Soliton Period

Author: the photonics expert Dr. Rüdiger Paschotta (RP)

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

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

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

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.

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

Case studies:

• Case Study: Numerical Experiments With Soliton Pulses in Fibers
• Case Study: Soliton Pulses in a Fiber Amplifier

Encyclopedia articles:

• solitons
• higher-order solitons
• adiabatic soliton compression

Questions and Comments from Users