Positive Third-order Dispersion Research Articles

Giant anomalous self-steepening and temporal soliton compression in silicon photonic crystal waveguides

Self-steepening (SS) is enhanced by slow-light effects in photonic crystal waveguides (PhCWs), with coefficients as large as hundreds of femtoseconds, and it plays an important role in temporally compressed solitons with narrow widths. Here, we investigate the soliton evolution in silicon PhCWs through experiments and numerical simulations; the simulated results agree well with the experimental measurements and help in revealing the physical mechanism of high-order soliton evolution. The dual opposite effects of giant anomalous SS on temporal soliton compression are demonstrated for the first time, i.e., the SS weakens or improves the compression competing with the effects of third-order dispersion (TOD) through two different physical mechanisms. It is also found that SS flattens or steepens the pulse leading edge depending on the strength of the positive TOD perturbation. These results promote the understanding of high-order solitons and can help with the design of suitable dispersion engineered silicon waveguides for superior on-chip temporal pulse compression for optical interconnects, data processing, and microwave photonics.

Effects of third-order dispersion on temporal soliton compression in dispersion-engineered silicon photonic crystal waveguides

High-order temporal soliton compression in dispersion-engineered silicon photonic crystal waveguides will play an important role in future integrated photonic circuits compatible with complementary metal–oxide–semiconductors. Here, we report the physical mechanisms of high-order temporal soliton compression affected by third-order dispersion (TOD) combined with free carrier dispersion (FCD) in a dispersion engineered silicon photonic crystal waveguide with wideband low anomalous dispersion. Through numerical temporal soliton evolution analysis, we report what we believe is the first demonstration of the dual opposite effects of TOD on temporal soliton compression, which are strengthening or weakening through two different physical mechanisms, not only depending on the sign of TOD but also the relative magnitude of TOD-induced equivalent group velocity dispersion (GVD) β 2 , equ to the original GVD β 2 . We further find that FCD counteracts the effects of negative TOD on the soliton compression, while it reinforces the effects of positive TOD on the soliton compression. These results will help to design suitable dispersion-engineered silicon waveguides for superior on-chip temporal pulse compression in optical communications and processing application fields.

Trajectory manipulation of an Airy pulse near zero-dispersion wavelength under a free-carrier-generated linear potential

We investigate the dynamics of an Airy pulse that experiences free carrier generated optical linear potential in the vicinity of zero group velocity dispersion (GVD) wavelength inside a Si based waveguide. The optically induced potential can be realized by an inhomogeneous medium which possesses a time dependent refractive index. We propose a pump-probe scheme in Si-based waveguide where a strong continuous wave (CW) pump excites free carriers that leads to a linear potential through a time dependent refractive index change which is experienced by the finite energy Airy pulse (FEAP) (probe). The linear potential significantly manipulate the dynamics of a FEAP and leads to a monotonous spectral shift. We mathematically model the dynamics of the Airy pulse using linear dispersion equation containing an optical potential term and establish the general solution of the pulse for non-vanishing third order dispersion (TOD). We derive the expression of the trajectory of FEAP which deviates significantly from its usual ballistic nature and can be tailored with the strength of the linear potential. For positive TOD, the propagating Airy pulse experiences a singularity and flips in time domain. We theoretically derive that for a specific potential strength the flipping region is squeezed to a point and revives thereafter. We propose an exact analytical solution beyond flipping region for this specific case. Our theoretical analysis corroborates well with the numerical results. The present study may be useful in applications related to pulse reshaping and trajectory manipulation

Role of third-order dispersion in chirped Airy pulse propagation in single-mode fibers

The dynamic propagation of the initial chirped Airy pulse in single-mode fibers is studied numerically, special attention being paid to the role of the third-order dispersion (TOD). It is shown that for the positive TOD, the Airy pulse experiences inversion irrespective of the sign of initial chirp. The role of TOD in the dynamic propagation of the initial chirped Airy pulse depends on the combined sign of the group-velocity dispersion (GVD) and the initial chirp. If the GVD and chirp have the opposite signs, the chirped Airy pulse compresses first and passes through a breakdown area, then reconstructs a new Airy pattern with opposite acceleration, with the breakdown area becoming small and the main peak of the new Airy pattern becoming asymmetric with an oscillatory structure due to the positive TOD. If the GVD and chirp have the same signs, the finite-energy Airy pulse compresses to a focal point and then inverses its acceleration, in the case of positive TOD, the distance to the focal point becoming smaller. At zero-dispersion point, the finite-energy Airy pulse inverses to the opposite acceleration at a focal point, with the tight-focusing effect being reduced by initial chirp. Under the effect of negative TOD, the initial chirped Airy pulse disperses and the lobes split. In addition, in the anomalous dispersion region, for strong nonlinearity, the initial chirped Airy pulse splits and enters a soliton shedding regime.

High power all-polarization-maintaining photonic crystal fiber monolithic femtosecond nonlinear chirped-pulse amplifier

We report on an experimental study on fully fusion spliced high power all-polarization-maintaining Yb-doped photonic crystal fiber (PCF) femtosecond nonlinear chirped-pulse amplifier (CPA), which features large values of the positive third-order dispersion (TOD) superposed from the single-mode fiber stretcher (SMFs) and grating-pair compressor. Compensation of the TOD is realized by means of self-phase modulation (SPM) induced nonlinear phase shift during amplification. Up to 9.8 W of compressed average power at 275 kHz repetition rates with 36 μJ pulse energy and 495 fs pulse width has been obtained. To the best of our knowledge, this is the highest output power generated from the strictly all-fiber nonlinear CPA amplifier in femtosecond domain, which provides a possibility for the industrialized promotion and development of the high energy femtosecond fiber laser.

Evolution of finite-energy Airy pulse interaction with high-power soliton pulse in optical fiber with higher-order effects

When a low-power finite-energy Airy pulse (FEAP) and a high-power soliton pulse simultaneously propagate in an optical fiber, we numerically study the evolution of the FEAP affected by higher-order effects, including third-order dispersion (TOD), Raman scattering and self-steepening (SS). It is found that shedding solitons are generated from the FEAP due to the effect of cross-phase modulation (XPM). The TOD only affects the center position of the shedding soliton, but does not change the spectrum structure. The truncation coefficient of a FEAP, TOD and SS can be used to manipulate the Raman-induced frequency shift (RIFS). It is demonstrated that the RIFS is suppressed obviously by both positive TOD, SS and a small truncation coefficient, but the RIFS is enhanced by the negative TOD and a larger truncation coefficient. Further, we comparatively study the simultaneous contributions of TOD, Raman, and SS to the evolution of a FEAP and a Sech pulse, respectively. It is shown that the FEAP generates some static solitons besides the conventional Raman soliton and the whole spectrum is broadened that extended towards to the blue-shifted side besides the conventional red-shifted components. Our results indicate that the FEAP has potential application in supercontinuum generation and broadband sources.

Role of positive and negative third order dispersion (TOD) on soliton interaction in 160Gbps telecommunication system

In this paper, we analyze the influence of positive and negative third order dispersion (TOD) on soliton interaction. The peculiar nature of soliton as massive particle results in interaction of in-phase soliton, which has resulted in perfect collision in 160[Formula: see text]Gbps system at the interaction point, [Formula: see text][Formula: see text]Km within one collision period of [Formula: see text][Formula: see text]Km. The TOD normally helps in soliton shift from its initial position. We demonstrate how this shifting of TOD helps in preventing the interaction at 2202.6[Formula: see text]Km with an initial relative spacing and pulse width of in-phase soliton [Formula: see text] and 1.77[Formula: see text]ps, respectively. As the TOD has its influence near zero dispersion point of fiber, we choose the dispersion parameter of fiber as [Formula: see text][Formula: see text]ps2/Km. On considering the positive and negative TOD, the interaction was prevented at [Formula: see text], which is characterized in terms of Q-value in a single channel telecommunication system. It is seen that for positive TOD with the values of [Formula: see text] and 0.07[Formula: see text]ps3/Km, the system yielded the Q-value of 88.33 and 54.81, respectively, while for negative TOD with the values of [Formula: see text] and [Formula: see text][Formula: see text]ps3/Km, the Q was 84.47 and 38.25, respectively.

Enhanced Femtosecond Optical Pulses Compression Induced by Negative Third-Order Dispersion in Solid-Core Photonic Crystal Fibers

In this paper, the chirped- free optical pulses compression through propagating in silica - index guiding photonic crystal fibers will be studied. The results show that the Raman Effect can enhances the quality of compressed pulses and also the positive third-order dispersion (TOD) can be considered as the main reason in limiting the optical pulses compression. We will show that, the combined effects of the Raman scattering and negative TODs can causes generating much further compressed pulses in comparison with applying the only Raman effect or combination of that with the positive TODs. In this paper, We also numerically present a novel technique to solve the wave propagation equation, which is known as the concrete algorithms of split-step fourier method and fourth order Runge-Kutta (RK4) method. This method has a higher accuracy, although the computational time is longer because the number of calculation steps is chosen very large.

Manipulating dispersive wave generation by anomalous self-steepening effect in metamaterials

We present a theoretical investigation of dispersive wave (DW) generation in nonlinear metamaterials (MMs). The role of the anomalous self-steepening (SS) effect, which can be either positive or negative, and the negative SS parameter can have a very large value compared to an ordinary positive-index material, in DW generation is particularly identified. It is demonstrated that the SS effect exerts a great impact on the peak power while has little effect on the frequency shift of DW. For positive third-order dispersion (TOD), the negative SS broadens the pulse spectrum and weakens the DW's peak power significantly, opposite to the case of positive SS. For negative TOD, however, the negative SS narrows the pulse spectrum and enhances the DW's peak power, also opposite to the case of positive SS. The results suggest that the DW generation in nonlinear MMs can be manipulated by SS effect to a large extent.

Numerical investigation on frequency-shifting-induced spectral compression of femtosecond solitons in highly nonlinear fiber

We present a numerical investigation on nonlinear propagation of femtosecond pulses in anomalously dispersive highly nonlinear fiber (HNLF) with positive third-order dispersion (TOD). Soliton self-frequency shift (SSFS) in the HNLF is shown to enable efficient spectral compression of ultrashort pulse whose parameters satisfy 0.8≤N≤1.3 for the soliton order N. A spectral-compression factor up to 2.5 can be achieved for 60-fs, 1550-nm fundamental solitons red-shifted to 1609nm in the HNLF. We show that the fiber TOD has significant influence on the SSFS-induced spectral-compression performance. Using HNLF with larger TOD parameter, greater spectral-compression factor can be obtained. We also find that the impact of initial pulse chirp on output spectral width is negligible, indicating SSFS-based spectral-compression method is efficient for both chirped pulses and transform-limited pulses.

Real-time observation of transient electron density in water irradiated with tailored femtosecond laser pulses

Ionization mechanisms in water irradiated with bandwidth-limited and temporally asymmetric femtosecond laser pulses are investigated via ultrafast spectral interferometry. By using a novel common-path interferometer with an enlarged temporal measurement window, we directly observe the dynamics of free-electron plasma generated by shaped pulses. We found that a temporally asymmetric pulse and its time-reversed counterpart address multiphoton and avalanche ionization mechanisms in a different fashion. Positive third-order dispersion shaped pulses produce a much higher free-electron density than negative ones at the same fluence, instantaneous frequency and focusing conditions. From the experimental data obtained after irradiation with bandwidth-limited and shaped pulses the multiphoton and avalanche coefficients were determined using a generic rate equation. We conclude that temporal tailored femtosecond pulses are suitable for manipulation of the initial steps in laser processing of high band gap materials.

Evolution of cubic–quintic complex Ginzburg–Landau erupting solitons under the effect of third-order dispersion and intrapulse Raman scattering

The effects of third-order dispersion (TOD) and intrapulse Raman scattering (IRS) on the erupting solitons of the complex cubic–quintic Ginzburg–Landau equation are investigated by direct numerical simulations and linear stability analysis. Our results indicate that positive TOD eliminates eruptions on the leading edge of the soliton, whereas negative TOD cancels them on the other side. Moreover, the combined action of TOD and IRS is in certain cases able to eliminate explosions on both sides of the soliton, at much lower IRS values than with IRS alone. The profiles of the stationary solutions are increasingly asymmetric with TOD, and their velocity varies almost linearly with IRS.

Controllable Raman soliton self-frequency shift in nonlinear metamaterials

Controllable and dispersive magnetic permeability in the metamaterials (MMs) provides us more freedom to harness the propagation of ultrashort electromagnetic pulses at will. Here we discuss the controllability of the Raman soliton self-frequency shift (SSFS) in the MMs with a nonlinear electric polarization. First, we derive a generalized nonlinear Schr\odinger equation suitable for few-cycle pulse propagation in the MMs with delayed Raman response, and demonstrate the Raman effect, high-order Raman-related nonlinearity, and high-order nonlinear dispersion terms occurring in this equation. Second, we present a theoretical investigation on the controllability of the Raman SSFS in the MMs. In particular, we identify the combined effects of the anomalous self-steepening (SS), third-order dispersion (TOD), and Raman effect on SSFS. It is shown that the positive SS effect suppresses SSFS; however, the negative SS effect enhances SSFS, and the positive TOD leads to the deceleration of SSFS. Finally, the effects of SS on the SSFS of the second-order soliton are also discussed.

Effects of chirp and pulse shape on high harmonic generation and absorption in overdense plasmas

AbstractUsing particle-in-cell simulations, we investigated the effect of group velocity dispersion (GVD) and third order dispersion (TOD) in the laser pulse on high-order harmonic generation and laser absorption in overdense plasmas. A 1020 W/cm−2, 35-fs transform-limited Gaussian pulse was stretched to 160 fs through chirping. When including GVD alone, the temporal pulse shape remains symmetric and no difference was seen in the harmonic spectra for opposite signs of GVD. However, when adding TOD to GVD, the pulse is no longer symmetric and noticeable differences in harmonics intensity were observed for opposite signs of TOD. We show that the higher harmonic intensity obtained with positive TOD is connected with a steeper front edge of the pulse and the appearance of strong modulations in the harmonic spectrum. The chirp broadens and shifts the harmonics. Laser energy absorption is also mostly affected by the pulse shape. Simple estimates indicate that, in the main example considered in this paper, about half the laser energy absorption (10%) is due to vacuum heating.

Change of gain characters for short pulses with third order dispersion in a fiber amplifier

The effect of the third order dispersion (TOD) induced into pulses before entering an Yb-doped fiber amplifier on their power gain characters is investigated using a model of which the pulse amplification process is described by nonlinear time-dependent radiation transfer equations. Numerical results show that peak power gain for the pulse with positive TOD is larger than that with zero and without TOD while the improvement of the peak power gain varies as the obtained output pulse energy changes. The improvement also depends on the ratio of dispersion lengths for group velocity dispersion and TOD.

Soliton explosion control by higher-order effects

We numerically study the impact of self-frequency shift, self-steepening, and third-order dispersion on the erupting soliton solutions of the quintic complex Ginzburg-Landau equation. We find that the pulse explosions can be completely eliminated if these higher-order effects are properly conjugated two by two. In particular, we observe that positive third-order dispersion can compensate the self-frequency shift effect, whereas negative third-order dispersion can compensate the self-steepening effect. A stable propagation of a fixed-shape pulse is found under the simultaneous presence of the three higher-order effects.

Enhanced compression of femtosecond pulse in hollow-core photonic bandgap fibers

Compression of chirped free femtosecond pulses in hollow-core photonic bandgap fibers is investigated numerically. The results show that intrapulse stimulated Raman scattering can improve the quality of the compressed pulse. Positive third-order dispersion is the main limitation on the compression of the femtosecond pulse. However, the combined effect of the intrapulse stimulated Raman scattering and the negative third-order dispersion can form still shorter pulses than is possible with intrapulse stimulated Raman scattering alone. We also investigate the influence of width and peak power of input pulse on pulse compression.

Spectral broadening and compression to few-cycle pulse widths in the regime of soliton-self-frequency shift

Soliton-self-frequency shift in fibers with a precisely controlled dispersion is shown to enable efficient spectral broadening and temporal compression of light fields to few-cycle pulse widths. Anomalously dispersive fibers with positive third-order dispersion can transform nano- and subnanojoule 100-200 fs laser pulses into smoothly wavelength-tunable and spectrally broadened solitons with a pulse width as short as two to five field cycles. This regime of soliton pulse transformation is ideally suited for the creation of compact frequency-tunable fiber sources as well as for ultrabroadband optical parametric chirped-pulse amplification with an optical synchronization between the pump and seed fields.

Dynamics of ultrashort pulses near zero dispersion wavelength

The adiabatic dynamics of solitons under the action of third-order dispersion (TOD), the Raman effect, and self-steepening is studied. Using equations that describe the evolution of the pulse parameters, it is shown that the interplay between these effects results in nontrivial pulse dynamics. It is found that positive TOD slows down the self-frequency shift. The theory also describes the eventual suppression of the self-frequency shift in fibers with negative TOD that was recently observed in experiments and described theoretically. The relations of our results to supercontinuum generation are discussed.

Enhanced pulse compression induced by the interaction between the third-order dispersion and the cross-phase modulation in birefringent fibres

In this paper, we report on the enhanced pulse compression due to the interaction between the positive third-order dispersion (TOD) and the nonlinear effect (cross-phase modulation effect) in birefringent fibres. Polarization soliton compression along the slow axis can be enhanced in a birefringent fibre with positive third-order dispersion, while the polarization soliton compression along the fast axis can be enhanced in the fibre with negative third-order dispersion. Moreover, there is an optimal third-order dispersion parameter for obtaining the optimal pulse compression. Redshifted initial chirp is helpful to the pulse compression, while blueshifted chirp is detrimental to the pulse compression. There is also an optimal chirp parameter to reach maximum pulse compression. The optimal pulse compression for TOD parameters under different N-order solitons is also found.