- #1
Oziyak
- 3
- 0
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}.
\begin{equation}<br /> S_{out}(\omega) = S_{in}(\omega)\exp\left<br /> [z\left(-\frac{\alpha}{2}-i\frac{\beta_{2}}{2}(\Delta\omega)^{2}-i\frac{\beta_{3}}{6}(\Delta\omega)^{3}\right)<br /> \right ]<br /> \end{equation}<br /> <br /> 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?<br /> <br /> When I look in a textbook I have they say the following equation dictates pulse evolution through a SMF:<br /> <br /> \begin{equation}<br /> \frac{\partial A}{\partial z}+ \frac{i\beta_{2}}{2}\frac{\partial ^{2}A}{\partial<br /> t^{2}}- \frac{\beta_{3}}{6}\frac{\partial ^{3}A}{\partial<br /> t^{3}} = 0<br /> \end{equation}<br />
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.
\begin{equation}<br /> S_{out}(\omega) = S_{in}(\omega)\exp\left<br /> [z\left(-\frac{\alpha}{2}-i\frac{\beta_{2}}{2}(\Delta\omega)^{2}-i\frac{\beta_{3}}{6}(\Delta\omega)^{3}\right)<br /> \right ]<br /> \end{equation}<br /> <br /> 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?<br /> <br /> When I look in a textbook I have they say the following equation dictates pulse evolution through a SMF:<br /> <br /> \begin{equation}<br /> \frac{\partial A}{\partial z}+ \frac{i\beta_{2}}{2}\frac{\partial ^{2}A}{\partial<br /> t^{2}}- \frac{\beta_{3}}{6}\frac{\partial ^{3}A}{\partial<br /> t^{3}} = 0<br /> \end{equation}<br />
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.