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.
Read more about this topic: Soliton (optics)
Famous quotes containing the words effect of, effect, power and/or losses:
“Reckoned physiologically, everything ugly weakens and afflicts man. It recalls decay, danger, impotence; he actually suffers a loss of energy in its presence. The effect of the ugly can be measured with a dynamometer. Whenever man feels in any way depressed, he senses the proximity of something “ugly.” His feeling of power, his will to power, his courage, his pride—they decline with the ugly, they increase with the beautiful.”
—Friedrich Nietzsche (1844–1900)
“What has been the effect of [religious] coercion? To make one half the world fools, and the other half hypocrites. To support roguery and error all over the earth.”
—Thomas Jefferson (1743–1826)
“We are expected to put the utmost energy, of every power that we have, into the service of our fellow men, never sparing ourselves, not condescending to think of what is going to happen to ourselves, but ready, if need be, to go to the utter length of self-sacrifice.”
—Woodrow Wilson (1856–1924)
“Hold back thy hours, dark Night, till we have done;
The Day will come too soon.
Young maids will curse thee, if thou steal’st away
And leav’st their losses open to the day.
Stay, stay, and hide
The blushes of the bride.”
—Francis Beaumont (1584-1616)