Soliton (optics) - Effect of Power Losses

Effect of Power Losses

As we have seen, in order to create a soliton it is necessary to have the right power when it is generated. If there are no losses in the medium, then we know that the soliton will keep on propagating forever without changing shape (1st order) or changing its shape periodically (higher orders). Unfortunately any medium introduces losses, so the actual behavior of power will be in the form:

this is a serious problem for temporal solitons propagating in fibers for several kilometers. Let us consider what happens for the temporal soliton, generalization to the spatial ones is immediate. We have proved that the relationship between power and impulse length is:

if the power changes, the only thing that can change in the second part of the relationship is . if we add losses to the power and solve the relationship in terms of we get:

the width of the impulse grows exponentially to balance the losses! this relationship is true as long as the soliton exists, i.e. until this perturbation is small, so it must be otherwise we can not use the equations for solitons and we have to study standard linear dispersion. If we want to create a transmission system using optical fibers and solitons, we have to add optical amplifiers in order to limit the loss of power.