- #1
superg33k
- 96
- 0
A plane wave can be described by the real part of the exponential wave equation:
[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 n2 is complex, then this leads to a complex Er0. What does this mean for the physical wave, the real part of E?
[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 what's going on.
[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 n2 is complex, then this leads to a complex Er0. What does this mean for the physical wave, the real part of E?
[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 what's going on.