Modal Dispersion | Webdemo | Institute of Telecommunications, University of Stuttgart

Modal Dispersion - Introduction

Demonstration of modal dispersion of a multi mode fiber (MMF).

Constants:

$c_0=299792458~\mathrm{m/s}$ (speed of light)

Parameters (with default values):
step index fiber

$l = 10~\mathrm{km}$ (fiber length)

$R_s = 1~\mathrm{MBd}$ (symbol rate)

$n_\mathrm{c}=1.46$ (core)

$n_\mathrm{cl}=1.445$ (cladding)

$d=50~\mathrm{\mu m}$ (core diameter)

$\lambda=1550~\mathrm{nm}$ (wave length)

plastic optical fiber (POF)

$l = 100~\mathrm{m}$

$R_s = 200~\mathrm{MBd}$

$n_\mathrm{c}=1.49$

$n_\mathrm{cl}=1.4036$

$d=900~\mathrm{\mu m}$

$\lambda=800~\mathrm{nm}$

Formula [1]:

$A_\mathrm{N}=\sqrt{n_\mathrm{c}^2-n_\mathrm{cl}^2}$ (numerical aperture)

$\gamma_\mathrm{a,crit}=\arcsin A_\mathrm{N}$ (critical angle, air)

$\gamma_\mathrm{c,crit}=\arcsin \frac{\sin \gamma_\mathrm{a,crit}}{n_\mathrm{c}}$ (critical angle, core)

$\Delta t_{\mathrm{Mo}}= \frac{n_\mathrm{c}\cdot l}{c}(\frac{n_\mathrm{c}}{n_\mathrm{cl}}-1)$ (modal dispersion)

$V=\frac{d \pi}{\lambda}A_\mathrm{N}$ (structual parameter)

$M \approx 4(\frac{V}{\pi})^2$ (number of modes)

Assumption: Input power is equally distributed among the $M$ modes between $-\gamma_\mathrm{c,crit}$ and $\gamma_\mathrm{c,crit}$ . Fiber propagation delay of received signal neglected.

References:
[1] Schiffner, Gerhard: Optische Nachrichtentechnik. Teubner, 1. Auflage, 2005