arXiv subjects

Rodislav Driben

Publications and source records attributed to Rodislav Driben.

20 records · Page 2Linked to original sources

arXiv2002

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.

nlin.PS↗

arXiv2000

Split-step solitons

We consider a long fiber-optical link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM), in which the dispersion and nonlinearity are completely separated. Passage of a soliton through one cell of the link is described by an analytically derived map. Numerical iterations of the map reveal that, at values of the system's stepsize (cell's size) L comparable to the pulse's dispersion length, SSM supports stable pulses which almost exactly coincide with fundamental solitons of the averaged NLS equation. However, in contrast with the NLS equation, the SSM soliton is a strong attractor, i.e., a perturbed soliton rapidly relaxes to it, emitting some radiation. A pulse whose initial amplitude is too large splits into two solitons; splitting can be suppressed by appropriately chirping the initial pulse. If the initial amplitude is too small, the pulse turns into a breather, and, below a certain threshold, it quickly decays into radiation. If L is essentially larger than the soliton's dispersion length, the soliton rapidly rearranges itself into another soliton, with nearly the same area but essentially smaller energy. At L still larger, the pulse becomes unstable, with a complex system of stability windows found inside the unstable region. Moving solitons are generated by lending them a frequency shift, which makes it possible to consider collisions between solitons.

nlin.PS↗