Refelction and Transmission

Now we define the incident plane wave

$${\bf E}={\bf E}_0 e^{i({\bf k}\cdot{\bf r} - \omega t)}, \ \... ...imes {\bf E}_0 }{\omega} e^{i({\bf k}\cdot{\bf r} - \omega t)}$$ (51)

reflected wave

$${\bf E}' ={\bf R}_0 e^{i({\bf k}'\cdot{\bf r} - \omega' t)},... ...s {\bf R}_0 }{\omega'} e^{i({\bf k}'\cdot{\bf r} - \omega' t)}$$ (52)

transmitted wave

$${\bf E}''={\bf T}_0 e^{i({\bf k}''\cdot{\bf r} - \omega'' t)... ... T}_0 }{\omega'' } e^{i({\bf k}'' \cdot{\bf r} - \omega'' t)}$$ (53)

図 3: Relection and Transmission of Light

From the Figure above

$${\bf k} = (k\sin\theta, 0, k\cos\theta)$$ (54)

$${\bf k}' = (k'\sin\theta', 0, k'\cos\theta'), \ \ \ \ \ \ \ e^{i(\pi - \theta')} = -\cos \theta' + i \sin\theta'$$ (55)

$${\bf k}'' = (k'' \sin\theta'' , 0, k'' \cos\theta'' )$$ (56)

The $p$-wave has component of $x$ and $z$, but $s$-wave has only $y$ component.