Estimation of the fourth-order dispersion coefficient \beta4

Abstract

The fourth-order dispersion coefficient of fibers are estimated by the iterations around the third-order dispersion and the high-order nonlinear items in the nonlinear Schordinger equation solved by Green's function approach. Our theoretical evaluation demonstrates that the fourth-order dispersion coefficient slightly varies with distance. The fibers also record β4 values of about 0.002, 0.003, and 0.00032 ps 4 /km for SMF, NZDSF and DCF, respectively. In the zero-dispersion regime, the high-order nonlinear effect (higher than self-steepening) has a strong impact on the transmitted short pulse. This red-shifts accelerates the symmetrical split of the pulse, although this effect is degraded rapidly with the increase of β2. Thus, the contributions to β4 of SMF, NZDSF, and DCF can be neglected.OCIS The determination of the fourth-order dispersion coefficient is important to various applications, such as super-continuum generation [1] , generation and transmission of new regime solitons [2] , and broadband parametric amplification [1] , among others. In ultra-high speed optical communications (femtosecond pulses), there is a need to clarify the general nature of pulse broadening induced by dispersion orders higher than three [3] , because even the residual fourth-order dispersion (e.g., small dispersion) causes significant broadening in extremely short pulses [4] . The analytical expressions that describe pulse shape (i.e., Gaussian pulse and interference) at the receiver in the presence of nth order dispersion have been reported in Ref. [5].Chromatic dispersion (CD) is determined by taking advantage of the interplay between dispersion and nonlinear effects, such as measuring the parametric four-wave mixing (FWM) conversion efficiency [6] or the modulation instability (MI) sidebands [7] . Both methods fundamentally rely on phase-matching condition that, in turn, depends on the dispersion coefficients and pump power; thus, the pump power should be high (>1 W) to achieve parametric amplification [8] . A method has been proposed to measure β 4 using a low-power tunable laser and low-power amplified spontaneous emission (ASE) noise source, which directly provides the ratio of β 3 /β [9] 4 . Scaling the MI emitted by soliton fission in the normal dispersion regime facilitates the retrieval of the fourth-order dispersion coefficient [10] . The FWM method for short, highly nonlinear fibers has been introduced and validated experimentally [11] . This method measures ultra-low values of the fourth-order dispersion coefficient.This letter presents a theoretical estimation of the fourth-order dispersion coefficient, which is based on the iteration method related to high-order dispersion and nonlinear items as well as the Green function solution of nonlinear Schordinger equation (NLSE). The values of β 4 slightly vary with the distance in some experiment results, but this estimation does not require pulse power and fiber parameters. The high-order nonlinear effect that is higher than self-steepening does not generate distinct i...