Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

All-fiber passively mode-locked femtosecond laser using a 45º-tilted fiber grating polarization element

We report on the demonstration of an all-fiber femtosecond erbium doped fiber laser passively mode-locked using a 45º tilted fiber grating as an in-fiber polarizer in the laser cavity. The laser generates 600 fs pulses with output pulse energies ~1 nJ. Since the 45° tilted grating has a broad polarization response, the laser output has shown a tunabilty in wavelength from 1548 nm to 1562 nm by simply adjusting the polarization controllers in the cavity.

Dispersion-managed solitons in fibre systems and lasers

Nonlinear systems with periodic variations of nonlinearity and/or dispersion occur in a variety of physical problems and engineering applications. The mathematical concept of dispersion managed solitons already has made an impact on the development of fibre communications, optical signal processing and laser science. We overview here the field of the dispersion managed solitons starting from mathematical theories of Hamiltonian and dissipative systems and then discuss recent advances in practical implementation of this concept in fibre-optics and lasers.

Impact of third-order dispersion on the evolution of parabolic pulses

We present a perturbation analysis that describes the effect of third-order dispersion on the similariton pulse solution of the nonlinear Schrödinger equation in a fibre gain medium. The theoretical model predicts with sufficient accuracy the pulse structural changes induced, which are observed through direct numerical simulations.

Parabolic optical pulses under the action of the third-order dispersion

Recent developments in nonlinear optics reveal an interesting class of pulses with a parabolic intensity profile in the energy-containing core and a linear frequency chirp that can propagate in a fiber with normal group-velocity dispersion. Parabolic pulses propagate in a stable selfsimilar manner, holding certain relations (scaling) between pulse power, width, and chirp parameter. In the additional presence of linear amplification, they enjoy the remarkable property of representing a common asymptotic state (or attractor) for arbitrary initial conditions. Analytically, self-similar (SS) parabolic pulses can be found as asymptotic, approximate solutions of the nonlinear Schr¨odinger equation (NLSE) with gain in the semi-classical (largeamplitude/small-dispersion) limit. By analogy with the well-known stable dynamics of solitary waves - solitons, these SS parabolic pulses have come to be known as similaritons. In practical fiber systems, inherent third-order dispersion (TOD) in the fiber always introduces a certain degree of asymmetry in the structure of the propagating pulse, eventually leading to pulse break-up. To date, there is no analytic theory of parabolic pulses under the action of TOD. Here, we develop aWKB perturbation analysis that describes the effect of weak TOD on the parabolic pulse solution of the NLSE in a fiber gain medium. The induced perturbation in phase and amplitude can be found to any order. The theoretical model predicts with sufficient accuracy the pulse structural changes induced by TOD, which are observed through direct numerical NLSE simulations.

Effects of fourth-order fiber dispersion on ultrashort parabolic optical pulses in the normal dispersion regime

We propose a new method for the generation of both triangular-shaped optical pulses and flat-top, coherent supercontinuum spectra using the effect of fourth-order dispersion on parabolic pulses in a passive, normally dispersive highly nonlinear fiber. The pulse reshaping process is described qualitatively and is compared to numerical simulations.

Intra-cavity dynamics in high power mode-locked fiber lasers

A theoretical model allows for the characterization and optimization of the intra-cavity pulse evolutions in high-power fiber lasers. Multi-parameter analysis of laser performance can be made at a fraction of the computational cost. © 2010 Optical Society of America.

Dispersion and nonlinearity-management in mode-locked fibre lasers

In this work we extend theory of dispersion-managed (DM) solitons to dissipative systems with the main focus on applications in mode-locked lasers. In general, pulses in mode-locked fibre lasers experience both nonlinear and dispersion management per cavity round trip. In stretched-pulse lasers, this concept was utilized to obtain high energy pulses. Here we model the pulse propagation in a mode-locked fibre laser with a distributed nonlinear and DM Ginzburg-Landau type equation. We extend existing results on DM solitons and investigate the impact on soliton properties of dissipative perturbations that occur due to the effects of gain amplification, saturable absorption, and loss. In conclusion, in contrast to standard DM solitons in Hamiltonian systems, dissipative DM solitons do exist at high map strengths, thus opening a way for the generation of stable, short pulses with high energy.

New developments in the study of optical parabolic pulses in normally dispersive fibers

We report two recent studies dealing with the evolution of parabolic pulses in normally dispersive fibres. On the one hand, the nonlinear reshaping from a Gaussian intensity profile towards the asymptotic parabolic shape is experimentally investigated in a Raman amplifier. On the other hand, the significant impact of the fourth order dispersion on a passive propagation is theoretically discussed: we numerically demonstrate flat-top, coherent supercontinuum generation in an all-normal dispersion-flattened photonic crystal fiber. This shape is associated to a strong reshaping of the temporal profile what becomes triangular.

Dissipative nonlinear structures in optical fiber systems I:dissipative dispersion managed solitons in mode-locked lasers

In this first talk on dissipative structures in fiber applications, we extend theory of dispersion-managed solitons to dissipative systems with a focus on mode-locked fibre lasers. Dissipative structures exist at high map strengths leading to the generation of stable, short pulses with high energy. Two types of intra-map pulse evolutions are observed depending on the net cavity dispersion. These are characterized by a reduced model and semi-analytical solutions are obtained.

Dissipative nonlinear structures in optical fiber systems II:self-similar parabolic pulses in active fibers

In this second talk on dissipative structures in fiber applications, we overview theoretical aspects of the generation, evolution and characterization of self-similar parabolic-shaped pulses in fiber amplifier media. In particular, we present a perturbation analysis that describes the structural changes induced by third-order fiber dispersion on the parabolic pulse solution of the nonlinear Schrödinger equation with gain. Promising applications of parabolic pulses in optical signal post-processing and regeneration in communication systems are also discussed.