A plane wave can be described by the real part of the exponential wave equation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\mathbf{E}=E_{0}e^{i(kz-wt)}[/tex]

Adding the subscript i or r for incident or reflected waves, the ratio of the amplitude of reflected to incident wave is given by:

[tex]\frac{E_{r0}}{E_{i0}} = \frac{n_1-n_2}{n_1+n_2}[/tex]

But if n_{2}is complex, then this leads to a complex E_{r0}. What does this mean for the physical wave, the real part ofE?

[tex]\mathbf{E}=E_{r0}e^{i(kz-wt)}=(Re\{E_{r0}\}+iIm\{E_{r0}\})e^{i(kz-wt)}=Re\{E_{r0}\}e^{i(kz-wt)}+Im\{E_{r0}\}e^{i(kz-wt+\pi/2)}[/tex]

To me it looks like 2 out of phase waves are reflected. If this is right can you point me somewhere I can read up more about it? Or have I abused some notation somewhere?

Thanks for your help understanding whats going on.

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# Reflected wave at complex refrective index

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