Calculating complex refractive index from complex dielectric function

I am attempting to obtain the complex refractive index of few amino acid crystals. The only data I have available is of their complex dielectric function and absorption curve. I am doing the following to calculate the real and imaginary parts of the refractive index.

$ \varepsilon_1 = n^2 - k^2 \quad \text{(1)}$

$ \varepsilon_2 = 2nk \quad \text{(2)}$

Solving for $n$ and $k$ in equations $（1）$and $（2）$, I get,

$n = \sqrt{\frac{\varepsilon_1 + \sqrt{\varepsilon_1^2 + \varepsilon_2^2}}{2}}$

$k = \sqrt{\frac{\sqrt{\varepsilon_1^2 + \varepsilon_2^2} - \varepsilon_1}{2}}$

I haven't come across anyone using this approach. It is usually calculated using absorption coefficient and refractance. Please let me know if the approach is correct or if there are better ways of calculating it with the data I have.

Thank you!