Normal Dispersion Fiber Research Articles

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.

2D IR spectroscopy at 100 kHz utilizing a Mid-IR OPCPA laser source.

We present a 100 kHz 2D IR spectrometer. The system utilizes a ytterbium all normal dispersion fiber oscillator as a common source for the pump and seed beams of a MgO:PPLN OPCPA. The 1030 nm OPCPA pump is generated by amplification of the oscillator in cryocooled Yb:YAG amplifiers, while the 1.68 μm seed is generated in a OPO pumped by the oscillator. The OPCPA outputs are used in a ZGP DFG stage to generate 4.65 μm pulses. A mid-IR pulse shaper delivers pulse pairs to a 2D IR spectrometer allowing for data collection at 100 kHz.

Vector gain-guided dissipative solitons in a net normal dispersive fiber laser

We report on the experimental observation of spontaneous vector dissipative soliton train formation in a dispersion-managed cavity fiber laser with net normal cavity dispersion. The formation of the dissipative solitons is triggered by the nonlinearity-induced wave mixing and gain bandwidth limitation. So, they are named the gain-guided dissipative solitons to differentiate from those of the dissipative solitons formed in the mode-locked fiber lasers. The vector dissipative solitons are phase locked, and the coherent energy exchange between their two orthogonal polarization components is first revealed. Noise-like pulse emission and vector soliton rain effect are also experimentally observed.

Output pulse compressibility of the chirped pulse fiber amplification based on the dissipative solitons

The all-normal-dispersion mode locked fiber laser can produce the dissipative soliton pulses because the laser can tolerate much more nonlinear phase shift than the other mode locked fiber lasers. Such large energy mode locked fiber lasers are excellent seed pulse sources for generating very large-energy ultrashort pulses with fiber chirped pulse amplification (CPA) systems. However, the spectral amplitude modulation carried by the dissipative soliton pulses will severely restrict the compressibility of the output pulses from the typical CPA system. Therefore, it is necessary to investigate and design a suitable CPA system for improving the compressibility of the output pulses according to the properties of dissipative solitons. In this paper, using the dissipative solitons generated by the all-normal-dispersion fiber laser with different spectral filter bandwidths as the input seed pulses, the compressible properties of the pulses for the CPA system with both the grating pair stretcher and the fiber stretcher are investigated. Our simulation results show that, for such a large-energy dissipative soliton seed pulse, when the grating pair stretcher is used in the CPA system, the spectral amplitude modulation of the seed pulse can be mapped to the temporal amplitude modulation by the stretcher, and amplified by the subsequent fiber amplifier, which introduces additional nonlinear phase, finally restricts the compressibility of the output pulses; when the normal-dispersion fiber stretcher is used, the interaction between the group velocity dispersion and the self-phase modulation can not only eliminate the influence of the modulated spectrum of the dissipative soliton on the compressible properties of the pulses, but also make it possible to evolve the pulse self-similarity in the fiber stretcher, and thus improve the compressibility of the output pulses of the CPA system. For the normal-dispersion fiber stretcher CPA system, the compressibility of the output pulses is mainly determined by the fiber stretcher length. If the fiber length is too short, the compressibility of the output pulses may be affected by the uncompleted self-similar evolution of the pulse, while the pulse compressibility is also restricted because the pulse spectral width may exceed the amplifier gain bandwidth due to the self-similar evolution process if the fiber length is too long. Moreover, for the dissipative soliton seed pulses, both the compressibility of the output pulses and the energy ratio of the main pulse to the total pulse for the CPA system with the fiber stretcher are better than those with the grating pair stretcher when the normal fiber stretcher length is suitably optimized.

Blue-Shifted Rogue Waves Generation in Normal Dispersion Fiber Laser

In the presence of noise in normal dispersion fiber mode-locked lasers, dissipative resonance disappears, which leads to instability of spectral broadening and makes the asymptotic accumulation of energy impossible. We experimentally generate dissipative soliton molecules-like spectral peaks and rogue waves in the frequency domain in a self-mode-locked fiber laser. Due to noise in the initial triangular-shaped mode locked wave, these molecules are arranged in the form of lobes on the longer wavelength side, thus forming three virtual groups of soliton molecules. Further dissipative accumulation of power in the mode-locked wave ultimately leads to the formation of a blue-shifted group of three rogue waves, due to the effective fusion of adjacent soliton molecules. This is the first report of an experimental observation of blue-shifted and three rogue waves in a single experiment. The results have far reaching implications for experimentation with soliton collisions, optical rogue waves, and understanding of hydrodynamics.

Characterization and analysis of timing jitter in normal-dispersion mode-locked Er-fiber lasers with intra-cavity filtering.

We characterize and analyze the timing jitter of normal-dispersion mode-locked Er-fiber lasers with intra-cavity filtering. The timing jitter of Er-fiber lasers with 9-nm bandpass filters operating at + 0.0084 ps(2) is measured to be 3.46 fs (rms) when integrated from 10 kHz to 10 MHz offset frequency, which is similar to the jitter level of typical stretched-pulse or soliton Er-fiber lasers. The numerical simulation based on split-step Fourier transform method shows that the measured high-frequency jitter is quantum noise-limited performance. We also develop an analytical model for filtered normal-dispersion fiber lasers by modifying the well-established noise model of stretched-pulse fiber lasers. The analytical modeling reveals that the jitter performance is improved mostly by reducing the chirp parameter by intra-cavity filtering. Both numerical simulation and analytical model fit fairly well with the measured timing jitter result.

Inverse four-wave-mixing and self-parametric amplification effect in optical fibre.

An important group of nonlinear processes in optical fibre involves the mixing of four waves due to the intensity dependence of the refractive index. It is customary to distinguish between nonlinear effects that require external/pumping waves (cross-phase modulation and parametric processes such as four-wave mixing) and self-action of the propagating optical field (self-phase modulation and modulation instability). Here, we present a new nonlinear self-action effect, self-parametric amplification (SPA), which manifests itself as optical spectrum narrowing in normal dispersion fibre, leading to very stable propagation with a distinctive spectral distribution. The narrowing results from an inverse four-wave mixing, resembling an effective parametric amplification of the central part of the spectrum by energy transfer from the spectral tails. SPA and the observed stable nonlinear spectral propagation with random temporal waveform can find applications in optical communications and high power fibre lasers with nonlinear intra-cavity dynamics.

Mode-Locked Thulium-Doped Fiber Lasers Based on Normal Dispersion Active Fiber

We report and compare three configurations of the semiconductor saturable absorber mirror mode-locked, linear cavity femtosecond all-fiber master oscillator power amplifier based on a highly Ge-doped thulium-doped normal dispersion fibers. We have studied the performance of the system and have obtained stable mode-locking in a wide cavity dispersion range $\sim 1.88~\mu \text{m}$ . In this letter, we focus our attention on three mode-locking regimes: laser operating in the anomalous, nearly zero and normal cavity dispersion regimes without the use of the additional dispersion compensating elements. For the nearly zero and normal cavity dispersion regimes the femtosecond pulses with several nanojoule energy could be obtained. The pulses were further compressed down to 630 fs using a simple fiber compressor consisting of a piece of the conventional telecommunication fiber, making the laser design particularly simple and cost effective.

Pump hysteresis and bistability of dissipative solitons in all-normal-dispersion fiber lasers

We report the results of numerical simulations on pump hysteresis and bistability of a dissipative soliton fiber laser. The fiber laser is made of normal-dispersion fibers and passively mode locked by using the nonlinear polarization rotation technique. The dependence of the final steady state on the initial light field is investigated. Bistability between the single-pulse state and the double-pulse state in the mode-locking regime is demonstrated. Different initial conditions could lead to different attractors, even with the same point in the parameter space.

High-energy dissipative solitons generation from a large normal dispersion Er-fiber laser.

We report on a passively mode-locked erbium-doped fiber laser featuring a large normal dispersion and emitting high-energy dissipative solitons. Mode-locking is stabilized by the combined actions of a high nonlinearity amplitude modulator and a narrow band spectral filter. The laser routinely delivers highly chirped pulses with more than 38 nJ energy that can be compressed down to 700 fs duration using bulk gratings. Numerical simulations confirm the experimental results and reveal the self-similar pulse evolution along the normal dispersion fibers included inside the cavity.

Silica based highly nonlinear fibers to generate parabolic self-similar pulses

Three different silica based normal dispersion fibers are designed to identify the best possible one for efficient parabolic pulse generation. Two of them resemble commonly used single core fibers and optimized in such a way that one has lower dispersion and nonlinear coefficient whereas the other possesses higher dispersion and lower nonlinearity. A silica based multi-cladded highly nonlinear fiber (ND-HNLF) is designed as well by successfully restricting its effective area to a very lower value. The comparative analysis among the three fibers suggests that the ND-HNLF would be the best choice for fiber optic manufacturers for parabolic similariton formation due to its smaller optimum length, no effect of higher order dispersion, high nonlinearity and less input power requirement. From our proposed ND-HNLF, a highly nonlinear dispersion decreasing fiber (HN-NDDF) is also designed and optimized by properly varying different fiber parameters as a function of fiber length. Our study also reveals that the HN-NDDF with a typical property of virtual gain would be beneficial for producing parabolic self-similar pulses at smaller optimum lengths with adequate spectral broadening in comparison to that of ND-HNLF.

Pulse-shaping mechanisms in passively mode-locked thulium-doped fiber lasers.

Different pulse-shaping mechanisms were investigated experimentally and numerically in passively mode-locked thulium-doped fiber lasers. Conventional solitons were demonstrated in a passively semiconductor saturable absorber mirror mode-locked anomalous dispersion thulium-doped fiber laser. With normal dispersion fiber and spectral filter added in cavity, pulse-shaping processes were theoretically analyzed in the presence of dispersion map and dissipation in thulium-doped fiber lasers. The existence of parabolic pulse as nonlinear attraction was proved and distinct pulse intensity profiles evolution from Gaussian shape to parabolic shape was proposed in dissipative dispersion-managed thulium-doped fiber lasers.

Formation and Energy Exchange of Vector Dark Solitons in Fiber Lasers

The mutual energy-exchange interactions in two orthogonally polarized components of vector dark soliton, which is automatically formed in a normal-dispersion fiber laser cavity in the presence of reverse saturable absorption, and dissipative cavity effects, had been theoretically and numerically investigated. Under specific cavity parameters, a vector dark soliton with periodic coherent energy exchange could be formed and well described by a semianalytic method. The multiple vector dark solitons with energy exchange were also demonstrated by combining gain bandwidth and a reverse saturable absorption effect.

Parabolic and semiparabolic pulse dynamics in optical fibers

Nonlinear pulse dynamics in two stages of different active or passive fibers are investigated in this work. Numerical approach of the symmetrized split step Fourier method is used to solve the nonlinear Schrödinger equation in the presence of fiber gain, nonlinearity, and dispersion. An input Gaussian pulse evolves into a linearly chirped perfect parabolic pulse (PP) when it propagates through a standard normal dispersion decreasing fiber amplifier. At the same time, for an erbium-doped dispersion decreasing fiber amplifier with a similar dispersion variation with length, the semiparabolic pulse (SPP) is produced at the output end of the fiber. To our knowledge, this is shown for the first time. In second stage, the so-obtained perfect PP, SPP, and also a chirp-free perfect PP are fed into the input of several normal dispersion fibers and the comparative pulse evolution is studied in detail with the variations of dispersion coefficient, gain, and nonlinearity. While using these pulses as the input of an anomalous dispersion fiber, our result shows that the linearly chirped PP is most efficient for compressing the pulses with a good quality factor without dropping significant pedestal energy.

Initial conditions for dark soliton generation in normal-dispersion fiber lasers.

We report results of numerical simulations on the various initial conditions for dark soliton generation in an all-normal-dispersion fiber laser. All the dark solitons generated are odd dark solitons. Differently from the dark soliton generation in fibers, where an arbitrary dip could evolve into a dark soliton, it is found that the dark soliton can originate only from an initial dip with a certain parameter requirement. A bright pulse with either a hyperbolic secant square, Gaussian, or Lorentz profile can be developed into a dark soliton, provided that the parameters of the initial bright pulse are selected. Dark solitons can be generated in fiber lasers only if there is a phase jump, and this phase jump can be maintained and evolve to π during the pulse evolution.

Reduction of timing jitter and intensity noise in normal-dispersion passively mode-locked fiber lasers by narrow band-pass filtering.

Fiber lasers mode-locked with normal cavity dispersion have recently attracted great attention due to large output pulse energy and femtosecond pulse duration. Here we accurately characterized the timing jitter of normal-dispersion fiber lasers using a balanced cross-correlation method. The timing jitter characterization experiments show that the timing jitter of normal-dispersion mode-locked fiber lasers can be significantly reduced by using narrow band-pass filtering (e.g., 7-nm bandwidth filtering in this work). We further identify that the timing jitter of the fiber laser is confined in a limited range, which is almost independent of cavity dispersion map due to the amplifier-similariton formation by insertion of the narrow bandpass filter. The lowest observed timing jitter reaches 0.57 fs (rms) integrated from 10 kHz to 10 MHz Fourier frequency. The rms relative intensity noise (RIN) is also reduced from 0.37% to 0.02% (integrated from 1 kHz to 5 MHz Fourier frequency) by the insertion of narrow band-pass filter.

Cross-modulation instability in inhomogeneous normal-dispersion fiber amplifiers

The conditions of the onset of a modulation instability of the signal wave in a doped fiber due to nonlinear cross-modulation interaction with the pump wave are investigated. The analysis takes into consideration the pump depletion and the group-velocity mismatch of the interacting waves. A dispersion relation coupling perturbation parameters with those of pump, analytic expressions governing the integral growth rate of a harmonic perturbation, and other important characteristics determining the dynamics of the signal-wave cross-modulation instability are obtained. Based on computer simulation, the behavior of the above characteristics as a function of the initial signal-wave power, fiber length, and group-velocity mismatch of the pump and signal waves is investigated.

Mode-locked ytterbium fiber lasers using a large modulation depth carbon nanotube saturable absorber without an additional spectral filter

We demonstrate an all-normal-dispersion ytterbium (Yb)-doped fiber laser mode-locked by a higher modulation depth carbon nanotube saturable absorber (CNT-SA) based on an evanescent field interaction scheme. The laser cavity consists of pure normal dispersion fibers without dispersion compensation and an additional spectral filter. It is exhibited that the higher modulation depth CNT-SA could contribute to stabilize the mode-locking operation within a limited range of pump power and generate the highly chirped pulses with a high-energy level in the cavity with large normal dispersion and strong nonlinearity. Stable mode-locked pulses with a maximal energy of 29 nJ with a 5.59 MHz repetition rate at the operating wavelength around 1085 nm have been obtained. The maximal time-bandwidth product is 262.4. The temporal and spectral characteristics of pulses versus pump power are demonstrated. The experimental results suggest that the CNT-SA provides a sufficient nonlinear loss to compensate high nonlinearity and catch up the gain at a different pump power and thus leads to the stable mode locking.

Cross modulation instability in normal-dispersion fibre lasers and amplifiers

This paper examines instability resulting from cross phase modulation interaction between signal and pump waves in normal-dispersion fibre lasers and amplifiers. From analysis of the dispersion relation for the wave vector of small harmonic perturbations, we derive dynamic spectral characteristics of the modulation gain coefficient. Its dependence on the group velocity difference between signal and pump waves is investigated. Analytical results are compared to numerical simulation data. We discuss how the general relationships obtained in this study can be used in practical applications.

Dark soliton synthesis using an optical pulse synthesizer and transmission through a normal-dispersion optical fiber

We precisely generate dark solitons using an optical pulse synthesizer (OPS) at a repetition rate of 25 GHz and experimentally investigate soliton transmission through a normal-dispersion fiber. Because of their particular waveform, there are not many experimental studies. The OPS provides frequency-domain line-by-line modulation and produces arbitrary pulse waveforms. The soliton waveform has an intensity contrast greater than 20 dB. At certain input peak power, the pulse exhibits soliton transmission and maintains its initial waveform. The power agrees with soliton transmission theory. We confirm that the π phase shift at the center of the dark soliton is maintained after transmission through the fiber. We also investigate the influence of stimulated Brillouin scattering for long-distance transmission.