Soliton (optics) - Dark Solitons

Dark Solitons

In the analysis of both types of solitons we have assumed particular conditions about the medium:

• in spatial solitons, that means the self-phase modulation causes self-focusing
• in temporal solitons, or, anomalous dispersion

Is it possible to obtain solitons if those conditions are not verified? if we assume or, we get the following differential equation (it has the same form in both cases, we will use only the notation of the temporal soliton):

This equation has soliton-like solutions. For the first order (N=1):

The plot of is shown in the picture on the right. For higher order solitons we can use the following closed form expression:

It is a soliton, in the sense that it propagates without changing its shape, but it is not made by a normal pulse; rather, it is a lack of energy in a continuous time beam. The intensity is constant, but for a short time during which it jumps to zero and back again, thus generating a "dark pulse"'. Those solitons can actually be generated introducing short dark pulses in much longer standard pulses. Dark solitons are more difficult to handle than standard solitons, but they have shown to be more stable and robust to losses.