The image above is some math for the Fabry-Perot laser model
I'm trying to get to the power reflected (last equation with sine) from the normalized reflection. I'm stuck because I don't know how to get $$E_{r}^{*}/E_{i}^{*} $$
I've tried setting $E_{r}$ to the numerator of the normalized equation and $E_{i}$ to the denominator and taking the conjugate of each inidividually, but it doesn't seem to be working. Am I missing something conceptual? What's the correct way to get from $E_{r}/E_{i}$ to $E_{r}E_{r}^{*}/E_{i}E_{i}^{*}$
Note: $r^{2} = R $
$$\frac{E_rE_r^*}{E_iE_i^*}= \frac{r(1-e^{i\delta})r(1-e^{-i\delta})}{(1-Re^{i\delta})(1-Re^{-i\delta})}=\frac{r^2(1+1-e^{i\delta}-e^{-i\delta})}{1+R^2-Re^{i\delta}-Re^{-i\delta}}$$
$$=\frac{R(2-2cos\delta)}{(1-R)^2+2R-2Rcos\delta}$$
$$=\frac{4Rsin^2(\delta/2)}{(1-R)^2+4Rsin^2(\delta/2)} $$