Modal Dispersion - Introduction
Demonstration of modal dispersion of a multi mode fiber (MMF).
Constants:
$c_0=299792458~\mathrm{m/s}$ (speed of light)
$c_0=299792458~\mathrm{m/s}$ (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)
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)
$\gamma_\mathrm{a,crit}=\arcsin A_\mathrm{N}$ (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)
$V=\frac{d \pi}{\lambda}A_\mathrm{N}$ (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