Radiacion: Reflexion en metales

Onda incidente:

$\mathbf {E_{0}} =\mathbf {e_{x}} E_{0}e^{i(\mathbf {k_{1}} Z-\omega t)}$

Onda reflejada:

$\mathbf {E_{1}} =-\mathbf {e_{x}} E'_{1}e^{i(-\mathbf {k_{1}} Z-\omega t)}$

Onda transmitida:

$\mathbf {E_{2}} =\mathbf {e_{x}} {E_{0}}^{2}e^{i(\mathbf {k_{1}} Z-\omega t)}$

constante de propagacion en conductor:

${\tilde {k_{2}}}^{2}={\frac {\omega ^{2}\epsilon _{2}}{c^{2}}}(1+i{\frac {4\sigma _{2}}{\omega \epsilon _{2}}})$

condiciones a la frontera (z=0)

$E_{1}^{0}=E_{0}{\frac {{\tilde {k}}_{2}-k_{1}}{{\tilde {k}}_{2}+k_{1}}}$

$E_{2}^{0}=E_{0}{\frac {2k_{1}}{{\tilde {k}}_{2}+k_{1}}}$

$E_{b}^{\prime \prime }=E_{a}{\frac {n-n^{\prime }}{n+n^{\prime }}}$

$E_{b}^{\prime }=E_{a}{\frac {2n}{n+n^{\prime }}}$

$n^{\prime }={\sqrt {{\frac {1}{2}}(k+{\sqrt {k^{2}+{({\frac {\sigma }{\omega \epsilon _{0}}})}^{2}}}}}$

$\eta ^{\prime }={\sqrt {{\frac {1}{2}}(-k+{\sqrt {k^{2}+{({\frac {\sigma }{\omega \epsilon _{0}}})}^{2}}}}}$