Pulses In Nonlinear Fibers Research Articles

Raman peak shifts due to walk-off in non-instantaneous Kerr media with higher-order effects

We study analytically and numerically the modulation instability (MI) of two incoherently co-propagating optical pulses in nonlinear fiber, taking into account high-order nonlinearity, walk-off effects, delay response time, and cross-phase modulation in several dispersion regimes. We show that higher-order nonlinearity is responsible for superposition of the secondary MI spectrum. We realize that there is a peak located in the emerged Raman band that we call “Raman peak” due to the combined effects of third-order dispersion, delay response time, and the opposite sign of the fourth-order dispersion parameter. These peaks are shifted toward higher frequencies when the walk-off increases.

Numerical methods for accurate description of ultrashort pulses in optical fibers

We consider a one-dimensional first-order nonlinear wave equation, the so-called forward Maxwell equation (FME), which applies to a few-cycle optical pulse propagating along a preferred direction in a nonlinear medium, e.g., ultrashort pulses in nonlinear fibers. The model is a good approximation to the standard second-order wave equation under assumption of weak nonlinearity and spatial homogeneity in the propagation direction. We compare FME to the commonly accepted generalized nonlinear Schrödinger equation, which quantifies the envelope of a quickly oscillating wave field based on the slowly varying envelope approximation. In our numerical example, we demonstrate that FME, in contrast to the envelope model, reveals new spectral lines when applied to few-cycle pulses. We analyze and compare pseudo-spectral numerical schemes employing symmetric splitting for both models. Finally, we adopt these schemes to a parallel computation and discuss scalability of the parallelization.

Combination and Compression of Multiple Optical Pulses in Nonlinear Fibers with the Exponentially Decreasing Dispersion

We propose a simple scheme to generate high-energy ultrashort pulses by combination and compression of multiple input pulses which share the same chirp profile. First, the multiple raised-cosine pulses in the input pulse train are modulated by a phase modulator, in which each modulation cycle covers two, three, four, or five pulses. Then, the modulated pulses are launched into a nonlinear fiber with the exponentially decreasing dispersion. We find that these pulses initially coalesce into a single pulse whose pulse profile is nearly hyperbolic secant, which then undergoes self-similar compression. Thus in the proposed method, first the combination of the multiple optical pulses occurs and then self-similar compression takes over. Besides, we also report the generation of ultrashort pulses by combination and compression of multiple hyperbolic secant pulses with the same chirp. The numerical results reveal that the resulting ultrashort pulse possesses a large portion of the input pulses for both raised-cosine and hyperbolic secant pulses. However, the compression factor and energy ratio are relatively higher for the hyperbolic secant pulses when compared with the raised-cosine pulses.

Ultrashort optical solitons in transparent nonlinear media with arbitrary dispersion

We consider the propagation of ultrashort optical pulses in nonlinear fibers and suggest a new theoretical framework for the description of pulse dynamics and exact characterization of solitary solutions. Our approach deals with a proper complex generalization of the nonlinear Maxwell equations and completely avoids the use of the slowly varying envelope approximation. The only essential restriction is that fiber dispersion does not favor both the so-called Cherenkov radiation, as well as the resonant generation of the third harmonics, as these effects destroy ultrashort solitons. Assuming that it is not the case, we derive a continuous family of solitary solutions connecting fundamental solitons to nearly single-cycle ultrashort ones for arbitrary anomalous dispersion and cubic nonlinearity.

Collisions of optical ultra-short vector pulses

Asymptotic two-pulse solutions of a modified (via attaching a nonlinear derivative term) vector nonlinear Schrödinger equation (MVNSE) are analyzed using the Hirota (bilinearization) method. This equation is known to describe the propagation of ultra-short optical pulses in nonlinear fibers (in particular, in the optical-crystal fibers). Some pulse-parameter regimes of applicability of the solutions to study the pulse collisions are estimated. It is found, for these regimes, that the collision of ultra-short vector pulses of almost equal velocities results in a transformation of their polarizations similar as that of the Manakov solitons whenever the pulse-interaction effects can be neglected.

Controlling soliton perturbations with phase-sensitive amplification

Short optical pulses in nonlinear fibers are susceptible to a variety of higher-order physical effects, including the Raman self-frequency shift and cubic and nonlinear dispersions. These effects directly modify pulse propagation and contribute to noise-induced phenomena such as the Gordon–Haus jitter. We show that phase-sensitive amplification, if used to compensate for loss, acts as a restoring force in frequency and compensates for the Raman self-frequency shift. Furthermore, phase-sensitive amplification controls the Gordon–Haus jitter, including the contributions of the Raman self-frequency shift and the third-order dispersion.