# How to calculate the dispersion parameter of a Fiber?

I am writing a presentation about DCF Fibers. From many articles i am reading, the dispersion parameter of Fibers are given. But it is not shown how it has been calculated.

For example ,in this sentence : Dispersion penalty for a 60 GHz signal over a fiber with D = 17 ps · nm -1 km-1.

the time ps, the lengths nm and km represent what ?

• https://paginas.fe.up.pt/~hsalgado/co/docs/phase_group_vel_dispersion.pdf

• https://www.researchgate.net/publication/329595254_Optimization_of_Hybrid_Fiber_Amplifier_Utilizing_Combined_Serial-Parallel_Configuration

• as far as i remember it is something not so simple. you should check a graduate level optics/photonics book, and corresponding chapter. – physshyp Dec 23 '18 at 14:54

## 1 Answer

The first paper you linked was pretty clear about how to calculate the dispersion penalty.

Dispersion penalty essentially quantifies the difference in arrival time of two similar frequencies:

Propagation speed in the fibre is given by the group velocity and will depend on frequency. The time for a wavepacket centered around a given frequency to travel down the wire is given by: $$τ = \frac{L}{V_g}$$ where $${V_g}$$ is the group velocity of that frequency.

We want to calculate the difference in this propagation time for two frequencies, To do so, simply take the change in group velocity per change in frequency, multiply it by the frequency difference of the two wavelengths, and work out the difference in their arrival time using these different group velocities.

This is done in (12) and (13) of the first paper.

So what do ps, km, and nm mean in “D = 17 ps · nm -1 km-1.” ?

Well that is simply the difference in arival time (ps) of two frequencies of light whose wavelengths differ by (nm) per (km) of optical fibre.

In terms of practical applications, a pulse of light will have a range of frequencies in it and you typically want to work out how much the wave packet smears out due to its component frequncies travelling at different speeds.

Hope this helps.