Self-similar Parabolic Pulses Research Articles

Spatiotemporal dynamics of self-similar parabolic pulse evolution in multimode fibers

In this paper, we have investigated for the first time, the spatiotemporal dynamics of self-similar parabolic pulse evolution in multimode fibers. Two types of fiber are considered, graded-index and step-index MMFs. For the quality of the generated parabolic pulse, the mismatch parameter is used. A thorough study of the evolution of the pulse parameters as a function of the initial parameters has been carried out. As a result, the initial pulse evolved into a linearly chirped pulse with a parabolic intensity shape in both fibers, under the predominantly excitation of the fundamental mode. It has been shown, in particular, that the pulse can be compressed to a temporal duration of about 40 fs. Moreover, a spatiotemporal nonlinear dynamic, beam auto-selection, of one specific mode, is investigated through graded-index MMF, under the different initial modes excitation. The parabolic pulse formation process plays a critical role in this nonlinear dynamic. This approach provides another framework to understand the complex nonlinear dynamics in MMFs.

Modelling self-similar parabolic pulses in optical fibres with a neural network

We expand our previous analysis of nonlinear pulse shaping in optical fibres using machine learning [Opt. Laser Technol., 131 (2020) 106439] to the case of pulse propagation in the presence of gain/loss, with a special focus on the generation of self-similar parabolic pulses. We use a supervised feedforward neural network paradigm to solve the direct and inverse problems relating to the pulse shaping, bypassing the need for direct numerical solution of the governing propagation model.

Toward Self-Similar Propagation of Optical Pulses in a Dispersion Tailored, Nonlinear, and Segmented Bragg-Fiber at 2.8 $\mu$m

We demonstrate self-similar stable propagation of parabolic optical pulses through a highly nonlinear specialty Bragg fiber at 2.8 $\mu$ m by a numerical approach. To obtain such propagation characteristics over a longer length of a Bragg fiber, we propose and verify a fiber design scheme that underpins passive introduction of a rapidly varying group-velocity dispersion around its zero dispersion wavelength and modulated nonlinear profile through suitable variation in its diameter. To implement the proposed scheme, we design a segmented and tapered chalcogenide Bragg fiber in which a Gaussian pulse is fed. Transformation of such a launched pulse to a self-similar parabolic pulse with full-width-at-half-maxima of 4.12 ps and energy of $\sim$ 39 pJ is obtained at the output. Furthermore, a linear chirp spanning across the entire pulse duration and 3 dB spectral broadening of about 38 nm at the output are reported. In principle, the proposed scheme could be implemented in any chosen set of materials.

Study of parabolic self-similar optical pulse generation in single mode fibers using variational approximation for the LP01 mode

A number of single and two parameter variational approximations for the LP01 mode are reported in the literature which has been used to compute the various propagation characteristic parameters, such as, propagation constant, normalised dispersion, splice loss, bending loss etc. for single mode fibers. These studies are limited to optically linear fibers. To our knowledge, these variational approximations have not been used to study the nonlinear optical processes in such fibers. In the present work, using these variational approximations, the generation of self-similar parabolic pulses in graded-index single mode normal dispersive active fibers has been studied. The optimum length Lopt of the fiber, after which an input Gaussian pulse turns into a self-similar parabolic pulse, has been computed and the accuracies obtained from these variational approximations have been compared.

Generation of the self-similar parabolic pulses by designing comb-like profiled dispersion fiber based on alternately arranged single-mode fibers and dispersion-shifted fibers

Based on the nonlinear Schrödinger equation and the linearly chirped parabolic pulse generation in the dispersion decreasing fiber with normal dispersion, a novel scheme for the generation of the self-similar parabolic pulse via a comb-like profiled dispersion fiber with normal group-velocity dispersion has been proposed and the corresponding model is established. We study, analytically and numerically, the evolution of the self-similar parabolic pulse in comb-like profiled dispersion fiber with dispersion profile close to that of the dispersion decreasing fiber, and the influence of different initial energies and pulse widths on the linearly chirped parabolic pulse formation in the comb-like profiled dispersion fiber. The results show that the evolution of the self-similar parabolic pulses can realized in the comb-like profiled dispersion fiber, the results of which are in good agreement with these of the dispersion decreasing fiber, and the best-matched scheme of designing and optimizing comb-like profiled dispersion fiber will help to obtain the ideal similaritons.

Distortion of parabolic pulse due to higher-order effects in a dispersion-decreasing fiber

Considering Third-order Dispersion (TOD) and Stimulated Raman Scattering effect (SRS) simultaneously, the properties of the self-similar parabolic pulse evolution in a dispersion-decreasing optical fiber with normal group-velocity dispersion are firstly investigated in our paper. Our results show that parabolic pulses are distorted and the characteristic of exactly self-similarity will be lost due to the High-order effects. When only the TOD is taken into account, the chirp still reveals highly linear but glows into asymmetric which causes the waveform appearing optical wave breaking. When only considering SRS, the pulse still reveals highly linear chirp only linearity range narrow down, resulting in delaying the self-similar evolution. When considering SRS and TOD simultaneously, parabolic pulses are distorted less and the characteristic of exactly self-similarity will be better due to SRS effect than only considering TOD effect. The highly linear chirp in optical pulse still allows for efficient and high-quality pulse compression by use of dispersion compensation technique.

Generation of excellent self-similar pulses in a dispersion-decreasing fiber

Pulses compression has been widely studied for a long time. In order to generate excellent self-similar pulses in a dispersion-decreasing optical fiber with normal group-velocity dispersion, the influence of initial pulse parameters on the properties of the self-similar parabolic pulses interaction are firstly investigated in the paper. We find that the phase of sinusoidal fit and asymptotic dark soliton change according to the changing of initial phase difference. Meanwhile, increasing the full-width at half-maximum and input energy or decreasing time-delay properly, the interaction between self-similar pulses enhances accordingly, which makes the interaction length shorter and reduce the lose of energy, resulting in high energy output. The results are beneficial in experimental studies by adjusting the initial parameters of pulses to generate high-quality self-similar pulse. It is important for Dense Wavelength Division Multiplexing (DWDM) transmission system which is in heavy demands of light source in wide-range wavelength.

Efficient dispersion tailoring by designing alternately arranged dispersion compensating fibers and fiber amplifiers to create self-similar parabolic pulses

The parabolic similariton pulse formation by alternate arrangements of passive and active dispersion compensating fibers (DCFs) is presented here. These combinations of passive and active DCFs with constant core radii and constant nonlinearities are suggested as equivalent profiles of a dispersion tailored fiber amplifier in normal dispersion regime. The dispersion tailored fibers, usually known as dispersion decreasing fibers (DDFs) in normal dispersion regime, are capable of producing linearly chirped parabolic self-similar pulses. The DDF is designed and optimized with proper choice of fiber parameters so that considerable variation of nonlinearity can be achieved, which in turn enhances the effective gain coefficient of the fiber. Inclusion of this nonlinear variation along the DDF amplifier length leads to obtain the simulated output pulses with very small misfit parameters with respect to perfect parabolic pulse at sufficiently reduced optimum length. At the same time to avoid the fabrication difficulties of the DDF, the alternately arranged passive and active DCFs are suggested as suitable alternatives of the DDF. The performances of the cascaded systems for generation of self-similar parabolic pulses are compared with that of the DDF amplifier as well as combined systems consisting of DCFs with equal gain. The results show that the proposed alternately arranged cascaded system with less pumping requirements, are efficient enough to produce similar parabolic pulses as compared to the previously designed DDF, even when considerable amount of splice loss at each joint is included.

All-fiber ring Raman laser generating parabolic pulses

We present theoretical and numerical results for an all-fiber laser using self-similar parabolic pulses (``similaritons'') designed to operate using self-similar propagation regimes. The similariton laser features a frequency filter and a Sagnac loop which operate together to generate an integrated all-fiber mode-locked laser. Numerical studies show that this laser generates parabolic pulses with linear chirp in good agreement with analytical predictions. The period for propagating similariton pulses in stable regimes can vary from one to two round trips for different laser parameters. Two-round-trip-period operation in the mode-locked laser appears at bifurcation points for certain cavity parameters. The stability of the similariton regimes has been confirmed by numerical simulations for large numbers of round trips.

A Bragg-like chirped clad all-solid microstructured optical fiber with ultra-wide bandwidth for short pulse delivery and pulse reshaping

Chirped cladding is proposed as a novel tailoring tool to simultaneously attain wider transmission window and reduced temporal dispersion in an all-solid Bragg-like microstructured optical fiber as compared to its perfectly periodic cladding counterpart. This design route for photonic bandgap microstructured fibers could be exploited as an additional degree of freedom for bandgap engineering. A suitably chirped clad fiber could be gainfully exploited to deliver femto-second pulse with ultra wide bandwidth. Further, generation of self-similar parabolic profile pulse is demonstrated by simulating propagation of an input Gaussian pulse through a 2 m long sample of such a linearly tapered Bragg like fiber.

Generation of Self-Similar Parabolic Pulses by Designing Normal Dispersion Decreasing Fiber Amplifier as Well as Its Staircase Substitutes

Generation of self-similar parabolic pulse is analytically and numerically demonstrated by designing parabolic index normal dispersion decreasing fiber (NDDF) amplifiers. The pulse transmission is extensively studied for NDDFs in presence of physical gain as well as virtual gain induced by two different dispersion profiles corresponding to two different physical gain coefficients. Here, we introduce the virtual gain arising from the unavoidable spatial nonlinear variation, which helps to obtain the self-similar parabolic pulses at smaller optimum length in comparison to NDDF with constant nonlinearity. The output power profiles resemble with a perfect parabolic shape giving rise to self-similar pulses with very small misfit parameters. Pulse propagation in presence of spatial gain variation is also studied. To avoid fabrication difficulties, we propose equivalent staircase dispersion profiles consisting of a number of constant dispersion fibers (CDFs), which are simple to manufacture and show performances excellently close to that of the proposed NDDF.

Interaction between parabolic pulses in a dispersion-decreasing fiber

The properties of the self-similar parabolic pulses interaction in a dispersion-decreasing optical fiber with normal group-velocity dispersion are firstly investigated in our paper. We find that two parabolic pulses separated by a time-delay create oscillation with a sinusoidal fit at the beginning of their overlap, and then further evolve into a train of asymptotic dark solitons. Additionally, outside the overlap regime, the evolution is equal to a single pulse’ propagating behavior. The chirp after interaction in the parabolic pulses still allows for efficient and high-quality pulse compression.

Self-similar parabolic pulses in optical fiber amplifiers with gain dispersion and gain saturation

The generation and propagation of an asymptotic parabolic pulse in an optical fiber amplifier with the gain dispersion effect and gain saturation effect is studied. It is found that initial input pulses with small amplitudes and widths can evolve into self-similar pulses at the asymptotic limit. The central region of the self-similar pulse is described by the invert parabola, and its width and power increase linearly, but with its peak amplitude and the width of its spectrum, remain constant. The parameter region for the existence of the parabolic pulse is given.

Dispersion managed self-similar parabolic pulses

We describe the propagation of a parabolic self-similar pulse in an anomalous dispersive nonlinear fibre. Given the capacity of a linearly chirped parabolic pulse to retain its typical shape over a short propagation distance, we introduce the concept of dispersion managed self-similar pulses and outline potential benefits in terms of spectral broadening enhancement.

Analytic theory of self-similar mode-locking

A theoretical model is developed to quantify the experimental observations of self-similar parabolic pulses in a mode-locked laser cavity with net-zero dispersion. The averaging procedure used shows the pulse amplitude to be governed by the porous media equation that has the well-known Barenblatt similarity (parabolic) solution, suggesting that it is a viable theoretical description of temporal profiles observed in mode-locked cavities. To the best of our knowledge, this is the first analytic model proposing a mechanism responsible for generating temporal parabolic pulses.

Higher-order effects on self-similar parabolic pulse in the microstructured fibre amplifier

By considering higher-order effects, the properties of self-similar parabolic pulses propagating in the microstructured fibre amplifier with a normal group-velocity dispersion have been investigated. The numerical results indicate that the higher-order effects can badly distort self-similar parabolic pulse shape and optical spectrum, and at the same time the peak shift and oscillation appear, while the pulse still reveals highly linear chirp but grows into asymmetry. The influence of different higher-order effects on self-similar parabolic pulse propagation has been analysed. It shows that the self-steepening plays a more important role. We can manipulate the geometrical parameters of the microstructured fibre amplifier to gain a suitable dispersion and nonlinearity coefficient which will keep high-quality self-similar parabolic pulse propagation. These results are significant for the further study of self-similar parabolic pulse propagation.

Spectral compression of optical parabolic similaritons

We numerically investigate the spectral recompression experienced by a self-similar parabolic pulse with an anormal initial chirp. Spectral compression factors above 10 and high-quality output pulses can be predicted.

Regenerative 40?Gbit?s wavelength converter based on similariton generation

We present an all-optical regeneration technique based on spectral filtering of self-similar parabolic pulses (similaritons). In particular, we demonstrate numerically and experimentally that ghost pulses, which occur in the zero bit slots of telecommunication pulse trains, can be effectively suppressed. These results are obtained with a 40 Gbit/s pulse train.