Third-order Dispersion Research Articles

Nonlinear compression of mid-infrared supercontinuum generation in dispersion-engineered As2S5 chalcogenide ridge waveguide

We numerically demonstrated nonlinear compression of mid-infrared (mid-IR) supercontinuum (SC) generation in As2S5 chalcogenide glass (ChG) ridge waveguides, achieving a small dispersion value at the pump wavelength of 2.5 µm by adjusting the waveguide width (normal dispersions of -10.547 ps.nm−1.km−1 and the anomalous dispersions of +5.314 ps.nm−1.km−1). These waveguides were designed using the negative slope of the dispersions with the negative third-order dispersion, which are applied to generate the nonlinear compression of SC generation. Using a 50-fs pulse with the peak power of 2000 W, the two waveguides could compress the maximum pulse peak power of 6900 W (> 3.4 octaves) and 6360 W (> 3.1 octaves) and generate the widest SC spectra, spanning from 1.20 µm to 12.96 µm and from 1.25 µm to >13 µm with only short waveguides 0.85 mm and 1 mm long, respectively. The key process behind SC formation in such ChG waveguides is related to self-phase modulation, four-wave mixing, and nonlinear compression. This particular design is effective, and ChG waveguides can generate high peak power and the widest spectra of SC generation. Moreover, the waveguides are also relatively flexible in design, which is concerned with optical design and engineering, and micro-optical devices. As the ultra-wideband mid-IR SC source, high pulse peak power, very short waveguides, and low-energy pulses (<1 pJ) are important for on-chip mid-IR SC sources, the proposed work would offer the greatest benefits in practical application.

Degradation of temporal contrast from post-pedestal interference with a chirped pulse in an optical parametric amplifier.

Pre-pedestal generation is observed in a 0.35-PW laser front end coming from a post-pedestal via instantaneous gain and pump depletion in an optical parametric amplifier during chirped-pulse amplification. Generalized simulations show how this effect arises from gain nonlinearity and applies to all optical parametric chirped-pulse-amplification systems with a post-pedestal. An experiment minimizing the effect of B-integral is used to isolate and study the newly observed conversion of a continuous post-pedestal into a continuous pre-pedestal. Matching numerical simulations confirm experimental results and additionally reveal how third-order dispersion largely controls the slope of the generated pre-pedestal.

Impact of third-order dispersion on the dynamics of dissipative solitons in an ultrafast fiber laser.

Dissipative solitons (DSs), due to the complex interplay among dispersion, nonlinear, gain and loss, illustrate abundant nonlinear dynamics behaviors. Especially, dispersion plays an important role in the research of DS dynamics in ultrafast fiber lasers. Previous studies have mainly focused on the effect of even-order dispersion, i.e., group velocity dispersion (GVD) and fourth-order dispersion. In fact, odd-order dispersions, such as third-order dispersion (TOD), also significantly influences the dynamics of DSs. However, due to the lack of dispersion engineering tools, few experimental researches in this domain have been reported. In this work, by employing a pulse shaper in ultrafast fiber laser, an in-depth exploration of the DS dynamics influenced by TOD was conducted. With the increase of TOD value, the stable single DS undergoes a splitting into two solitons and then enters explosion state, and ultimately evolves into a chaotic state. The laser operation state is correlated to dispersion profile, which could be controlled by TOD. Here, the positive dispersion at long-wavelength side will be gradually shifted to negative dispersion by increasing the TOD, where soliton effect will drive the transitions. These findings offer valuable insights into the nonlinear dynamics of ultrafast lasers and may also foster applications involving higher-order dispersion.

Soliton and dispersive wave generation with third-order dispersion and temporal boundary

We investigate the pulse evolution and energy conservation condition at the temporal boundary under third-order dispersion. When the fundamental soliton crosses the temporal boundary and forms two reflected pulses and one transmitted pulse, the power of the transmitted pulse first increases and then decreases as the incident spectrum shifts toward the blue side. If the transmitted spectrum lies in the anomalous group-velocity dispersion region, second-order soliton is formed and dispersive wave is radiated. We present a modified phase-matching condition to predict the resonance frequencies. The predicted results are in good agreement with the results obtained by numerically solving the nonlinear Schrödinger equation.

Optical and optoelectronic properties of gallium oxide films fabricated by the chemical vapour deposition method

The present work investigated the influence of growth time on the structural, optical, and optoelectronic properties of β-Ga2O3 films produced on Si substrates by the chemical vapour deposition method. The prepared films were characterized by X-ray diffraction, field-emission scanning electron microscope, and UV–Vis spectrophotometer. The films exhibited a mixed phase (β-α)-Ga2O3 crystal structure. The crystallite size ranged between 34.98 and 164.69 nm. The bandgap increased from 4.74 to 4.88 eV. The absorption and extinction coefficients were in the orders of 103 and 10−1, respectively. The refractive index, dispersive energy and single oscillator energy increased from 1.86 to 1.87, 19.24 to 28.64, and 8.36 to 9.54, respectively, with an increase of growth time. The oscillator strength, oscillator wavelength, third-order nonlinear optical susceptibility and dispersion of refractive index were in the orders of 10−4, 10−2, 10−10 and 10−9, respectively. The carrier concentration, optical conductivity, optical mobility, and optical resistivity were also evaluated. The real and imaginary dielectric constants, and plasmon frequency were also determined.

Analysis and optimization of optical frequency comb spectra of magnesium fluoride microbottle resonator

<sec>Optical frequency comb has shown great potential applications in many areas including molecular spectroscopy, RF photonics, millimeter wave generation, frequency metrology, atomic clock, and dense/ultra-dense wavelength division multiplexed high speed optical communications. Optical frequency comb in the microresonator supporting whispering-gallery mode has attracted widespread interest because of its advantages such as flexible repetition rate, wide bandwidth, and compact size. The exceptionally long photon lifetime and small modal volume enhance light-matter interaction, which enables us to realize intracavity nonlinear frequency conversions with low pump threshold. With the advantages of small size, low power consumption, wide spectral coverage and adjustable dispersion, the magnesium fluoride microresonator optical frequency comb has potential applications in optical communication and mid-infrared spectroscopy.</sec><sec>In this work, the spectral characteristics of the optical frequency comb generated by a magnesium fluoride whispering-gallery mode microbottle resonator platform are investigated. In order to optimize the spectral distribution of the optical frequency comb of the magnesium fluoride microbottle resonator, the second-order dispersion and higher-order dispersion of the bottle resonator structure under different curvatures and axial modes are solved iteratively by the finite element method, and the spectral evolutions of the optical frequency comb under different axial mode excitations are simulated by solving the nonlinear Schrödinger equation through the split-step Fourier method. The results show that near-zero anomalous dispersion tuning can be achieved in a wide bandwidth range by exciting low-order axial mode at an optimal radius of curvature, while the high-order axial mode will lead the microbottle resonator to present the weak normal dispersion. The weaker anomalous dispersion in the lower-order axial mode broadens the bandwidth of the optical comb, demonstrating that the third-order dispersion and the negative fourth-order dispersion can broaden the Kerr soliton optical comb; the weak normal dispersion in the higher-order axial mode suppresses the generation of the Kerr optical comb, and the Raman optical comb dominates. The selective excitation of Kerr soliton combs and Raman combs can be achieved by modulating the axial mode of the microbottle resonator under suitable pumping conditions. The present work provides guidance for designing the dispersion in magnesium fluoride microresonator and the experimental tuning of broadband Kerr soliton optical combs and Raman optical combs.</sec>

Few-cycle two-frequency spatiotemporal solitons in the absence of group velocity dispersion at one of the components

The second harmonic generation by few-cycle pulses is studied when the group velocity dispersion coefficient is equal to zero at the fundamental or doubled frequency. Using numerical simulation, it is shown that in both cases, in the presence of a negative third-order dispersion, the formation of stable two-frequency spatiotemporal solitons is possible.

Optical solitons of stochastic perturbed Radhakrishnan–Kundu–Lakshmanan model with Kerr law of self-phase-modulation

This study aims to obtain the optical soliton solutions of the stochastic perturbed Radhakrishnan–Kundu–Lakshmanan equation which models the optical solitons in optical waveguides such as silica fibers with Kerr law in the presence of chromatic and third-order dispersions by multiplicative white noise in Itô calculus. The study constitutes one of the works aimed at adapting the model in accordance with the importance of the noise effect in nonlinear optics. In the first step, the nonlinear ordinary differential form of the investigated problem has been obtained by using an appropriate complex wave transformation. The enhanced Kudryashov technique, which is the combination of Kudryashov and the new Kudryashov methods, is applied to the nonlinear ordinary differential form. As the result, bright, dark and singular stochastic soliton solutions of the analyzed problem have been carried out by assigning appropriate parameter values and the impact of noise effect on the soliton behavior has been investigated. Lastly, the graphical representations and required comments have been presented in the related sections.

Pure-quartic Bragg solitons in chip-scale nonlinear integrated circuits

Pure-quartic solitons have gained significant attention recently due to their ability to achieve higher energy than classical solitons for short pulse durations, leveraging the interaction between self-phase modulation and anomalous fourth-order dispersion. However, challenges in generating the required dispersion profile and the scarcity of sufficiently low-loss devices with high nonlinearity and negligible nonlinear loss have restricted experimental progress. In this paper, we report a class of pure-quartic Bragg solitons that balances self-phase modulation and the ultra-strong Bragg-grating-induced negative fourth-order dispersion in combination with negligible group velocity dispersion and negligible third-order dispersion. We demonstrate pure-quartic Bragg soliton-effect compression of 2.4× in a compact millimeter-scale integrated low-loss and highly nonlinear waveguide circuit. Our findings show the potential of exploiting the exceptional dispersion profile of nonlinear Bragg gratings for advanced soliton generation and pulse shaping, particularly the advantageous energy scaling and associated compression of pure-quartic solitons.

Highly dispersive solitons in polarization-preserving fibers by Adomian decomposition method

This paper numerically studies the existence and characteristics of highly dispersive bright optical solitons in polarization-preserving fibers. The numerical strategy adopted here is the Adomian decomposition method (ADM). The governing model is without self-phase modulation as its influence is negligible. We consider the impacts of group velocity dispersion, third-order dispersions, spatiotemporal dispersion, and nonlinear dispersions on the evolution of bright soliton. We have numerically obtained the bright soliton, which is formed as a result of robust balance among linear and nonlinear temporal as well as spatiotemporal dispersions. To check the accuracy of our numerical results we compare them with the analytical solution. The absolute error is very small and negligible even at large values of propagation time.

Significant enhancement of multiple resonant sidebands in a soliton fiber laser

Resonant sidebands in soliton fiber lasers have garnered substantial interest in recent years due to their crucial role in understanding soliton propagation and interaction dynamics. However, most previous studies and applications were restricted to focusing on only the first few low-order resonant sidebands because higher-order sidebands usually decay exponentially as their wavelengths shift far away from the soliton center and are negligibly weak. Here we report numerically and experimentally significant enhancement of multiple resonant sidebands in a soliton fiber laser mode-locked by a nonlinear polarization evolution mechanism. The birefringence and the gain profile of the laser cavity were shown to be critical for this phenomenon. Multiple intense resonant sidebands were generated whose maximum intensity was more than 30 dB higher than that of the soliton, which is the highest yet reported, to our knowledge. To accurately predict the wavelengths of all high-order resonant sidebands, an explicit formula was derived by taking the third-order dispersion effect into account. The temporal features of multiple orders of resonant sidebands were characterized, which all exhibit exponentially decaying leading edges. This study provides insight into understanding the properties of high-order resonant sidebands in a soliton laser and opens possibilities for constructing multi-wavelength laser sources.

Injection-locked soliton microcomb against temporal drifting

The soliton microcomb offers a unique and compact solution for photonics applications. However, the microcomb is suffering from the perturbations arising from complex higher-order effects such as self-steepening and third-order dispersion, leading to the temporal drift of soliton and the deviation of repetition rate. It is unfavorable to the stability in time and frequency domains. In this work, we numerically and theoretically demonstrate that the injection-locking scheme can effectively eliminate the soliton temporal drift and repetition rate deviation caused by complex higher-order effects. The mechanism of eliminating drift and deviation is explained, and the theoretically predicted stable soliton temporal position agrees well with the simulation. The modulation depth plays a key role in suppressing drift, and an experimental guide for adjusting modulation depth is given. This work enriches soliton dynamics under complex higher-order effects and provides a scheme to improve the stability and controllability of microcombs.

417 W, 2.38 mJ Innoslab amplifier compressible to a high pulse quality of 406 fs.

We demonstrate a 417 W, 175 kHz Innoslab chirped pulse amplification laser compressible to short and clean 406 fs pulse duration. A spectral bandwidth (full width at half maximum, FWHM) of ∼3 nm was maintained at full pump power, and the pulses exhibited good pulse quality in a wide tunable pulse energy range from 1.7 mJ to a maximum of 2.38 mJ. At the maximum output power, the compressed pulses were nearly pedestal free. The comprehensive effects of residual high-order dispersion from the front end, the gain shaping effects of the amplifier, and the slight mismatch of third-order dispersion (TOD) between the stretcher (CFBG) and the gating compressor, along with the small nonlinear phase shift accumulated in the amplifier, could have facilitated the high pulse quality. To the best of our knowledge, this is the shortest pulse duration from the Innoslab amplifiers at hundreds of watts average power in the millijoule energy regime.

Double and triple-pole solutions for the third-order flow equation of the Kaup-Newell system with zero/nonzero boundary conditions

In this work, the double and triple-pole solutions for the third-order flow equation of Kaup-Newell system (TOFKN) with zero boundary conditions (ZBCs) and non-zero boundary conditions (NZBCs) are investigated by means of the Riemann-Hilbert (RH) approach stemming from the inverse scattering transformation. Starting from spectral problem of the TOFKN, the analyticity, symmetries, asymptotic behavior of the Jost function and scattering matrix, the matrix RH problem with ZBCs and NZBCs are constructed. Then the obtained RH problem with ZBCs and NZBCs can be solved in the case of scattering coefficients with double or triple zeros, and the reconstruction formula of potential, trace formula as well as theta condition are also derived correspondingly. Specifically, the general formulas of N-double and N-triple poles solutions with ZBCs and NZBCs are derived systematically by means of determinants. The vivid plots and dynamics analyses for double and triple-pole soliton solutions with the ZBCs as well as double and triple-pole interaction solutions with the NZBCs are exhibited in details. Compared with the most classical second-order flow Kaup-Newell system, we find the third-order dispersion and quintic nonlinear term of the Kaup-Newell system change the trajectory and velocity of solutions. Furthermore, the asymptotic states of the 1-double poles soliton solution and the 1-triple poles soliton solution are analyzed when t tends to infinity.

Tunable modulation instability spectra in negative index materials

This paper investigates the formation of tunable modulation instability windows in metamaterials. We consider the influence of third-order dispersion, fourth-order dispersion, cubic nonlinearity, quintic nonlinearity, detuning parameter, self-steepening and higher-order nonlinear dispersions on the gain spectrum in addition to the basic requirement to observe modulation instability such as group velocity dispersion and self-phase modulation. As the metamaterials provide engineering freedom, all the material parameters are tunable, which leads to tunable modulation instability gain spectrum formation. This tunable gain spectrum provides additional ways to form solitons and ultrashort pulses with desired parameters.

Hybridization of solitons in realistic non-instantaneous fibers

Non-local nonlinearities are an integral part of numerous physical systems. Yet, their dissipative nature makes it hard to identify and verify stable eigenstates rigorously. This work sheds new light onto the existence of temporally non-local solitons – a class of dissipative self-maintaining states in time theoretically predicted to emerge in media with a time-delayed (i.e., non-instantaneous) nonlinear response. Revisiting the non-instantaneous nonlinear Schrödinger equation introduced by Conti et al., I introduce a semi-analytical approach to reveal such non-instantaneous solitons in liquid-type media which exhibit realistic non-exponential response functions featuring both rise and decay times. I investigate the susceptibility of such states to typical perturbations, such as third-order dispersion, instantaneous Kerr nonlinearity, and causality of the material response. Empirical numeric experiments illustrate how non-instantaneous solitons may compete against and even fuse with instantaneous (Kerr-type) solitons to an inseparable hybrid solitary waves. While finding a numerical solution to define the nature of this mixed state remains a challenge, I introduce a phase balance condition and other benchmarks which will allow to identify the occurrence of such states in realistic liquid-core fiber systems in future work. The findings of this study give reason to hypothetize a new type of dissipative solitary state and provide new means to understanding information transport and system dynamics of highly non-instantaneous nonlinear systems, particularly liquid-core optical fibers and waveguides.

Pure-Cubic Optical Solitons and Stability Analysis with Kerr Law Nonlinearity

In this research paper, we investigate the effects of third-order dispersion and nonlinear dispersion terms on soliton behavior for pure-cubic solitons in the absence of chromatic dispersion. The research proceeds in several stages. First, we derive the nonlinear ordinary differential equation form by utilizing the complex wave transform. In the second stage, we employ a simplified version of the new extended auxiliary equation method to derive both bright and singular optical solitons. Subsequently, we examine the influence of model parameters on these bright and singular solitons in the third stage. To support our findings, we present solution functions accompanied by effective graphical simulations. We report observations regarding the effects of parameters in the relevant sections. The validity of our results is confirmed through their satisfaction of the model equation. Furthermore, we apply the Vakhitov-Kolokolov stability criterion to ensure the stability of the obtained bright soliton solution. Notably, the novelty of this paper lies in its application of a simplified version of the extended auxiliary equation approach to recover optical solitons. This study stands apart from previously published works that utilized various expansion approaches, yielding a distinct spectrum of results.

High-order effect on the transmission of two optical solitons

For optical solitons with the pulse width in the subpicosecond and femtosecond scales in optical fibers, a modified model containing higher-order effects such as third-order dispersion and third-order nonlinearity is needed. In this paper, in order to study the dynamic mechanism of femtosecond solitons in different media, we take the nonlinear Schrödinger equation considering higher-order effects as the theoretical model, discuss the propagation of solitons in single-mode fibers, and explore the third-order dispersion and third-order nonlinear effects on the generation of optical solitons. The exact solution of the theoretical model is obtained through the bilinear method, and the transmission characteristics of two solitons with exact soliton solutions in actual fiber systems are analyzed and studied. The influence of various conditions on the transmission and interaction of optical solitons is explored. Methods for optimizing the transmission characteristics of optical solitons in optical communication systems are suggested. The relevant conclusions of this paper have guiding significance for improving the quality of fiber optic communication and increasing bit rates.

Study of a nonlinear Schrodinger equation with truncated M proportional derivative

In this work, we introduce a novel truncated M proportional (T-MP) derivative and consider a T-MP perturbed derivative nonlinear Schrodinger equation (PDNLSE). The PDNLSE is a nonlinear model which arises in nano optical fibers (photonic nanowires). While the DNLSE exhibits self-steepening (SS), the PDNLSE exhibits self-phase modulation (SPM) and Raman scattering (RS) effects, Here, the exact solutions of the PDENLSE are derived, here, by implementing the unified method. These solutions are displayed in graphs. It is found that a sufficient condition for a hyper-chaotic solution to hold is that an elliptic function solution exists. Non elliptic solutions may be, also, hyper-chaotic. It is worth mentioning that hyper chaotic may occur in economic and financial mathematics. Nonchaotic solutions exhibit many geometric structures, chirped solitons, and rhombus-shaped and M-shaped solitons. It is found that modulation instability triggers when the coefficient of the third-order dispersion exceeds a critical value. Further, the global bifurcation is investigated via phase portrait by constructing the Hamiltonian function.

Distance controlled resonant radiation from modulated Airy pulses

We investigate the dynamic evolution of resonant radiation (RR) emitted from modulated Airy pulses in an optical fiber with emphasis on the third-order dispersion. We show that the process of RRs emission strongly depends on the parameters of the predesigned spectral phase imposed on the Airy pulses, which is attributed to its linear focusing behaviors. A localized pulse formed at the distance-controlled focusing can effectively generate a large amount of RR after a prescribed propagation distance. At variance with the case of fundamental soliton, the minimum value of third-order dispersion required for the onset of RRs emission becomes much smaller for the modulated Airy pulse. The conversion efficiency of RRs increases with an increasing linear focusing point, but decreases with an increasing truncated coefficient. There is an optimal value of the truncated coefficient for the RRs having highest peak intensity and largest frequency shift. The impact of Raman effects on the RRs is also revealed. Our results not only provide a simply route to actively manipulate the efficient emission of RRs in conventional optical fiber, also could have significant implications of pulse shaping technology in novel highly efficient light sources based on the RRs emission for a variety of application.