Four-wave mixing in wavelength-division-multiplexed soliton systems: damping and amplification

Abstract

Four-wave mixing in wavelength-division-multiplexed soliton systems with damping and amplification is studied. An analytical model is introduced that explains the dramatic growth of the four-wave terms. The model yields a resonance condition relating the soliton frequency and the amplifier distance. It correctly predicts all essential features regarding the resonant growth of the four-wave contributions.

Monotonic continuous-time random walks with drift and stochastic reset events

“…Recently, we have shown that energy dissipation of optical beams in a self-defocusing medium like an optical fiber with random inhomogeneities is also described in terms of a CTRW with a drift [39,40]; see also [41]. Typically, in such a situation signal's losses may be significant and may require the incorporation of periodic all-optical amplifiers [42] to upgrade the signal strength to the initial amplitude. Thus, in this context, the exogenous reset mechanism proposed here might be incorporated to the model in a natural way.…”

Importance Sampling for Dispersion-Managed Solitons

“…This implies σ 2 A = σ 2 k 1 /k 2 3 and σ 2 Φ = σ 2 k 2 /(k 3 A) 2 . Note that the constants, k 1 , k 2 , k 3 , depend on the map strength.…”

“…The Euler-Lagrange equation associated to this functional is trivially integrated to giveΩ = c σ 2 Ω , where c is an integration constant. Even though σ Ω depends on the A, it is independent of Ω, and therefore it is constant to first order in the perturbation expansion.…”

Exact analytical Helmholtz bright and dark solitons

“…As the interaction angle increases, the phase-sensitive terms become non-resonant and can be neglected in the analysis. Within a full NHE description, or that given by the NLS, their effect is to produce new spectral components in the interaction region that are reabsorbed by the propagating solitons after their collision [18]. NHEgoverned evolution of two interacting beams then reduces to two-coupled equations: whereby collision effects can be understood in terms of respective beam intensities.…”

“…We denote this as ∆ and define its meaning in Figure 3. It is important to note that, in a paraxial description, ∆ goes monotonically to zero as the interaction angle increases [18]. Figure 3 shows the geometry of Helmholtz soliton collisions in the absence of phasesensitive terms in the evolution equations; a clear symmetry arises in the problem when the interaction is dominated by the intensities of the beams.…”