Higher-order Dispersion Effects Research Articles

Solitons and frequency combs in silica microring resonators: Interplay of the Raman and higher-order dispersion effects

The influence of Raman scattering and higher order dispersions on solitons and frequency comb generation in silica microring resonators is investigated. The Raman effect introduces a threshold value in the resonator quality factor above which the frequency locked solitons can not exist and, instead, a rich dynamics characterized by generation of self-frequency shift- ing solitons and dispersive waves is observed. A mechanism of broadening of the Cherenkov radiation through Hopf instability of the frequency locked solitons is also reported.

Design of an As2Se3-based photonic quasi-crystal fiber with highly nonlinear and dual zero-dispersion wavelengths

We propose an As2Se3-based highly nonlinear photonic quasi-crystal fiber with dual zero-dispersion wavelengths (ZDWs). Using a full-vector finite element method, the proposed fiber is optimized to obtain high nonlinear coefficient, low confinement loss and two zero-dispersion points by optimizing the structure parameters. Numerical results demonstrate that the proposed photonic quasi-crystal fiber (PQF) has dual ZDWs and the nonlinear coefficient up to 2600 W−1 km−1 within the wavelength range from 2 to 5.5 μm. Due to the introduction of the large air holes in the third ring of the proposed fiber, the ability of confining the fundamental mode field can be improved effectively and thus the low confinement loss can be obtained. The proposed PQF with high nonlinearity and dual ZDWs will have a number of potential applications in four-wave mixing, super-continuum generation, and higher-order dispersion effects.

Attenuation, dispersion and nonlinearity effects in graphene-based waveguides.

We simulated and analyzed in detail the behavior of ultrashort optical pulses, which are typically used in telecommunications, propagating through graphene-based nanoribbon waveguides. In this work, we showed the changes that occur in the Gaussian and hyperbolic secant input pulses due to the attenuation, high-order dispersive effects and nonlinear effects. We concluded that it is possible to control the shape of the output pulses with the value of the input signal power and the chemical potential of the graphene nanoribbon. We believe that the obtained results will be highly relevant since they can be applied to other nanophotonic devices, for example, filters, modulators, antennas, switches and other devices.

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.

Hamiltonian formulation of the extended Green–Naghdi equations

A novel method is developed for extending the Green–Naghdi (GN) shallow-water model equation to the general system which incorporates the arbitrary higher-order dispersive effects. As an illustrative example, we derive a model equation which is accurate to the fourth power of the shallowness parameter while preserving the full nonlinearity of the GN equation, and obtain its solitary wave solutions by means of a singular perturbation analysis. We show that the extended GN equations have the same Hamiltonian structure as that of the GN equation. We also demonstrate that Zakharov’s Hamiltonian formulation of surface gravity waves is equivalent to that of the extended GN system by rewriting the former system in terms of the momentum density instead of the velocity potential at the free surface.

Periodic and Chaotic Exploding Dissipative Solitons

This article shows for the first time the existence of periodic exploding dissipative solitons. These non-chaotic explosions appear when higher-order non-linear and dispersive effects are added to the complex cubic–quintic Ginzburg–Landau equation modeling soliton transmission lines. This counter-intuitive phenomenon is the result of period-halving bifurcations leading to order (periodic explosions), followed by period-doubling bifurcations leading to chaos (chaotic explosions). This periodic behavior is persistent even when small amounts of noise are added to the system. Since for ultrashort optical pulses it is necessary to include these higher-order effects, it is conjectured that the predictions can be tested in mode-locked lasers.

Generation of Multiple Mid-Infrared Wavelengths by Soliton Fission in a Photonic Crystal Fiber

Higher-order solitons are formed by coupling femtosecond pulses into the fundamental mode of a highly nonlinear silica photonic crystal fiber (HNL-SPCF) fabricated in our laboratory. It is experimentally observed that the higher-order solitons break up into a series of stable and broadband discrete fundamental solitons at the mid-infrared wavelength longer than 2000 nm through the process of soliton self-frequency shift due to the perturbations induced by the higher-order dispersive and nonlinear effects. The maximum soliton red-shift and the tunable wavelength range can be up to 1600 nm and over 400 nm, respectively. The nonlinear dynamic processes of femtosecond pulse breakup are consistent with the solution of the generalized nonlinear Schrodinger equation. This multiple stable and broadband mid-infrared wavelengths generated in such an HNL-SPCF can be used as all-fiber multiwavelength ultrashort pulse sources for multiphoton microscopy and ultrafast photonics.

Dynamics of cascaded resonant radiations in a dispersion-varying optical fiber

Temporal solitons propagating in the vicinity of a zero-dispersion wavelength in an optical fiber emit phase-matched resonant radiations (RRs) as a result of perturbations due to higher-order dispersion effects. These RRs propagate linearly and they usually rapidly spread out in time, thus having a very low peak power. Here, we show that the use of an engineered dispersion-varying optical fiber allows us to induce a completely new dynamics, in which a new physical mechanism—cascade of RRs—is discovered. It is explained by the fact that the RR is temporally recompressed thanks to the change of dispersion sign induced by the varying geometry along the fiber. In addition, we report the experimental evidence of physical processes that had remained unobserved experimentally so far, such as the emission of multiple RRs from a single soliton and the generation of a 500 nm continuum exclusively composed of polychromatic RRs.

The analysis of all-optical logic gates based with tunable femtosecond soliton self-frequency shift

A type of tunable femtosecond soliton logic gate based on fiber Raman Self-Frequency Shift (SFS) is studied in this paper. The Raman SFSs of femtosecond solitons governed by the Newton's cradle mechanism in logic gate are analyzed with an Improved Split-Step Fast Fourier Transform (ISSFFT) algorithm. The impact factors of the solitonic pulse frequency shift and temporal time shift, which are included the Third-Order Dispersion (TOD) effect, are investigated. The existing theoretical equation of SFS is modified into a new expression for this type of soliton logic gate. A lower switching power and the small size of the soliton logic gate device is designed to realize the logic functions of AND, NOT, and XOR. The results demonstrate that the logic gate based on SFS is belonged to the asynchronous system and can be achieved with Milli-Watt switching power and good extinction ratio. ISSFFT is effective and accurately to analyze higher-order dispersive and nonlinear effects in the logic gates.

Photonic generation of chirped microwave signals with high time-bandwidth product

A photonic approach to generating chirped microwave signal with high time-bandwidth product (TBWP) is proposed. The scheme utilizes the linear frequency-to-time mapping of a spectrally-shaped optical pulse propagating through a dispersive element. A mode-locked laser for generating short optical pulses and a programmable optical filter (POF) to shape the spectrum of the pulses are employed. Experiment results show that the chirped signal with a TBWP and compression ratio both in excess of 60 is achieved. We also estimate theoretically the maximum TBWP that can be achieved over 300 under the constraint of the finite frequency resolution of the applied POF. The effect of higher order dispersion on the generated RF pulses and the TBWP is also investigated.

Optical rogue waves in the generalized inhomogeneous higher-order nonlinear Schrödinger equation with modulating coefficients

Higher-order dispersive and nonlinear effects (alias the perturbation terms) such as third-order dispersion, self-steepening, and the self-frequency shift play important roles in the study of ultra-short optical pulse propagation. We consider optical rogue wave solutions and interactions for the generalized higher-order nonlinear Schrödinger (NLS) equation with space- and time-modulated parameters. An appropriate transformation is presented to reduce the generalized higher-order NLS equation to an integrable Hirota equation with constant coefficients. This transformation allows us to relate a certain class of exact solutions of the generalized higher-order NLS equation to the variety of solutions of the integrable Hirota equation. In particular, we illustrate the approach in terms of the two lowest-order rational solutions of the Hirota equation as seeding functions, to generate rogue wave solutions localized in time that have complicated evolution in space, with or without the differential gain or loss term. We simply analyze the physical mechanisms of the obtained optical rogue waves on the basis of these constraints. Finally, the stability of the obtained rogue wave solutions is addressed numerically. The obtained rogue wave solutions may raise the possibility of related experiments and potential applications in nonlinear optics and other fields of nonlinear science, such as Bose–Einstein condensates and ocean waves.

Modulation instability in nonlinear metamaterials induced by cubic–quintic nonlinearities and higher order dispersive effects

We have investigated modulation instability (MI) in metamaterials (MM) with both cubic and quintic nonlinearities, based on a model appropriate for pulse propagation in MM with cubic–quintic nonlinearities and higher order dispersive effects. We have included loss into account in our analysis and found that loss distorts the sidebands of the MI gain spectrum. We found that the combined effect of cubic–quintic nonlinearity increases the MI gain. The role of higher order nonlinear dispersive effects on MI has also been discussed.

SOLITON INTERACTIONS FOR A HIROTA–MAXWELL–BLOCH SYSTEM IN THE INHOMOGENEOUS ERBIUM-DOPED FIBER

In this paper, we consider a generalized Hirota–Maxwell–Bloch system with the higher-order dispersion and self-steepening effects, which describes the propagation of ultrashort optical pulse in the inhomogeneous erbium-doped fiber. Under certain coefficient constraints, N-soliton solutions are obtained through the Hirota method and symbolic computation. Soliton interactions are graphically presented and analyzed in the different fibers. Compared with the Hirota equation without the Maxwell–Bloch parts, the self-induced transparency effect caused by the doped erbium atoms is found to lead to the change of the soliton velocity and phase. In addition, the amplitudes and widths of solitons are respectively observed to decrease and increase in the dispersion-decreasing and dispersion-increasing fibers. Finally, we give the modulational instability condition through the linear stability analysis.

Modulational instability with higher-order dispersion and walk-off in Kerr media with cross-phase modulation

We investigate the cross-phase-modulation-induced modulational instability (MI) of two co-propagating optical beams in the system of relaxing Kerr nonlinearity with the effect of higher-order dispersion (HOD) and walk-off effect. We identify and discuss the salient features of relaxation of nonlinear responses and HOD using suitable theoretical model. First, we analyzed the impact of HOD and walk-off on the MI spectrum and found both analytically and numerically that the MI exhibits alternate characteristics like the evolution of different spectral bands in addition to the conventional MI bands. The walk-off effects in the virtue of HOD not only consist of the conventional group velocity mismatch (GVM) but also the difference in third-order dispersion (TOD) of the two beams, and thereby significantly modify the dynamical behavior of the MI. We also consider the combined effect of relaxation of nonlinear response and the HOD effects, and we observe that any finite value of delay leads to the evolution of two unstable modes and thereby extends the range of unstable frequency; HOD on the other hand along with the walk-off effect brings other characteristic spectral bands. A detailed discussion about the various combinations of parameters and the relative competence of one over the other on the MI spectrum is presented. Thus the evolution of MI from cross-phase modulation in the system of relaxing Kerr nonlinearity is emphasized in detail and the influence of HOD and the walk-off effect are highlighted.

Sub-picosecond chirped pulse propagation in concave-dispersion-flattened fibers

Tianjin University of Technology and Springer-Verlag Berlin Heidelberg 2012 C We propose the sub-picosecond chirped soliton pulse propagation in concave-dispersion-flattened fibers (CDFF). The effects of pulse characteristics and the fiber dispersion parameters on propagation characteristics of the chirped soliton pulse are numerically investigated in the CDFF by the split-step Fourier method (SSFM). The unchirped soliton pulse can stably propagate with unchanged pulse width in the CDFF. The temporal full width at half maximum (FWHM) of the chirped soliton performs a damped oscillation with the increase of propagation distance. The period and amplitude of the oscillation increase with the increase of the chirp parameter |C|. The effect of high-order dispersion (β3−β6) on soliton propagation characteristics can be neglected. The soliton pulse slightly broadens with the increase of propagation distance and still maintains soliton characteristics when the fiber loss (ATT) is further considered. The variation of root-meansquare (RMS) spectral width with propagation distance is opposite to that of the temporal width. The output spectrum of soliton has a single peak for the unchirped case, while has multi-peak for chirped case. The temporal width of the soliton obviously increases with the increase of the initial width, decreases with the increase of dispersion peak D0 of the fiber, and slightly increases with the decrease of dispersion coefficients k1 and k2 of the fiber.

Enhanced red-shifted radiation by pulse trapping in photonic crystal fibers with two zero-dispersion wavelengths

A theoretical investigation on the two pulses copropagation and the red-shifted radiation generation in a photonic crystal fiber with two zero-dispersion wavelengths are presented. It is found the intensity of the red-shifted radiation components can be enhanced when the fiber is pumped with two pulses and the pulse trapping occurs. As the input peak power of the pump pulse is increased under the phenomenon of pulse trapping, the intensity of the red-shift radiation can be further enhanced. The above effects can be explained by the energy transfer from the Raman soliton to the red-shifted radiation components due to the effect of pulse trapping and the effect of higher-order dispersion.

Design and optimization of high-birefringence low-loss crystal fiber with two zero-dispersion wavelengths for nonlinear effects

A photonic crystal fiber (PCF) is proposed that is composed of a central defect core and cladding with elliptical air holes along the fiber length. In the structure, two circular air holes are enlarged near the central region to reduce core size and induce high nonlinearity. Its dispersion, birefringence, nonlinearity coefficient, and confinement loss are investigated simultaneously by using the full-vectorial finite element method with anisotropic perfectly matched layers. Numerical results indicate that the proposed PCF has two zero-dispersion wavelengths (ZDWs) and stronger confinement ability in its guide mode, in which the confinement loss is lower than 10−2 dB m−1. The two high-birefringence ZDWs can be optimized by adjusting the geometric parameters of the proposed fiber, such as air-filling fraction d/Λ and air-hole ellipticity η. With the fixed parameters d/Λ=0.6 and η=2.85, the two ZDWs are present in the communication window, and the corresponding birefringence and nonlinearity coefficient are as high as 4.8×10−2 and 105 W−1 km−1, respectively. The proposed two-ZDW PCF with high birefringence and nonlinearity will have important applications in four-wave mixing and higher-order dispersion effects.

Higher order dispersion effects in the noninstantaneous nonlinear Schrödinger equation

We present a systematic analysis of the effects, of higher-order dispersion, noninstantaneous nonlinear response, as well as stochastic coefficients in optical fiber. This study is motivated by recent experimental observation of a new modulational instability spectral window induced by fourth-order dispersion in a normally dispersive single-mode optical fiber. Analytical expression of pulse amplitude is deduced with the second-order gain nonuniformity and the stimulated-Brillouin scattering-induced third-order as well as fourth-order dispersion effects involved. The influence of stochasticity, as well as the delayed Raman response in the nonconventional sidebands obtained due to the fourth-order dispersion, is considered. We note that the shape of the spectrum, and in particular the relative intensities of the higher order harmonics, is highly sensitive to the initial presence of classical noise, and can therefore be taken as a signature that the MI is seeded by vacuum fluctuations. Some direct simulations to see the evolution of different continuous wave states are reported. These show the formation of modulation instability pulses as well as transitions from lower amplitude continuous wave states to higher amplitude continuous wave states. The present results fit well with recent experimental investigations.

Origin and effect of high-order dispersion in ultrashort pulse multiphoton microscopy in the 10 fs regime

Short pulses can induce high nonlinear excitation, and thus they should be favorable for use in multiphoton microscopy. However, the large spectral dispersion can easily destroy the advantages of the ultrashort pulse if there is no compensation. The group delay dispersion (GDD), third-order dispersion, and their effects on the intensity and bandwidth of second-harmonic generation (SHG) signal were analyzed. We found that the prism pair used for compensating the GDD of the two-photon microscope actually introduces significant negative high-order dispersion (HOD), which dramatically narrowed down the two-photon absorption probability for ultrashort pulses. We also investigated the SHG signal after GDD and HOD compensation for different pulse durations. Without HOD compensation, the SHG efficiency dropped significantly for a pulse duration below 20 fs. We experimentally compared the SHG and two-photon excited fluorescence (TPEF) signal intensity for 11 fs versus 50 fs pulses, a pulse duration close to that commonly used in conventional multiphoton microscopy. The result suggested that after adaptive phase compensation, the 11fs pulse can yield a 3.2- to 6.0-fold TPEF intensity and a 5.1-fold SHG intensity, compared to 50 fs pulses.

Accuracy of Waveform Spectrum Analysis for Ultrashort Optical Pulses

We investigate the waveform power spectrum (WPS) measurement of ultrashort pulses using the nonlinear Kerr effect in an optical waveguide. Our study focuses on a recent experiment reporting the WPS measurement of 260-fs pulses using a 6-cm-long, highly nonlinear chalcogenide (ChG) planar waveguide. By numerical simulation of the underpinning nonlinear propagation, we show the importance of low chromatic dispersion in the waveguide for avoiding measurement inaccuracy due to bandwidth narrowing and asymmetric distortion of the WPS. We also show the distortion effect of excessive input power on broadening the WPS bandwidth. In comparison to using conventional nonlinear fibers, highly nonlinear ChG waveguides are shown to generally enable a more accurate and broadband measurement of shorter pulses over a multiterahertz frequency range, and for a wider ranging signal wavelength. Furthermore, higher order dispersion effects are also avoided. Experiments with nonlinear fiber show its capability to measure the WPS of high-speed 640-Gb/s data signals, albeit for broader pulses and with less wavelength flexibility. Furthermore, the WPS is used to effectively retrieve the signal autocorrelation waveform. The factors impacting the measurement accuracy is compared to other recent experiments using ChG and silicon waveguides. Analysis shows that extending the technique to pulses shorter than 260 fs requires further optimizing the ChG waveguide dispersion, which would benefit broadband signal processing in general.