Nonlinearity measurement undergoing dispersion and loss

Abstract

Accurate knowledge of the nonlinear coefficient is extremely important to make reliable predictions about optical pulses propagating along waveguides. Nevertheless, determining this parameter when dispersion and loss are as important as nonlinear effects brings both theoretical and experimental challenges that have not yet been solved. A general method for measuring the nonlinear coefficient of waveguides under these demanding conditions is here derived and demonstrated experimentally in a kilometer-long standard silica fiber pumped close to 2 µm.

Soliton-number measurement in lossy waveguides

“…2(b), corresponding to the first iteration. This value already agrees with β 2 /γ = −110±6 ps 2 W obtained using β 2 = 75±4 ps 2 km −1 , which we directly measured using a standard method [8], and γ = 0.68 ± 0.06 W −1 km −1 , which we calculated numerically based on the experimental γ value at 1.55 µm [5]. No more iterations were carried out since the experimental errors due to the relatively small ∆ values produced in this proof of concept set the attainable accuracy.…”

“…where 0 < < L, with L being the output distance, ∆ = e αL ρ(L) − ρ(0), and ∆µ 2 = µ 2 (L) − µ 2 (0) [8]. When losses are negligible, Eq.…”

“…where η is a fitting parameter, ρ 0 = ρ(0) and µ 2,0 = µ 2 (0) [8], which will allow determining , and thus β 2 /γ, as follows. For each ρ 0 and µ 2,0 values, η will be fitted so that Eq.…”

“…Let us consider 90 ps long sech pulses propagating 1.16 km along a fiber with α = 2.5×10 −3 m −1 , thus αL ∼ 3, β 2 = −75 ps 2 km −1 and γ = 0.68 W −1 km −1 . These parameters correspond to a SMF28e+ fiber at 1.951 µm [8]. To check the proposal numerically, Eq.…”

“…The spectra and temporal pulses were measured using an OSA and a digital sampling oscilloscope together with a 2 µm InGaAs photodetector, respectively. A variable optical attenuator was employed to fix the operation of the PM amplifier and select input peak powers between 14 W and 37 W [8].…”