \end{equation}  With the coordinate origin on the boundary, at the point $\mathbf{r}=0$, Eq. \ref{eq:eboundary} becomes