Parabolic Pulses Research Articles

Efficient femtosecond pulse generation using a parabolic amplifier combined with a pulse compressor I Stimulated Raman-scattering effects

The effects of stimulated Raman scattering on femtosecond pulse generation using a parabolic amplifier and a grating-pair compressor are presented. We derive an explicit analytical form for the Stokes pulse evolution. We find that the evolution of the Stokes pulse can be divided into four regimes; small Gaussian Stokes pulse, small asymmetric Stokes pulse, signal depletion, and parabolic Raman pulse. To achieve efficient pulse compression, one should operate the parabolic amplifier in the small Stokes pulse regime where the signal pulse is not seriously distorted. We also derive an analytical expression to obtain a critical fiber length for the small Stokes pulse regime. The derived theory is applied to a realistic high-power femtosecond pulse generation process through a split-step Fourier numerical simulation. The pulse compression results confirm that our derived critical fiber length leads to the highest peak power and shortest width of compressed pulse.

Generation of parabolic bound pulses from a Yb-fiber laser

We report the observation of self-similar propagation of bound-state pulses in an ytterbium-doped double-clad fiber laser. A bound state of two positively chirped parabolic pulses with 5.4 ps duration separated by 14.9 ps is obtained, with 1.7 nJ of energy per pulse. These pulses are extra-cavity compressed to 100 fs. For higher pumping power and a different setting of the intra-cavity polarization controllers, the laser generates a bound state of three chirped parabolic pulses with different time separations and more than 1.5 nJ energy per pulse. Perturbation of this bound state by decreasing pump power results in the generation of a single pulse and a two-pulse bound state both structures traveling at the same velocity along the cavity. A possible explanation of the zero relative speed by a particular phase relation of the bound states is discussed.

High-power, high repetition rate picosecond and femtosecond sources based on Yb-doped fiber amplification of VECSELs

Picosecond pulses at gigahertz repetition rates from two different passively mode-locked VECSELs are amplified to high powers in cascaded ytterbium doped fiber amplifiers. Small differences in pulse durations between the two VECSELs led to amplification in different nonlinear regimes. The shorter 0.5 ps pulses could be amplified to 53 W of average power in the parabolic pulse regime. This was confirmed by excellent pulse compression down to 110 fs. The VECSEL producing longer 4.6 ps pulses was amplified in an SPM dominated regime up to 200 W of average power but with poor recompressed pulse quality.

Efficient femtosecond pulse generation using a parabolic amplifier combined with a pulse compressor II Finite gain-bandwidth effect

A derivation of an analytical expression for the propagation of a parabolic pulse in an optical fiber amplifier with a finite Lorentzian gain bandwidth is presented. Through a separation of variables combined with the method of stationary phase, we derive equations in both time and frequency spaces to obtain the analytical solution. This results in a compact analytical form that has a number of physical meanings. It shows that the finite gain bandwidth seriously limits the performance of parabolic amplification by distorting both the chirp and the frequency envelope, thus preventing efficient pulse compression required for high-power femtosecond pulse generation. The validity of the analytical derivation is verified through numerical simulations using the split-step Fourier method, showing an excellent agreement with the derived analytical solution, in pulse shape, chirp, and the optical spectrum.

Generation of 20-GHz picosecond pulse trains in the normal and anomalous dispersion regimes of optical fibers

In this paper, we numerically and experimentally study two methods to generate 20-GHz pulse trains at 1550nm from a dual-frequency beat-signal. The first method is based on the multiple four-wave mixing temporal compression occurring in the anomalous dispersion regime of a standard optical fiber (SMF). In the second original method, the initial sinusoidal signal is first converted into a parabolic pulses train through nonlinear propagation in a normally dispersive fiber. A subsequent linear compression in an anomalous dispersive fiber leads to well-separated picosecond pulses.

Self-similar evolutions of parabolic, Hermite-Gaussian, and hybrid optical pulses: Universality and diversity

Three novel types of self-similar solutions, termed parabolic, Hermite-Gaussian, and hybrid pulses, of the generalized nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption are obtained. The properties of the self-similar evolutions in various nonlinear media are confirmed by numerical simulations. Despite the diversity of their formations, these self-similar pulses exhibit many universal features which can facilitate significantly the achievement of well-defined linearly chirped output pulses from an optical fiber, an amplifier, or an absorption medium, under certain parametric conditions. The other intrinsic characteristics of each type of self-similar pulses are also discussed.

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.

Self-similar parabolic beam generation and propagation

The (1+1) -dimensional and (2+1) -dimensional amplified nonlinear Schrödinger equations incorporating diffraction, Kerr nonlinearity, and gain are solved analytically and numerically. An asymptotic solution is found corresponding to self-similar propagation of a beam with parabolic amplitude and phase profiles. While the (1+1) -dimensional solution is directly analogous to parabolic pulse propagation in nonlinear dispersive media, the existence of self-similar propagation in (2+1) dimensions is a nontrivial question, given that spatial solitons are unstable in bulk media with nonsaturating nonlinearities. We show that self-similar parabolic beams are possible in such media with gain and a negative nonlinear index.

Intermediate asymptotic evolution and photonic bandgap fiber compression of optical similaritons around 1550 nm

We report the complete characterization of the self-similar scaling of parabolic pulse similaritons in an optical fiber amplifier. High dynamic range frequency resolved optical gating allows the direct observation of the evolution of a hyperbolic secant-like input pulse to an asymptotic amplifier similariton, and reveals the presence of intermediate asymptotic wings about the parabolic pulse core. These results are used to optimize additional self-similar propagation in highly-nonlinear fiber and subsequent compression in hollow-core photonic bandgap fiber.

Interaction between optical parabolic pulses in a Raman fiber amplifier

We investigate the interaction between optical parabolic pulses in a Raman fiber amplifier. Self-similar amplification of two identical time-delayed pulses creates an oscillation which further evolves into a train of dark solitons through the combined effects of non-linearity, normal dispersion and adiabatic Raman gain. Theoretical predictions are in good agreement with experimental results.

Dependence of parabolic pulse amplification on stimulated Raman scattering and gain bandwidth

An analytical model has been developed and verified by numerical simulations to determine limits induced by stimulated Raman scattering (SRS) on parabolic pulse evolution in high-power, high-energy Yb-fiber amplifiers. Our results show that the maximum achievable parabolic pulse energies are limited by SRS at low amplifier gains and by the finite gain bandwidth at high gains. Therefore, an optimum gain value exists that maximizes the achievable output pulse energy.

Asymptotic characteristics of parabolic similariton pulses in optical fiber amplifiers

The fundamental asymptotic nature of parabolic similariton pulses in normal-dispersion fiber amplifiers is experimentally demonstrated. With frequency-resolved optical gating characterization measurements with a fixed input pulse energy, the output parabolic pulse characteristics are shown to be invariant with the input pulse profile and duration and to be completely determined only by the amplifier parameters.

Numerical and experimental study of parabolic pulses generated via Raman amplification in standard optical fibers

Parabolic pulse generation by Raman amplification has been numerically and experimentally investigated around 1550 nm using a standard normally dispersive nonzero dispersion shifted fiber (NZ-DSF). The output pulses, characterized in intensity and phase using frequency-resolved optical gating, exhibit parabolic features in good agreement with numerical simulations based on two coupled extended nonlinear Schro/spl uml/dinger equations. The influence of the energy and duration of the input pulse has been studied. The ability of the parabolic pulses to propagate self-similarly during additional propagation over 800 m of NZ-DSF has also been demonstrated.

Self-similar evolution of parabolic pulses in a laser.

Self-similar propagation of ultrashort, parabolic pulses in a laser resonator is observed theoretically and experimentally. This constitutes a new type of pulse shaping in mode-locked lasers: in contrast to the well-known static (solitonlike) and breathing (dispersion-managed soliton) pulse evolutions, asymptotic solutions to the nonlinear wave equation that governs pulse propagation in most of the laser cavity are observed. Stable self-similar pulses exist with energies much greater than can be tolerated in solitonlike pulse shaping, and this has implications for practical lasers.

Parabolic pulse generation by use of a dispersion-decreasing fiber with normal group-velocity dispersion.

We propose a new method for generating a parabolic pulse by use of a dispersion-decreasing fiber with normal group-velocity dispersion. When a hyperbolic dispersion-decreasing structure is employed, the pulse evolves into a linearly chirped pulse with an exact parabolic intensity profile without radiating dispersive waves. The highly linear chirp in the parabolic pulse allows for efficient and high-quality pulse compression.

Linear dynamical systems under random trains of non-overlapping, arbitrary-shape pulses: generalized approach

The excitation considered is a train of non-overlapping pulses, defined as a train of alternate random pulse durations and time gaps between the consecutive pulses. The time gaps and durations are assumed to be independent, continuous random variables. In this model the pulses are not only non-overlapping, but they are also non-adjoining, i.e. they can only adjoin with probability zero. All durations are assumed to be characterized by one common, Erlang (or integer parameter gamma) type, probability distribution. Likewise, the time gaps are all identically, Erlang distributed, but the probability distributions of the durations and of the time gaps have different parameters. Pulse shapes are given by an arbitrary, deterministic function and pulse heights are given by independent, identically distributed random variables. The mean value and autocorrelation function of the pulse train are evaluated analytically and are shown to be expressed in terms of the renewal densities of the renewal process governing the pulse arrivals. It is shown that for rectangular pulses with equal, deterministic heights these expressions reduce to the ones obtained independently with the aid of another approach, where the mean value and autocorrelation function are given in terms of Markov ‘on’ state probabilities. The mean value and variance of the response of a linear oscillator are obtained via a time domain analysis. Illustrative numerical analysis is carried out for example trains of pulses with parabolic and rectangular pulse shapes.

Nonlinear Interaction of an Elastic Pulse With a Frictional Contact Interface Between Two Anisotropic Dissimilar Media

The paper analyses the interaction of an elastic pulse of arbitrary form with a frictional contact interface between two anisotropic solids which are pressed together and at the same time loaded by the in-plane and anti-plane shearing tractions. The incident pulse is assumed strong enough to break friction so that localized separation and slip take place. Coulomb friction, which causes the non-linear coupling between the in-plane and anti-plane motions, is supposed along the contact interface. The sub-critical angle incidence is first considered. By using Fourier analysis, the problem is reduced to a set of algebraic equations. A method to get the solution of the equations with determination of the slip/stick/separation zones is developed. As an example, the detailed computation for the case of an incident parabolic stress pulse is carried out. Numerical results of the interface tractions and the slip velocities are presented for two contacting half-spaces of the same materials in the same orientation. The super-critical angle incidence is discussed. In this case the problem is cast to a set of non-linear Cauchy singular integral equations whose solution is still an open question in mathematics.

Symmetry analysis of cylindrical implosions driven by high-frequency rotating ion beams

A symmetry analysis of the cylindrical target implosion driven by a high-frequency rotating beam of heavy ions is presented. The non-uniformity generated by such a system is studied by developing an analytical model and by performing two-dimensional simulations. The results show that the asymmetry in the driving pressure depends on the number N of beam revolutions as N−n and the power index n is determined by the time variation of the power pulse. For a box pulse, it is n = 1 and for a parabolic pulse, it is n = 2. In the latter case symmetry of 1% can be achieved at the end of the pulse by using N = 10.

Experimental generation of parabolic pulses via Raman amplification in optical fiber

Parabolic pulse generation via Raman amplification is experimentally demonstrated in 5.3 km of non-zero dispersion shifted fiber presenting normal group velocity dispersion at the injected signal pulse wavelength of 1550 nm. The fiber is pumped by a commercially-available continuous wave source at 1455 nm, and the intensity and chirp of the amplifier output are characterized using frequency-resolved optical gating. For 2.4 pJ input pulses of 10 ps duration, the output pulse characteristics are studied as a function of amplifier gain over the range 11-24 dB, allowing the evolution of the input pulse to a parabolic pulse to be clearly seen for amplifier gains exceeding 15 dB. Numerical compression of the output pulses show that near chirp-free pulses can be obtained using only linear chirp compensation.

Numerical study of parabolic pulse generation in microstructured fibre Raman amplifiers

Numerical simulations are used to demonstrate parabolic pulse generation in a highly nonlinear, normally dispersive microstructured fibre Raman amplifier. The dependence of the parabolic pulse solution on the parameters of the microstructured fibre is discussed. In particular, it is shown that the effects of pump depletion can be reduced with the appropriate sign of the third order dispersion. Additional simulations are conducted to establish the input pulse parameters which allow for the most efficient convergence to the parabolic pulse regime.