Second-order Dispersion Research Articles

Low-noise soliton molecules generation with in-phase controllable pulse number by thirdand second-order dispersion compensation in an all-fiber erbium-doped oscillator

Low-noise soliton molecules generation with in-phase controllable pulse number by thirdand second-order dispersion compensation in an all-fiber erbium-doped oscillator

Pure-quartic soliton attracted state and multi-soliton molecules in mode-locked fiber lasers

This article explores the dynamic model of pure-quartic solitons (PQSs) in mode-locked fiber lasers. Firstly, the formation and dynamic behavior of the PQS attracted state in fiber lasers are investigated to demonstrate their exceptional stability, robustness, and predictability. Next, the transmission characteristics of single PQS in mode-locked fiber lasers is subsequently analyzed and compared to those of solitons generated while considering the effect of second-order dispersion. Finally, the evolution of multi-PQS molecules is explored, and a stability analysis method for these soliton molecules is proposed. The findings of this research are not only significant for a deeper understanding of nonlinear interaction mechanisms but also contribute to the development of ultrafast optical devices and offer new insights into the understanding and application of complex nonlinear systems.

Investigating the impact of cavity parameters on an ultrashort pulse in a fiber laser

Fiber lasers have numerous applications in various fields due to their compact design, low noise levels, high efficiency, and robust stability. We present a study focusing on the impact of cavity parameters on ultrashort pulses in fiber lasers, proposing an ultrafast laser that utilizes a MoTe2 saturable absorber (SA). Here numerical simulations allowed us to analyze the diverse pulse dynamics within a laser cavity, incorporating a SA, a segment of passive fiber, and erbium-doped fiber (EDF). Key factors of second-order dispersion, nonlinearity, gain saturation energy, small signal gain coefficient, and modulation depth and saturable energy of the SA were simulated. According to the simulations, we obtained the parameter settings for the minimum output pulse duration using a neural network and genetic algorithm. Then we proposed a normal dispersion laser with a MoTe2 mode-locker, capable of emitting dissipative soliton with a pulse duration of 824 fs and a spectrum bandwidth of 13.2 nm. These simulations provide valuable guidance for the design and optimization of fiber lasers, presenting a versatile and practical approach for applications.

On chip broadband and high extinction ratios Mach-Zehnder interferometer for DPSK signal demodulation

Differential phase shift keying (DPSK) signals are widely employed in optical communication systems due to the high sensitivity and simple self-delay interference demodulation scheme. In this paper, we demonstrate a broadband on-chip Mach-Zehnder interferometer (MZI) for multiple channel DPSK signal demodulation. The chip is constructed using a single-mode high-index doped silica glass waveguide with fiber-to-fiber insert loss less than 3 dB and small second-order dispersion. The MZI interference fringe extinction ratio is over 25 dB in the range of C- and L-bands. The MZI is employed to demodulate four parallel DPSK signals simultaneously with similar performance, indicating that the broad bandwidth MZI is suitable for a receiver of massive parallel optical communications.

Wavy approach for fluid–structure interaction with high Froude number and undamped structure

This paper addresses the fluid–structure interaction problem, with an interest on the interaction of a gravity wave with a flexible floating structure, anchored to a seabed of constant depth. To achieve this goal, we make use of the model equations, namely, the Navier–Stokes equations and the Navier–Lamé equation, as well as the associated the boundary conditions. Applying the multi-scale expansion method, these set of equations are reduced to a pair of nonlinearly coupled complex cubic Ginzburg–Landau equations (CCGLE). By applying the proposed modified expansion method, the group velocity dispersion and second-order dispersion relation are deduced. In the same vein, modulation instability (MI) is investigated as a mechanism of formation of pulse trains in fluid–structure system using a CCGLE. For the analytical analysis, we made use of the inverse scattering method to find analytical solutions to the coupled nonlinear equations. Through that method, the obtained solutions depict rogue-shaped waves. Our results suggest that uncontrolled MI within the interaction between a flexible body and gravity waves in viscous flow may be considered as the principal source of many structural ruptures, which are the first cause of critical damage due to the great energy and unpredictability of rogue waves. The present work aims to provide tools to model a wide range of physical problems regarding the interaction of surface gravity waves and an offshore-anchored structure, and it aims to be essential to our understanding of the nonlinear characteristics of offshore structures in real-sea states.

Pure-high-even-order dispersion bound solitons complexes in ultra-fast fiber lasers

Temporal solitons have been the focus of much research due to their fascinating physical properties. These solitons can form bound states, which are fundamentally crucial modes in fiber laser and present striking analogies with their matter molecules counterparts, which means they have potential applications in large-capacity transmission and all-optical information storage. Although traditionally, second-order dispersion has been the dominant dispersion for conventional solitons, recent experimental and theoretical research has shown that pure-high-even-order dispersion (PHEOD) solitons with energy-width scaling can arise from the interaction of arbitrary negative-even-order dispersion and Kerr nonlinearity. Despite these advancements, research on the bound states of PHEOD solitons is currently non-existent. In this study, we obtained PHEOD bound solitons in a fiber laser using an intra-cavity spectral pulse shaper for high-order dispersion management. Specifically, we experimentally demonstrate the existence of PHEOD solitons and PHEOD bound solitons with pure-quartic, -sextic, -octic, and -decic dispersion. Numerical simulations corroborate these experimental observations. Furthermore, vibrating phase PHEOD bound soliton pairs, sliding phase PHEOD bound soliton pairs, and hybrid phase PHEOD bound tri-soliton are discovered and characterized. These results broaden the fundamental understanding of solitons and show the universality of multi-soliton patterns.

Dynamics of optical pulses with the effect of second-order spatiotemporal dispersion

Dynamics of optical pulses with the effect of second-order spatiotemporal dispersion

Optical nondegenerate solitons in a birefringent fiber with a 35 degree elliptical angle.

In this paper, we investigate the optical nondegenerate solitons in a birefringent fiber with a 35 degree elliptical angle. We derive the nondegenerate bright one- and two-soliton solutions by solving the coupled Schrödinger equation. The formation of nondegenerate solitons is related to the wave numbers of the solitons, and we further demonstrate that it is caused by the incoherent addition of different components. We note that the interaction between two degenerate solitons or a nondegenerate soliton and a degenerate soliton is usually inelastic. This is led to the incoherent interaction between solitons of different components and the coherent interaction between solitons of the same component. Through the asymptotic analysis, we find that the two degenerate solitons are elastic interactions under certain conditions, and analyzed the influence of the Kerr nonlinear intensity coefficient γ and the second-order group velocity dispersion β2 in this system on solitons: the velocity and amplitude of the solitons are proportional to |β2|, while the amplitude of the solitons is inversely proportional to γ. Two nondegenerate solitons are elastic interactions, but the phase of the soliton can be adjusted to make it inelastic. Furthermore, regardless of the situation mentioned above, total intensities of the solitons before the interaction are equal to that after the soliton interaction.

Dual Galilean invariance in a temporally dispersive medium.

The bidispersive equation, accounting for second-order temporal dispersion in a lossless medium, is examined under a Galilei-like transformation, as well as a conditional ordinary Galilei transformation. In the former case, the roles of space and time are reversed by comparison to the application of the same transformation to the quantum mechanical Schrödinger equation. Such an invariance can result in envelope speeds that can assume values above or below the group speed of the medium; also, they can be negative. Conditional Galilei transformation results in a decrease in dimensionality.

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>

Novel investigations of dual-wave solutions to the Kadomtsev–Petviashvili model involving second-order temporal and spatial–temporal dispersion terms

Our work presents a novel insight into a higher dimensional Kadomtsev–Petviashvili (KP) model, wherein we observe that the propagation of the proposed model is characterized by the movement of symmetric dual waves. These waves are the result of the superposition of two waves with equal amplitude and opposite phase, which arises due to the involvement of a second-order temporal dispersion term in the model. Our study involves several schemes, leading to the discovery of various physical structures associated with the KP model. In summary, our research emphasizes that the simultaneous propagation of symmetric waves has significant practical applications in numerous fields where precise measurement, control, or analysis of waves is crucial.

AlGaAs soliton microcombs at room temperature.

Soliton mode locking in high-Q microcavities provides a way to integrate frequency comb systems. Among material platforms, AlGaAs has one of the largest optical nonlinearity coefficients, and is advantageous for low-pump-threshold comb generation. However, AlGaAs also has a very large thermo-optic effect that destabilizes soliton formation, and femtosecond soliton pulse generation has only been possible at cryogenic temperatures. Here, soliton generation in AlGaAs microresonators at room temperature is reported for the first time, to the best of our knowledge. The destabilizing thermo-optic effect is shown to instead provide stability in the high-repetition-rate soliton regime (corresponding to a large, normalized second-order dispersion parameter D2/κ). Single soliton and soliton crystal generation with sub-milliwatt optical pump power are demonstrated. The generality of this approach is verified in a high-Q silica microtoroid where manual tuning into the soliton regime is demonstrated. Besides the advantages of large optical nonlinearity, these AlGaAs devices are natural candidates for integration with semiconductor pump lasers. Furthermore, the approach should generalize to any high-Q resonator material platform.

Physical compensation method for dispersion of multiple materials in swept source optical coherence tomography.

An ophthalmic swept source-optical coherence tomography (SS-OCT) system based on a high-speed scanning laser at 1060 nm with a scanning rate of 100 KHz is constructed. Since the sample arm of the interferometer is comprised of multiple glass materials, the ensuing dispersion severely degrades imaging quality. In this article, second-order dispersion simulation analysis for various materials was performed first, and dispersion equilibrium was implemented utilizing physical compensation methods. After dispersion compensation, an imaging depth in air of 4.013 mm was achieved in model eye experiments, and signal-to-noise ratio was enhanced by 11.6%, with a value of 53.8 dB. In vivo imaging of the human retina was performed to demonstrate structurally distinguishable retinal images, characterized by an axial resolution improvement of 19.8%, with a value of 7.7 μm close to the theoretical value of 7.5 μm. The proposed physical dispersion compensation method enhances imaging performance in SS-OCT systems, enabling visualization of several low scattering mediums.

High Efficiency Third-Harmonic Generation in a Medium with Quadratic Susceptibility Due to Cubic-like Nonlinearity Caused by Cascaded Second-Harmonic Generation

Third-harmonic generation (THG) is of interest for its various applications. We propose using the cascaded second-harmonic generation (SHG) to implement the frequency conversion process, which is similar to that occurring in a medium with cubic susceptibility. Physically, the process is based on consecutive generation of the second-harmonic and the sum frequency in the same crystal with quadratic susceptibility at large phase mismatching between the fundamental wave and the second-harmonic wave. In this case, at phase matching between the fundamental wave and the third-harmonic wave, THG occurs with high efficiency. To demonstrate such a possibility theoretically, we apply the multi-scale method to a set of Schrödinger equations, describing a three-wave interaction with the frequencies ω,2ω and 3ω in a medium with quadratic susceptibility, to derive modified equations describing the frequency tripling process. These equations are solved without using the fundamental wave energy non-depletion approximation. A THG efficiency equal to 94.5% is predicted theoretically. The analytical solution is confirmed by computer simulation results. We study how various factors, such as the incident pulse intensity, phase mismatching between interacting waves, group velocity mismatching of the pulses, and second-order dispersion of the wave packets influence the THG process.

Single-beam technique for ultrashort pulse characterization based on the nonlinear ellipse rotation signal

We present a single-beam method based on the third-order nonlinear-ellipse-rotation (NER) measurement in thick samples to determine the pulse properties, including the duration and linear chirp. Our approach exploits the influence of the intrinsic second-order dispersions of the nonlinear materials, which affect the NER signal as a function of propagation. Two advantages can be highlighted: no delay line is required, and there are no phase-matching issues. To test our method, we characterized ultrafast chirped pulses from a Ti:sapphire amplified laser system and tunable pulses from an optical parametric amplifier using two samples with high dispersions and nonlinearities: SF6 and LaSF-N30 optical glasses.

Various exact optical soliton solutions for time fractional Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients

Various exact optical soliton solutions for time fractional Schrodinger equation with second-order spatiotemporal and group velocity dispersion coefficients

Predicting nonlinear reshaping of periodic signals in optical fibre with a neural network

We deploy a supervised machine-learning model based on a neural network to predict the temporal and spectral reshaping of a simple sinusoidal modulation into a pulse train having a comb structure in the frequency domain, which occurs upon nonlinear propagation in an optical fibre. Both normal and anomalous second-order dispersion regimes of the fibre are studied, and the speed of the neural network is leveraged to probe the space of input parameters for the generation of custom combs or the occurrence of significant temporal or spectral focusing.

Compact Metasurface-Based Optical Pulse-Shaping Device.

Dispersion is present in every optical setup and is often an undesired effect, especially in nonlinear-optical experiments where ultrashort laser pulses are needed. Typically, bulky pulse compressors consisting of gratings or prisms are used to address this issue by precompensating the dispersion of the optical components. However, these devices are only able to compensate for a part of the dispersion (second-order dispersion). Here, we present a compact pulse-shaping device that uses plasmonic metasurfaces to apply an arbitrarily designed spectral phase delay allowing for a full dispersion control. Furthermore, with specific phase encodings, this device can be used to temporally reshape the incident laser pulses into more complex pulse forms such as a double pulse. We verify the performance of our device by using an SHG-FROG measurement setup together with a retrieval algorithm to extract the dispersion that our device applies to an incident laser pulse.

Computational design of the novel building blocks for the metal-organic frameworks based on the organic ligand protected Cu4 cluster

Abstract Metal-organic frameworks (MOFs) are tunable porous network compounds composed of inorganic nodes bound by various organic linkers. Here we report the density functional theory (DFT) study of the MOF novel building blocks made of the Cu4 clusters protected by four organic ligands having two phenyl rings and terminated either with Cl or Br atom (precursors 1 and 2, respectively). The research was performed both in the gas phase and with the implicit effects of acetonitrile included, with two functionals, B3LYP and PBE, both with and without the second-order dispersion correction. We analyzed the structural features of the precursors 1 and 2, their electronic structures, molecular electrostatic potential (MEP) distribution, and global reactivity parameters (GRPs). Both functionals resulted in the singlets of the precursors 1 and 2 as the most stable species. The precursor structures optimized with the hybrid functional were found to be quite similar for both halogens, both containing somewhat distorted from planarity Cu4 cluster, with the outer phenyls of the ligands rotated relative to the inner phenyls. With both halogens and both DFT approaches, the frontier molecular orbitals (FMOs) of the precursors 1 and 2 were shown to have quite similar compositions. The change of the substituent from Br to Cl was found to cause slight stabilizations or destabilizations of the HOMOs and LUMOs. The central parts and especially the inner phenyl ring parts of the precursors 1 and 2 were suggested to play a role of nucleophile in various chemical reactions due to the significant accumulation of negative electrostatic potential. Also, weak intermolecular interactions might exist between the ligands of neighboring precursor molecules. Finally, with both substituents the precursors 1 and 2 should be relatively unreactive and demonstrate thermodynamic stability. Further, the precursors 1 and 2 should be quite stable in oxidation reactions and more active in reduction processes. Generally, the substituent nature was shown not to affect significantly the reactivity of the precursors 1 and 2, as well as their other properties.

Wideband multimode optical parametric oscillation in a Kerr microresonator.

Parametric oscillation in Kerr microresonators provides an attractive pathway for the generation of new optical frequencies in a low-power, small-footprint device. The frequency shift of the newly generated parametric sidebands is set by the phasematching of the underlying four-wave-mixing process, with the generation of large frequency shift sidebands typically placing exacting requirements on a resonator's dispersion profile. In practice, this limits the range of viable pump wavelengths, and ultimately the range of output frequencies. In this paper, we consider a multimode four-wave-mixing process in which the pump and sidebands propagate in different mode families of the resonator. We show that this multimode configuration yields a considerable relaxation in the phasematching requirements needed to generate large frequency shift parametric sidebands, allowing their formation even in resonators with strong second-order dispersion. Experimentally we use a magnesium-fluoride micro-disk resonator to demonstrate this multimode phasematching. By accessing different pump and sideband modes, four distinct multimode parametric processes generating frequency shifts between 118 and 216 THz are reported. The resulting separation between the two sidebands is almost three octaves.