Solitons: Lower Dispersion, Stronger Dispersive Effects!

Posted on 2008-04-02. Permanent link: http://www.rp-photonics.com/spotlight_2008_04_02.html

Ref.: encyclopedia article on solitons

Soliton pulses (propagating e.g. in an optical fiber) exhibit a situation where the effects of the Kerr nonlinearity and of chromatic dispersion essentially cancel each other. It is instructive to consider one aspect which may seem quite surprising: if the dispersion of the fiber is reduced while the pulse energy stays unchanged, the pulse duration is reduced and the peak power increases. Therefore, nonlinear effects become stronger. But how can then the balance of nonlinear and dispersive effects stay in place? After all, we have less dispersion but stronger nonlinear effects!

The resolution of this conundrum is obtained by considering what exactly determines how strong dispersive effects are. It turns out that it is not just the magnitude of dispersion, but also the pulse bandwidth. For example, if we reduce the fiber dispersion by one half (while maintaining the pulse energy), the pulse bandwidth doubles. As changes of the spectral phase are proportional to the dispersion times the square of the frequency offset from the center optical frequency of the pulse, the phase shifts within the pulse spectrum scale with the magnitude of dispersion times the square of the pulse bandwidth. In our example, overall the strength of dispersive effects is doubled, and this is exactly what we need to compensate the doubled nonlinear effects resulting from the doubled peak power.