Equilibrium and nonequilibrium solitons in a lossy split-step system with lumped amplification

We propose a more realistic version of the recently introduced split-step model (SSM), which consists of periodically alternating dispersive and nonlinear segments, by adding uniformly distributed loss and lumped gain to it. In the case when the loss is exactly balanced by gain, a family of stable equilibrium solitons (ESs) is found. Unless the system's period L is very small, saturation is observed in the dependence of the amplitude of the established ES vs. that of the initial pulse. Stable nonequilibrium solitons (NESs) are found in the case when the gain slightly exceeds (by up to 3%) the value necessary to balance the loss. The existence of NESs is possible as the excessive energy pump is offset by permanent radiation loss, which is confirmed by computation of the corresponding Poynting vector. Unlike ESs that form a continuous family of solutions, NES is an isolated solution, which disappears in the limit of small L, i.e., it cannot be found in the overpumped nonlinear Schroedinger equation. Interactions between ESs turn out to be essentially the same as in SSM without loss and gain, while interactions between NESs are different: two NESs perturb each other by the radiation jets emanating from them, even if they are separated by a large distance. Moving NESs survive collisions, changing their velocities.Comment: a latex text file and seven jpg figure files. Physics Letter A, in pres

Criteria for selecting children for speech therapy in the public schools

Thesis (Ed.M.)--Boston Universit

Accelerated rogue waves generated by soliton fusion at the advanced stage of supercontinuum formation in photonic crystal fibers

Soliton fusion is a fascinating and delicate phenomenon that manifests itself in optical fibers in case of interaction between co-propagating solitons with small temporal and wavelengths separation. We show that the mechanism of acceleration of trailing soliton by dispersive waves radiated from the preceding one provides necessary conditions for soliton fusion at the advanced stage of supercontinuum generation in photonic crystal fibers. As a result of fusion large intensity robust light structures arise and propagate over significant distances. In presence of small random noise the delicate condition for the effective fusion between solitons can easily be broken, making the fusion induced giant waves a rare statistical event. Thus oblong-shaped giant accelerated waves become excellent candidates for optical rogue waves.Comment: Optics Letters Journal. In pres