Encyclopedia … combined with a great Buyer's Guide!

# Soliton Period

Definition: the distance over which higher-order solitons reproduce their temporal and spectral shape

German: Solitonenperiode

Units: m

Formula symbol: <$z_\textrm{s}$>

Author:

Get citation code:

The soliton period is defined as the period with which higher-order soliton pulses evolve: after that propagation distance, they reproduce their original temporal and spectral shape.

The soliton period can be calculated according to

$${z_{\rm{s}}} \approx \frac{{\pi \;{{({\tau _{\rm{p}}}/1.7627)}^2}}}{{{\rm{2}}\left| {{\beta _2}} \right|}} \approx \frac{{{\tau _{\rm{p}}}^2}}{{{\rm{2}}\left| {{\beta _2}} \right|}}$$

where <$\tau_\textrm{p}$> is the pulse duration (full width at half-maximum, FWHM) and <$\beta_2$> is the group delay dispersion of the fiber (in s2/m).

Although fundamental solitons do not exhibit a periodic behavior, their soliton period is often calculated because it is related to the propagation distance over which nonlinear phase shifts become substantial. We can use the fundamental soliton equation

$${E_{\rm{p}}} = \frac{{2\left| {{\beta _2}} \right|}}{{\left| \gamma \right|\tau }}$$

in order to rewrite the equation for the soliton period of a fundamental soliton to

$${z_{\rm{s}}} = \frac{\pi }{{2\left| \gamma \right|{P_{\rm{p}}}}}$$

This shows that the nonlinear phase shift for the peak of that pulse in a non-dispersive fiber would be <$\pi / 2$>. The influence of chromatic dispersion is to obtain only a <$\pi / 4$> phase shift, but this for the whole soliton pulse and not only for its peak.

## Calculator for Soliton Period

 Pulse duration (FWHM): Group velocity dispersion: Soliton period: calc

Enter input values with units, where appropriate. After you have modified some inputs, click the “calc” button to recalculate the output.

In situations where solitons are periodically disturbed (e.g. in a soliton mode-locked laser or in an amplified optical fiber communications system), the effect of these disturbances depends strongly on the ratio of the period of the disturbances to the soliton period. If this ratio is well below unity (as is often the case in lasers), the solitons essentially experience just the average values of chromatic dispersion and Kerr nonlinearity, but for larger values of this ratio solitons can become unstable.

## More to Learn

Encyclopedia articles:

## Questions and Comments from Users

Here you can submit questions and comments. As far as they get accepted by the author, they will appear above this paragraph together with the author’s answer. The author will decide on acceptance based on certain criteria. Essentially, the issue must be of sufficiently broad interest.