I Dielectric constant, dispersion and response of the medium

[riharenda009]

TL;DR Summary

Electric flux density in a dispersive medium.

Hello,

for my PhD, I've been studying an influence of a gain medium on spectral linewidth of light inside a fiber cavity. I've encountered a formula in one paper to which I don't how to get to (see screenshot), it's the formula (A3).

On the left hand side there is electric flux density, the right hand side is expanded to the first derivative. I'm not sure what justifies the expansion and how you can get to it. You can find the whole paper here, but the formula (A3) stands separtely in the text.

I've performed my own search already, found only this, but didn't help me to derive/justify (A3).

I would really appreciate the explanation or to be directed to right references.

Thank you.

 

[riharenda009]

I've found the justification by myself, thanks everyone who attempted to tackle it.