In the air, a uniform plane wave propagating along the positive z-direction is incident on an ideal conductive plane at $z=0$. The instantaneous vector of the incident wave's electric field intensity is
$$
E_{i} = a_{x} E_{x0} \cos(\omega t - \beta z) + a_{y} E_{y0} \sin(\omega t - \beta z) \quad\mathrm{V/m}
$$
Derive the complex vector of the electromagnetic field intensity of the composite wave in the space for $z < 0$ and the expression for the induced surface current density on the ideal conductive plane.

Options:
A. $$
\begin{array} {l} {{\dot{\dot{E}}_{1}=\dot{\bar{E}}_{1}+\dot{\bar{E}}_{r}=( a_{y} E_{x 0}-j a_{z} E_{y 0} ) ( e^{-j 8y}+e^{j 8y} )}} \\ {{=2 ( j E_{y0 } a_{z}-a_{y} E_{x 0} ) \mathrm{s i n} \, \beta z}} \\ {{\dot{\bar{H}}_{1}=\dot{\bar{H}}_{1}+\dot{\bar{H}}_{r}=\frac{2} {\eta_0} ( E_{x 0} a_{z}+j E_{y 0} a_{y} ) \mathrm{c o s} \, \beta z}} \\ \end{array}
$$
$$
\dot{J}_{S}=\left. ( a_{z} \times\dot{H}_{1} ) \right|_{z=0}=\left. (-a_{x} \times\dot{H}_{1} ) \right|_{z=0}=\frac{2} {\eta_{0}} ( E_{y0} a_{x}+j E_{x0} a_{z} )
$$
B. $$
\begin{array} {l} {{\dot{\dot{E}}_{1}=\dot{\bar{E}}_{1}+\dot{\bar{E}}_{r}=( a_{y} E_{z 0}+j a_{x} E_{y 0} ) ( e^{j 8x}-e^{-j 8x} )}} \\ {{=-2 ( j E_{y0 } a_{z}-a_{x} E_{z 0} ) \mathrm{c o s} \, \beta z}} \\ {{\dot{\bar{H}}_{1}=\dot{\bar{H}}_{1}+\dot{\bar{H}}_{r}=\frac{2} {\eta_0} ( E_{z 0} a_{y}+j E_{x 0} a_{z} ) \mathrm{s i n} \, \beta z}} \\ \end{array}
$$
$$
\dot{J}_{S}=\left. ( a_{x} \times\dot{H}_{1} ) \right|_{z=0}=\left. (-a_{x} \times\dot{H}_{1} ) \right|_{z=0}=\frac{2} {\eta_{0}} ( E_{y0} a_{z}-j E_{x0} a_{y} )
$$
C. $$
\begin{array} {l} {{\dot{\dot{E}}_{1}=\dot{\bar{E}}_{1}+\dot{\bar{E}}_{r}=( a_{x} E_{y 0}-j a_{z} E_{x 0} ) ( e^{-j 8z}+e^{j 8z} )}} \\ {{=2 ( j E_{x0 } a_{x}-a_{z} E_{y 0} ) \mathrm{s i n} \, \beta z}} \\ {{\dot{\bar{H}}_{1}=\dot{\bar{H}}_{1}+\dot{\bar{H}}_{r}=\frac{2} {\eta_0} ( E_{x 0} a_{z}+j E_{y 0} a_{x} ) \mathrm{c o s} \, \beta z}} \\ \end{array}
$$
$$
\dot{J}_{S}=\left. ( a_{z} \times\dot{H}_{1} ) \right|_{z=0}=\left. (-a_{y} \times\dot{H}_{1} ) \right|_{z=0}=\frac{2} {\eta_{0}} ( E_{z0} a_{y}+j E_{y0} a_{x} )
$$
D. $$
\begin{array} {l} {{\dot{\dot{E}}_{1}=\dot{\bar{E}}_{1}+\dot{\bar{E}}_{r}=( a_{x} E_{z 0}+j a_{x} E_{y 0} ) ( e^{j 8y}+e^{-j 8y} )}} \\ {{=2 ( j E_{x0 } a_{y}+a_{z} E_{z 0} ) \mathrm{c o s} \, \beta z}} \\ {{\dot{\bar{H}}_{1}=\dot{\bar{H}}_{1}+\dot{\bar{H}}_{r}=\frac{2} {\eta_0} ( E_{y 0} a_{z}+j E_{x 0} a_{x} ) \mathrm{s i n} \, \beta z}} \\ \end{array}
$$
$$
\dot{J}_{S}=\left. ( a_{x} \times\dot{H}_{1} ) \right|_{z=0}=\left. (-a_{x} \times\dot{H}_{1} ) \right|_{z=0}=\frac{2} {\eta_{0}} ( E_{z0} a_{x}-j E_{x0} a_{z} )
$$
E. $$
\begin{array} {l} {{\dot{\dot{E}}_{1}=\dot{\bar{E}}_{1}+\dot{\bar{E}}_{x}=( a_{x} E_{x o}-j a_{y} E_{y o} ) ( e^{-j 8x}-e^{j 8x} )}} \\ {{=-2 ( j E_{x0 } a_{x}+a_{y} E_{y 0} ) \mathrm{s i n} \, \beta z}} \\ {{\dot{\bar{H}}_{1}=\dot{\bar{H}}_{1}+\dot{\bar{H}}_{r}=\frac{2} {\eta_0} ( E_{x 0} a_{y}+j E_{y 0} a_{x} ) \mathrm{c o s} \, \beta z}} \\ \end{array}
$$
$$
\dot{J}_{S}=\left. ( a_{n} \times\dot{H}_{1} ) \right|_{z=0}=\left. (-a_{z} \times\dot{H}_{1} ) \right|_{z=0}=\frac{2} {\eta_{0}} ( E_{x0} a_{x}-\mathrm{j} E_{y0} a_{y} )
$$
F. $$
\begin{array} {l} {{\dot{\dot{E}}_{1}=\dot{\bar{E}}_{1}+\dot{\bar{E}}_{r}=( a_{z} E_{z 0}-j a_{y} E_{x 0} ) ( e^{-j 8z}-e^{j 8z} )}} \\ {{=-2 ( j E_{z0 } a_{y}-a_{x} E_{x 0} ) \mathrm{s i n} \, \beta z}} \\ {{\dot{\bar{H}}_{1}=\dot{\bar{H}}_{1}+\dot{\bar{H}}_{r}=\frac{2} {\eta_0} ( E_{x 0} a_{z}+j E_{y 0} a_{x} ) \mathrm{c o s} \, \beta z}} \\ \end{array}
$$
$$
\dot{J}_{S}=\left. ( a_{x} \times\dot{H}_{1} ) \right|_{z=0}=\left. (-a_{z} \times\dot{H}_{1} ) \right|_{z=0}=\frac{2} {\eta_{0}} ( E_{y0} a_{z}+j E_{x0} a_{y} )
$$
G. $$
\begin{array} {l} {{\dot{\dot{E}}_{1}=\dot{\bar{E}}_{1}+\dot{\bar{E}}_{r}=( a_{z} E_{z 0}+j a_{y} E_{y 0} ) ( e^{j 8z}-e^{-j 8z} )}} \\ {{=-2 ( j E_{z0 } a_{z}+a_{y} E_{y 0} ) \mathrm{c o s} \, \beta z}} \\ {{\dot{\bar{H}}_{1}=\dot{\bar{H}}_{1}+\dot{\bar{H}}_{r}=\frac{2} {\eta_0} ( E_{z 0} a_{x}+j E_{y 0} a_{y} ) \mathrm{s i n} \, \beta z}} \\ \end{array}
$$
$$
\dot{J}_{S}=\left. ( a_{y} \times\dot{H}_{1} ) \right|_{z=0}=\left. (-a_{y} \times\dot{H}_{1} ) \right|_{z=0}=\frac{2} {\eta_{0}} ( E_{z0} a_{y}-j E_{y0} a_{z} )
$$
H. $$
\begin{array} {l} {{\dot{\dot{E}}_{1}=\dot{\bar{E}}_{1}+\dot{\bar{E}}_{r}=( a_{z} E_{y o}-j a_{x} E_{z 0} ) ( e^{j 8y}-e^{-j 8y} )}} \\ {{=-2 ( j E_{y0 } a_{z}+a_{x} E_{z 0} ) \mathrm{s i n} \, \beta z}} \\ {{\dot{\bar{H}}_{1}=\dot{\bar{H}}_{1}+\dot{\bar{H}}_{r}=\frac{2} {\eta_0} ( E_{y 0} a_{x}+j E_{z 0} a_{z} ) \mathrm{c o s} \, \beta z}} \\ \end{array}
$$
$$
\dot{J}_{S}=\left. ( a_{x} \times\dot{H}_{1} ) \right|_{z=0}=\left. (-a_{x} \times\dot{H}_{1} ) \right|_{z=0}=\frac{2} {\eta_{0}} ( E_{z0} a_{z}+j E_{y0} a_{y} )
$$
I. $$
\begin{array} {l} {{\dot{\dot{E}}_{1}=\dot{\bar{E}}_{1}+\dot{\bar{E}}_{r}=( a_{x} E_{z 0}+j a_{z} E_{x 0} ) ( e^{j 8y}-e^{-j 8y} )}} \\ {{=-2 ( j E_{x0 } a_{z}-a_{x} E_{z 0} ) \mathrm{c o s} \, \beta z}} \\ {{\dot{\bar{H}}_{1}=\dot{\bar{H}}_{1}+\dot{\bar{H}}_{r}=\frac{2} {\eta_0} ( E_{z 0} a_{y}+j E_{x 0} a_{x} ) \mathrm{s i n} \, \beta z}} \\ \end{array}
$$
$$
\dot{J}_{S}=\left. ( a_{y} \times\dot{H}_{1} ) \right|_{z=0}=\left. (-a_{z} \times\dot{H}_{1} ) \right|_{z=0}=\frac{2} {\eta_{0}} ( E_{x0} a_{z}-j E_{z0} a_{x} )
$$
J. $$
\begin{array} {l} {{\dot{\dot{E}}_{1}=\dot{\bar{E}}_{1}+\dot{\bar{E}}_{r}=( a_{y} E_{y 0}+j a_{x} E_{x 0} ) ( e^{-j 8x}+e^{j 8x} )}} \\ {{=2 ( j E_{x 0} a_{y}-a_{x} E_{y 0} ) \mathrm{c o s} \, \beta z}} \\ {{\dot{\bar{H}}_{1}=\dot{\bar{H}}_{1}+\dot{\bar{H}}_{r}=\frac{2} {\eta_0} ( E_{x 0} a_{x}-j E_{y 0} a_{y} ) \mathrm{s i n} \, \beta z}} \\ \end{array}
$$
$$
\dot{J}_{S}=\left. ( a_{m} \times\dot{H}_{1} ) \right|_{z=0}=\left. (-a_{y} \times\dot{H}_{1} ) \right|_{z=0}=\frac{2} {\eta_{0}} ( E_{y0} a_{y}+j E_{x0} a_{x} )
$$
Answer: E