Derivation of complex refractive index

[OneMoreName]

Hi,

Got a problem with the following derivation:

Coming from the Helmholtz equation one gets:

\textbf{n}^2=\muc^{2}(\epsilon+i\frac{\sigma}{\omega})

which is of course something like:

\textbf{n}=n+i\kappa

My question is, how do you obtain the following relations?

n^{2}=\frac{1}{2}\muc^{2}\epsilon(\sqrt{1+(\frac{\sigma}{\epsilon\omega})^{2}}+1)
\kappa^{2}=\frac{1}{2}\muc^{2}\epsilon(\sqrt{1+(\frac{\sigma}{\epsilon\omega})^{2}}-1)

Maybe it's obvious, but I am arriving at everything but this. Enlighten me guys and thanks if you do.

 

[andrien]

n=n+ik, put into n^2 and you will have two eqn ,one equating the real part and other equating the imaginary part which you can solve to get.if that is what you are asking.

 

[OneMoreName]

That's right, but the problem is you cannot separate n or κ out. For example you get something like

n^{2}(n^{2}-\muc^{2}\epsilon)=(\frac{μc^{2}σ}{2ω})^{2}

and I don't see how to get to n².

Oh, OK, just have to solve the quadratic equation after substitution and one gets to the results, duh! Thanks!