Understanding the equations of a paper

[Ecthe]

Hello there,

First of all, I am not fully sure that this is the right place to post this. This post is about equations but the paper is a bout physics... so if an admin find a better place for it please feel free to move it.

I am currently trying to fully understand this paper http://link.springer.com/article/10.1007/BF01091215
I hope some people have acces to it because I don't think putting only the equation I don't understand is usefull.
So on that paper, I went through all the equations to be sure I understand how he goes from one to another. However, I can't manage to go from A3 to A4. Could someone help me with that ? He does some simplifications which I tried to use but I am allways ending up stucked.

Thanks in advance for your help.

PS: please forgive my english. It is not my native language and I am not fully comfortable in writting it.

 

[blue_leaf77]

Divide the integration interval into smaller interval, each of which is equal to one wavelength in the gain medium. Thus this interval will be $\Delta z' = \lambda/n$. Doing this you will get summation over successive intervals making up the (approximate) length of the gain medium. After this, find out terms which slowly varies over one wavelength, which are $S(z)$ and $\exp(i2(k_n-k_{0g})z)$ (the latter is based on my guess though since the frequency of this oscillation is much smaller than $\exp(i2k_{0g}z)$).