# Optical Fiber Transfer Function (attenuation and dispersion)

1. Oct 16, 2008

### Oziyak

I have a few questions regarding the transfer function of a SMF. I'm using the below equation to simulate the effect a single mode fiber (SMF) has on the optical field after some distance $$\textit{z}$$.
$$S_{out}(\omega) = S_{in}(\omega)\exp\left [z\left(-\frac{\alpha}{2}-i\frac{\beta_{2}}{2}(\Delta\omega)^{2}-i\frac{\beta_{3}}{6}(\Delta\omega)^{3}\right) \right ] My question is in regards to the origin of this equation. I understand the inclusion of the \beta terms, and realize that \alpha represents the attenuation, but why is it alpha divided by 2? When I look in a text book I have they say the following equation dictates pulse evolution through a SMF: \frac{\partial A}{\partial z}+ \frac{i\beta_{2}}{2}\frac{\partial ^{2}A}{\partial t^{2}}- \frac{\beta_{3}}{6}\frac{\partial ^{3}A}{\partial t^{3}} = 0$$

I suppose I'm looking for the relationship between equations (1) and (2) of this post as well. In equation (2) A is the slowly varying amplitude (or envelope) of the pulse.

Thank you very much for reading, and also for any assistance you can provide. If you require anymore detail from me or if I have missed something please let me know.

2. Oct 20, 2008

### Oziyak

I've been trying to reply to my own post for those who are interested... but everytime I try to use more TEX coding for equations it never displays it properly in the preview, so I'm assuming it wouldn't in the post either.... can an admin help me with this?

everytime I use a tex tag it just puts beta in it?

3. Oct 20, 2008

### Staff: Mentor

The admins just did a server upgrade over the weekend, and Latex is one of the things that got broken. Check out the Forum Feedback and Announcements forum to see what the progress of the fix is.