Higher-order Dispersion Research Articles

Ultrafast polarization characterization with Mueller matrix based on optical time-stretch and spectral encoding.

High-speed optical polarization characterization is highly desirable for a wide range of applications, including remote sensing, telecommunication, and medical diagnosis. The utilization of the Mueller matrix provides a superior systematic and comprehensive approach to represent polarization attributes when matter interacts with optical beams. However, the current measurement speed of Mueller matrix is limited to only seconds or milliseconds. In this study, we present an ultrafast Mueller matrix polarimetry (MMP) technique based on optical time-stretch and spectral encoding that enables us to achieve an impressive temporal resolution of 4.83 nanoseconds for accurate Mueller matrix measurements. The unique feature of optical time-stretch technology enables continuous, ultrafast single-shot spectroscopy, resulting in a remarkable speed of up to 207 MHz for spectral encoding Mueller matrix measurement. We have employed an effective Mueller linear reconstruction algorithm based on the measured modulation matrix, accounting for all potential non-ideal effects of polarization components like retardance error and azimuth error. To ensure high precision, prior to the actual measurement, high-order dispersion induced by time-stretch requires adjustment through proper modulation matrix design. Upon such correction, both the results of static and rapid dynamic samples measurements exhibit exceptional accuracy with root-mean-square error (RMSE) approximately equal to 0.04 and 0.07 respectively. This presented ultrafast MMP provides a significant advance over preceding endeavors, enabling superior accuracy and increased speed concurrently.

Modulation instability with high-order dispersion: fundamental limitations of pattern formation.

We theoretically and numerically investigate modulation instability in the presence of even, high-order dispersion, focusing on general trends rather than on specific results for a particular dispersion order. We show that high-order dispersion leads to increasingly poor phase matching between the three central waves (i.e. the pump and the ±1 sidebands) and the higher sideband orders, inhibiting in effect four-wave mixing frequency generation. For sufficiently large dispersion orders, the problem in effect can reduce to a three-wave system. Our predictions are in excellent agreement with numerical simulations and show that high-order dispersion imposes a fundamental limit on modulation instability dynamics.

Shortcuts to adiabatic soliton compression in active nonlinear Kerr media.

We implement variational shortcuts to adiabaticity for optical pulse compression in an active nonlinear Kerr medium with distributed amplification and spatially varying dispersion and nonlinearity. Starting with the hyperbolic secant ansatz, we employ a variational approximation to systematically derive dynamical equations, establishing analytical relationships linking the amplitude, width, and chirp of the pulse. Through the inverse engineering approach, we manipulate the distributed gain/loss, nonlinearity and dispersion profiles to efficiently compress the optical pulse over a reduced distance with high fidelity. In addition, we explore the dynamical stability of the system to illustrate the advantage of our protocol over conventional adiabatic approaches. Finally, we analyze the impact of tailored higher-order dispersion on soliton self-compression and derive physical constraints on the final soliton width for the complementary case of soliton expansion. The broader implications of our findings extend beyond optical systems, encompassing areas such as cold-atom and magnetic systems highlighting the versatility and relevance of our approach in various physical contexts.

Neutral delay differential equationmodel of an optically injected Kerr cavity.

A neutral delay differential equation(NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second- and higher-order dispersion being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the low dissipation limit, where the model can be reduced to the Lugiato-Lefever equation(LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE, the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes.

Solitonic rogue and modulated wave patterns in the monoatomic chain with anharmonic potential

Modulation instability and rogue wave structures have been investigated in this work. This study is an extension of the work in Abbagari (2023), where a nonlinear Schrödinger equation with higher-order dispersion is derived to show only the development of the modulated waves bounded to bright soliton as a nonlinear exhibition of modulation instability. Here, the coupled nonlinear Schrödinger equation is derived by using the multi-scale scheme. An overview of the analytical calculations of the perturbed plane wave is carried out to show the effects of the nonlinear chain parameters on the modulation instability growth rate and bandwidths. The interest of this study lies equally in the nonlinear modes of excitation, where solitonic waves are generated under certain conditions in lower and upper frequency bands. On the other hand, relevant results have been developed to show the features of the type I and type II rogue waves of the Manakov system. Such investigations are obtained under the variation of the interaction potential parameters and the free parameter of the similarity method. Via a numerical simulation, rogue wave structures have been generated as a consequence of the long-time evolution of the perturbed plane wave. At a specific time of propagation, another localized object has been obtained to show the Akhmediev breathers and Kuznetsov-Ma solitons clusters under a strong perturbed wave number. These results have opened up new features, and many applications could follow in the future.

Impact of higher-order dispersion on frequency-modulated combs.

Frequency-modulated (FM) combs form spontaneously in free-running semiconductor lasers and possess a vast potential for spectroscopic applications. Despite recent progress in obtaining a conclusive theoretical description, experimental FM combs often exhibit non-ideal traits, which prevents their widespread use. Here we explain this by providing a clear theoretical and experimental study of the impact of the higher-order dispersion on FM combs. We reveal that spectrally dependent dispersion is detrimental for comb performance and leads to a decreased comb bandwidth and the appearance of spectral holes. These undesirable traits can be mended by applying a radio frequency modulation of the laser bias. We show that electrical injection-locking of the laser leads to a significant increase of the comb bandwidth, a uniform-like spectral amplitudes, and the rectification of the instantaneous frequency to recover a nearly linear frequency chirp of FM combs.

Research on the influence of intra-cavity dispersion on pulse characteristics of a quartic soliton fiber laser

Abstract We numerically investigate the influence of higher-order dispersion on the dynamics of quartic solitons in a passively mode-locked fiber laser. The simulation results show that the output pulse characteristics of the quartic soliton fiber laser are not only affected by the intra-cavity net dispersion but also related to the position of the single-mode fiber (SMF). For different intra-cavity net higher-order dispersion values, the quartic soliton undergoes multiple alternations between the stable single soliton state and pulsating state in the fiber laser, and the number and intensity of Kelly sidebands in the output pulse spectrum are significantly different. For different positions of the SMF, the dynamics of the quartic soliton are also different. In addition, we also observe two types of novel pulsation-creeping behavior and time shift. These findings provide new insights into the output characteristics of quartic solitons in fiber lasers.

Bragg scattering of nonlinear surface waves by sinusoidal sandbars

Based on the multiple-scale expansion technique, a new set of extended nonlinear Schrödinger (ENLS) equations up to the third order is derived to account for the additional high-order bottom and dispersion effects as well as the nonlinear wave interaction on wave transformation over periodic sandbars of sinusoidal geometry. By employing the small-amplitude wave assumption, a closed-form analytical solution for Bragg scattering is obtained from the linearised ENLS equations, which demonstrates that a downshift of wave frequency of the maximum reflection is mainly due to the inclusion of the high-order bottom effect. The factors that affect the downshift of the resonant frequency are identified and a theoretical expression in parabolic form is derived to quantify the downshift magnitude. The fully ENLS equations are further analysed to reveal the additional wave nonlinear effects on Bragg scattering characteristics. Under the condition of infinitesimal sandbar amplitude, the ENLS equations render a theoretical expression of the critical value of $kh$ when the nonlinear wave self-modulation effect and the nonlinear wave cross-modulation effect are equal, whereas the former effect is responsible for wavenumber upshifting and the latter downshifting. When $kh$ is larger than the critical value, the increase of wave nonlinearity will enhance the downshift magnitude of the Bragg resonance, and vice versa. For finite amplitude of the bottom sandbar, the ENLS equations are solved numerically to examine the influence of both wave nonlinearity and sandbar amplitude on the characteristics of Bragg resonance. The results reveal that as the increase of sandbar amplitude, the critical $kh$ increases monotonically.

28 THz soliton frequency comb in a continuous-wave pumped fiber Fabry–Pérot resonator

We report the generation of an optical frequency comb featuring a 28 THz bandwidth, sustained by a single 80 fs cavity soliton recirculating in a fiber Fabry–Pérot resonator. This large spectrum is comparable to frequency combs obtained with microresonators operating in the anomalous dispersion regime. Thanks to the compact design and the easy coupling of the resonator, cavity solitons can be generated in an all-fiber experimental setup with a continuous wave pumping scheme. We also observe the generation of a dispersive wave at higher frequencies, which is supported by higher-order dispersion. These observations align remarkably well with both numerical simulations and the established theory of cavity solitons.

Doubly charged single Weyl pair with complete spin polarization

An ideal charge-two single Weyl pair with complete spin polarization has been unveiled in the Cu-doped lead apatite Pb9Cu(PO4)6O, laying the groundwork for exploring the topological properties with both magnetic ordering and high-order dispersion.

Broadband near-visible frequency comb generation via high-order mode dispersion engineering in a microbubble resonator

Broadband near-visible frequency comb generation via high-order mode dispersion engineering in a microbubble resonator

The novel numerical solutions for time-fractional Fornberg-Whitham equation by using fractional natural transform decomposition method

<p>The time-fractional partial differential equations were solved by the fractional natural transform decomposition method. Fractional derivatives are Caputo sense. The Fornberg-Whitham equation is a generalization of the Korteweg-de Vries (KdV) equation, which describes the propagation of long waves in shallow water. It includes higher-order dispersion terms, making it applicable to a wider range of dispersive media the fractional natural transform decomposition method (FNTDM) was also used to examine applications, and the solutions obtained by this method have been compared to those obtained by the variational iteration method, fractional variational iteration method, and homotopy perturbation method. In addition, the MAPLE package drew graphs of the solutions of nonlinear time-fractional partial differential equations, taking into account physics. The method described in this study exhibited a notable degree of computational precision and straightforwardness when used to the analysis and resolution of intricate phenomena pertaining to fractional nonlinear partial differential equations within the domains of science and technology.</p>

Extraction of new solitary wave solutions in a generalized nonlinear Schrödinger equation comprising weak nonlocality.

This article delves into examining exact soliton solutions within the context of the generalized nonlinear Schrödinger equation. It covers higher-order dispersion with higher order nonlinearity and a parameter associated with weak nonlocality. To tackle this equation, two reputable methods are harnessed: the sine-Gordon expansion method and the [Formula: see text]-expansion method. These methods are employed alongside suitable traveling wave transformation to yield novel, efficient single-wave soliton solutions for the governing model. To deepen our grasp of the equation's physical significance, we utilize Wolfram Mathematica 12, a computational tool, to produce both 3D and 2D visual depictions. These graphical representations shed light on diverse facets of the equation's dynamics, offering invaluable insights. Through the manipulation of parameter values, we achieve an array of solutions, encompassing kink-type, dark soliton, and solitary wave solutions. Our computational analysis affirms the effectiveness and versatility of our methods in tackling a wide spectrum of nonlinear challenges within the domains of mathematical science and engineering.

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>

Efficient dual-stage all-solid-state post-compression for 100 W level ultrafast lasers

Abstract We demonstrate efficient and economical all-solid-state post-compression based on dual-stage periodically placed thin fused silica plates driven by a more than 100 W ytterbium-doped yttrium aluminum garnet Innoslab amplifier seeded by a fiber frontend. Not only is a more than eight-fold pulse compression with 94% transmission achieved, but also the pulse quality and spatial mode are improved, which can be attributed to the compensation for the residual high-order dispersion and the spatial mode self-cleaning effect during the nonlinear process. It enables a high-power ultrafast laser source with 64 fs pulse duration, 96 W average power at 175 kHz repetition rates and good spatiotemporal quality. These results highlight that this all-solid-state post-compression can overcome the bandwidth limitation of Yb-based lasers with exceptional efficiency and mitigate the spatiotemporal degradation originating from the Innoslab amplifier and fiber frontend, which provides an efficient and economical complement for the Innoslab laser system and facilitates this robust and compact combination as a promising scheme for high-quality higher-power few-cycle laser generation.

Study of Soliton Interaction in Optical Fibers with Third Order Dispersion and Higher Order Nonlinear Effects

In this paper, we present a numerical approach to solve the GNLSE and analyze soliton interaction phenomena using COMSOL environment. By leveraging the capabilities of COMSOL's PDE module, we can accurately capture the dynamics of solitons and investigate their interactions. We analyze the impact of different parameters such as soliton power, initial separation distance, and dispersion characteristics on the soliton dynamics. Furthermore, we examine the role of higher-order dispersion terms in shaping the soliton interactions. Our findings demonstrate the effectiveness of the proposed numerical approach in accurately simulating and analyzing soliton interaction phenomena. The COMSOL-based methodology provides a flexible and efficient framework for studying complex nonlinear optical systems, enabling researchers to gain insights into the behavior of solitons in different media and design optimized communication systems. This paper contributes to the understanding of soliton dynamics and provides a practical tool for investigating the behavior of solitons in nonlinear dispersive media. The presented numerical approach using COMSOL opens avenues for further research in nonlinear optics and fiber optic communication systems.

On the persistence of spatial analyticity for generalized KdV equation with higher order dispersion

AbstractPersistence of spatial analyticity is studied for solutions of the generalized Korteweg‐de Vries (KdV) equation with higher order dispersion where , are integers. For a class of analytic initial data with a fixed radius of analyticity , we show that the uniform radius of spatial analyticity of solutions at time cannot decay faster than as . In particular, this improves a recent result due to Petronilho and Silva [Math. Nachr. 292 (2019), no. 9, 2032–2047] for the modified Kawahara equation (, ), where they obtained a decay rate of order . Our proof relies on an approximate conservation law in a modified Gevrey spaces, local smoothing, and maximal function estimates.

Cavity soliton formation in Kerr comb oscillators via input phase and amplitude modulation in the presence of high order dispersion

The generation of dissipative cavity solitons (CSs) in Kerr microresonators through pulsed driving is an effective method for generating coherent optical microcombs. Yet, the underlying physics has not been fully investigated. Our study investigates the effect of high-order dispersion on the generation of Kerr frequency combs in Si3N4 microresonator driven by phase- and amplitude-modulated inhomogeneities of the pump which had not been studied before. Here, we present a numerical and theoretical analysis of the effects of desynchronization and the pulsed driving chirp parameter on the train of solitons circulating in the cavity for various detunings. In this case, deterministic production of a K-band single soliton, as well single breather soliton has been investigated. Our results show that high-order dispersion can also affect CSs positioning, stability, and existence.

Modeling of Nonlinear Sea Wave Modulation in the Presence of Ice Coverage

A model accounting for the influence of ice coverage on the propagation of surface sea waves is suggested. The model includes higher-order linear and nonlinear terms in the equation of wave motion. The asymptotic solution is obtained to account for nonlinear modulated wave propagation and attenuation. Two kinds of attenuation are revealed. The influence of the higher-order nonlinear, dispersion, and dissipative terms on the shape and velocity of the modulated nonlinear wave is studied. Despite the presence of higher-order terms in the original equation, the modulated solitary wave solution contains free parameters, which is important for the possible generation of such waves.

Design and pulse-formation properties of chirped pulse Kerr solitons.

Kerr resonators generate stable frequency combs and ultrashort pulses with applications in telecommunications, biomedicine, and metrology. Chirped pulse solitons recently observed in normal dispersion Kerr resonators with an intracavity spectral filter can enable new material design freedom, reduced fabrication requirements, and the potential for improved ultrashort pulse peak powers. This study examines the design and formation properties of chirped-pulse Kerr solitons essential for enabling these advances. First, prior theoretical predictions that chirped pulse solitons are relatively insensitive to cavity loss and the strength of the dispersion map are experimentally validated. The loss insensitivity property is applied toward demonstrating high energy pulses in a cavity with large output coupling and the map insensitivity property is applied toward demonstrating femtosecond pulses, for the first time from chirped-pulse solitons, in a dispersion-mapped cavity with small net-normal dispersion. The relationship between chirped pulses and bright pulses enabled by higher order dispersion is examined with respect to pulse formation, cavity design parameters, and performance properties. Finally, guidelines for additional improvements are detailed for chirped pulse soliton-based high-performance pulse generation.