Solitons: Lower Dispersion, Stronger Dispersive Effects!
Posted on 2008-04-02 as a part of the Photonics Spotlight (available as e-mail newsletter!)
Permanent link: https://www.rp-photonics.com/spotlight_2008_04_02.html
Abstract: At a first glance, it seems that the balance between dispersive and nonlinear effects in a soliton pulse cannot be maintained e.g. when the fiber dispersion is reduced to one half the original value. A closer inspection shows that this is not the case.
Ref.: encyclopedia articles 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 in 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.
This article is a posting of the Photonics Spotlight, authored by Dr. Rüdiger Paschotta. You may link to this page and cite it, because its location is permanent. See also the RP Photonics Encyclopedia.
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