Hi! I've stumbled upon an equation of the form:

$\displaystyle e^{-i k x} + R e^{i (k x + \theta)} = i k \xi \left( e^{-i k x} - R e^{i (k x + \theta)}\right) $

I wish to solve the equation for complex $\displaystyle k$. Every other constants are known and real. $\displaystyle 0 \leq R \leq 1,~\xi > 0$. Does there exist a complete analytic solution for $\displaystyle k$, or perhaps a solution in some approximate limit? At least I know that for $\displaystyle R = 0,~k = -\frac{i}{\xi}$.