Onda incidente:
E 0 = e x E 0 0 e i ( k 1 Z − ω t ) {\displaystyle \mathbf {E_{0}} =\mathbf {e_{x}} E_{0}^{0}e^{i(k_{1}Z-\omega t)}}
Onda reflejada:
E 1 = − e x E 1 0 e i ( − k 1 Z − ω t ) {\displaystyle \mathbf {E_{1}} =-\mathbf {e_{x}} E_{1}^{0}e^{i(-k_{1}Z-\omega t)}}
Onda transmitida:
E 2 = e x E 2 0 e i ( k 1 Z − ω t ) {\displaystyle \mathbf {E_{2}} =\mathbf {e_{x}} E_{2}^{0}e^{i(k_{1}Z-\omega t)}}
constante de propagacion en conductor:
k 2 ~ 2 = ω 2 ϵ 2 c 2 ( 1 + i 4 π σ 2 ω ϵ 2 ) {\displaystyle {\tilde {k_{2}}}^{2}={\frac {\omega ^{2}\epsilon _{2}}{c^{2}}}(1+i{\frac {4\pi \sigma _{2}}{\omega \epsilon _{2}}})}
condiciones a la frontera (z=0)
E 0 0 − E 1 0 = E 2 0 {\displaystyle E_{0}^{0}-E_{1}^{0}=E_{2}^{0}}
k 1 ( E 0 0 + E 1 0 ) = k 2 ~ E 2 0 {\displaystyle k_{1}(E_{0}^{0}+E_{1}^{0})={\tilde {k_{2}}}E_{2}^{0}}
E 1 0 = E 0 k ~ 2 − k 1 k ~ 2 + k 1 {\displaystyle E_{1}^{0}=E_{0}{\frac {{\tilde {k}}_{2}-k_{1}}{{\tilde {k}}_{2}+k_{1}}}}
E 2 0 = E 0 2 k 1 k ~ 2 + k 1 {\displaystyle E_{2}^{0}=E_{0}{\frac {2k_{1}}{{\tilde {k}}_{2}+k_{1}}}}
E b ′ ′ = E a n − n ′ n + n ′ {\displaystyle E_{b}^{\prime \prime }=E_{a}{\frac {n-n^{\prime }}{n+n^{\prime }}}}
E b ′ = E a 2 n n + n ′ {\displaystyle E_{b}^{\prime }=E_{a}{\frac {2n}{n+n^{\prime }}}}