Solitons in fibers with loss beyond small perturbation

Abstract

We consider the evolution of fiber-optic solitons in the presence of loss. Localized power reduction can be cast into a well-known form for which changes of all parameters are known explicitly. We proceed to a sequence of such perturbations with the same total loss, so that still all parameters are known, and eventually take the limit to infinitely many steps. This establishes the connection with distributed loss, and in the limit of vanishing loss reproduces the known results from perturbation theory. Outside this adiabatic limit the mechanism becomes clear that causes deviations: interference between solitons and radiation upsets the balance of dispersive and nonlinear effects characteristic of solitons; as one consequence the soliton continually sheds energy, which goes into radiation. We derive an expression for the radiation production rate in a lossy fiber, and predict quantitatively the distance until the soliton finally decays. Our approach provides quantitative results for fibers with loss small or strong, localized or distributed, and numerical results confirm predictions. It can be generalized to gain rather than loss.

Impact of fiber loss on two-soliton states: Substantial changes in eigenvalue spectrum

“…[13]; in Ref. [12] the energy was attenuated by so that M = √ ). For each ξ we vary M and apply numerical the direct scattering transform [18] to calculate the soliton content of the resulting pulse Mu(ξ, τ ).…”

“…[6][7][8][9][10][11]), which is applicable only to small perturbations. We have recently described how loss of arbitrary strength can be treated up to and including the assessment of soliton annihilation [12]; and meanwhile we have generalized this approach to amplifying fibers, including the generation of new solitons [13].…”

On the Creation of Solitons in Amplifying Optical Fibers

“…By varying for the best match of both evolutions we find = 0.42 [12]. We now proceed by considering a pulse amplitude that is not vanishingly small.…”

“…We could recently demonstrate [12] that SY can be used to cover lossy fiber by interpreting continuous loss as a sequence of infinitely many infinitesimal localized losses, each of which can be treated by SY. It became clear, among other things, what the mechanism for the eventual death of a soliton is.…”

Study on soliton pulse and its characteristics for fiber optic communication

“…Very recently, the development of optical fiber fabrication techniques that suppress the water absorption peak in the 1400nm wavelength region improves the possibility of massive wavelength-division multiplexing across the whole wavelength range to from 1200 to 1600nm. [17]. Increasing the number of channels and increasing the single channel bit rate are the two complementary methods to have a tremendous increase in the capacity.…”