Quartic Solitons Research Articles

Generic quartic solitons in optical media

Our analysis suggests strongly that stationary pulses exist in nonlinear media with second-, third-, and fourth-order dispersion. A theory, based on the variational approach, is developed for finding approximate parameters of such solitons. It is obtained that the soliton velocity in the retarded reference frame can be different from the inverse of the group velocity of linear waves. It is shown that the interaction of the pulse spectrum with that of linear waves can affect the existence of stationary solitons. These theoretical results are supported by numerical simulations. Transformations between solitons of different systems are derived. A generalization for solitons in media with the highest even-order dispersion is suggested. Published by the American Physical Society 2024

Transition Between Quadratic and Quartic Solitons With OAM Modes in Passive Driven Fiber Resonator

Transition Between Quadratic and Quartic Solitons With OAM Modes in Passive Driven Fiber Resonator

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.

Frequency-tunable quartic soliton in nonlinear negative-index metamaterials

An exact quartic soliton solution along with its constraint conditions in metamaterials (MMs) is presented on the basis of the nonlinear Schrödinger equation (NLSE) with second-, third- and fourth-order diffraction. Through analyzing the parameter relations based on the Drude model, it is demonstrated that the quartic soliton can only exist in the negative-index region (NIR) of self-focusing nonlinear MMs. With insight into the underlying parameter relations of quartic soliton, it is found that by selecting suitable frequency of incident wave, the quartic soliton in negative-index MMs (NIMs) exhibits frequency tunability or frequency stability. Particularly, the quartic solitons with different frequencies can propagate in an identical velocity, which provides a theoretical basis for realizing frequency division multiplexing (FDM) technology in nonlinear MMs. Different from pure-quartic soliton (PQS) in ordinary materials exhibiting oscillatory decaying tails in spatial domain and a flat top in frequency domain on logarithmic scale, the quartic soliton reported here possesses triangular distributions in both spatial and frequency domains. The presented results contribute to a fundamental theoretical support for future application of quartic soliton and are beneficial for exploring new solitary waves in MMs.

Quartic solitons of a mode-locked laser distributed model.

Dissipative quartic solitons have gained interest in the field of mode-locked lasers for their energy-width scaling which allows the generation of ultrashort pulses with high energies. Pursuing the characterization of such pulses, here we found soliton solutions of a distributed model for mode-locked lasers in the presence of either positive or negative fourth-order dispersion (4OD). We studied the impact the laser parameters may have on the profiles, range of existence, and energy-width relation of the output pulses. The most energetic and narrowest solutions occur for negative 4OD, with the energy having an inverse cubic dependence with the width in most cases. Our simulations showed that the spectral filtering has the biggest contribution in the generation of short (widths as low as 39 fs) and very energetic (391 nJ) optical pulses.

Cubic–Quartic Optical Soliton Perturbation for Fokas–Lenells Equation with Power Law by Semi-Inverse Variation

The current work addresses cubic–quartic solitons to compensate for the low count of the chromatic dispersion that is one of the major hindrances of soliton transmission through optical fibers. Thus, the present paper handles the cubic–quartic version of the perturbed Fokas–Lenells equation that governs soliton communications across trans-oceanic and trans-continental distances. The model is also considered with the power-law form of nonlinear refractive index that is a sequel to the previously reported result. This is a tremendous advancement to the previously known result that was only with the Kerr-law form of nonlinear refractive index. The present paper mainly contributes by generalizing the Kerr law of nonlinearity to the power law of nonlinearity. The prior results therefore fall back as a special case to the results of this paper. The semi-inverse variational principle yields a bright 1-soliton solution that is imperative for the telecommunication engineers to carry out experimental investigation before the rubber meets the road. Hamiltonian perturbation terms are included that come with maximum intensity. The soliton amplitude–width relation is retrievable from a polynomial equation with arbitrary degree. The parameter constraints are also identified for the soliton to exist.

Raman-induced frequency shift of pure quartic solitons in optical fiber with quartic dispersion.

We investigate the impact of Raman scattering on pure quartic solitons (PQSs) in an optical fiber with quartic dispersion. An analytical expression of the Raman-induced frequency shift (RIFS) of a PQS is obtained by using the variational approach with the Gaussian function ansatz. We find the RIFS of a PQS is inversely proportional to the sixth power of pulse width, when the fiber is short enough. The RIFS of a PQS is more sensitive to the pulse width, compared with that of a conventional soliton which is inversely proportional to the fourth power of pulse width. The theoretical predictions show good agreement with numerical results. In addition, we also discuss the RIFS of the other three typical pulses with the same peak power and pulse width as the PQS. These results provide a thorough understanding of the role of higher-order nonlinear effects on the propagation dynamics of PQSs.

Cubic–quartic solitons in twin-core couplers with optical metamaterials having Kudryashov’s sextic power law of arbitrary refractive index by using improved modified extended tanh-function method

In this article, the improved modified extended tanh-function method is applied to obtain optical solitons for the cubic–quartic (CQ) twin-core couplers in optical metamaterials having Kudryashov’s sextic power law of arbitrary refractive index. Various types of solutions are raised such as bright solitons, dark solitons, singular solitons, periodic solutions, singular periodic solutions, hyperbolic-type solutions, rational-type solution, Jacobi elliptic wave solutions, exponential wave solutions and Weierstrass elliptic doubly periodic-type solutions. Moreover, for the physical illustration of the obtained solutions 2D, 3D and contour graphs are presented.

Construction cubic-quartic solitons in optical metamaterials for the perturbed twin-core couplers with Kudryashov's sextic power law using extended F-expansion method

In this article, we consider the twin-core couplers with Kudryashov's sextic power law of refractive index and perturbation terms. The extended F-expansion method is implemented to construct cubic–quartic solitons in optical metamaterials and other solutions for the proposed model. Bright soliton solutions, singular soliton solutions, periodic solutions and combo periodic solutions are obtained. Moreover, for the physical illustration, some of the obtained solutions are represented graphically.

Cubic–quartic optical solitons in fiber Bragg gratings with anti-cubic nonlinearity using the modified extended direct algebraic method

Objective:This paper obtains cubic–quartic solitons in fiber Bragg gratings with anti-cubic nonlinearity. Methods:The extended direct algebraic integration algorithm is adopted. Results:Dark, bright and singular solitons are recovered along with their respective parameter constraints for their existence. Conclusion:The integration tool yields solutions in terms of Jacobi’s elliptic functions which led to the emergence of optical solitons from the limiting operation applied to the modulus of ellipticity. The results are thus extremely promising to move ahead with this approach to study additional forms of self-phase modulation coupled with other forms of dispersive effects.

Cubic–quartic optical soliton perturbation with Fokas–Lenells equation having maximum intensity

Objective:This paper reviews cubic–quartic Fokas–Lenells equation with perturbation terms having power-law of nonlinear refractive index for the first time. Methods:Six integration algorithms granted success with this retrieval. Results:Mathematical formulations yield bright and singular solitons with the model along with their corresponding existence criterion. Conclusion:The novelty of this paper is the extension of Kerr law to power-law and that too for cubic–quartic solitons that have emerged from the model. It has been verified if the power law nonlinearity parameter collapses to unity, all results of the paper reduce to the ones for Kerr law which are visible all over.

Dark gap solitons in one-dimensional nonlinear periodic media with fourth-order dispersion

The studies of solitons are usually confined to the models with normal two-order dispersion or diffraction; while recent theoretical predictions and experimental observations have confirmed the important role that the fourth-order dispersion played in, leading to the discovery of a new class of solitons—quartic solitons in fibers. We here theoretically consider the one-dimensional (1D) periodic nonlinear media with both second-order and fourth-order dispersions, and uncover numerically the existence, properties, and stabilities of dark gap solitons populated within the associated linear photonic band gaps. Such gaps, particularly, are affected drastically by normal or anomalous fourth-order dispersion; the dark gap solitons are always found to be unstable for the latter, and are robustly stable and have a wide stability region for the former case, verified by linear-stability analysis and direct perturbed simulations. The obtained results provide insights into physics of dark gap solitons in higher-order dispersion regime.

Cubic-quartic optical solitons and other solutions for twin-core couplers with polynomial law of nonlinearity using the extended F-expansion method

In this article, the extended F-expansion method is applied to secure cubic–quartic optical solitons for twin-core couplers with polynomial law of nonlinearity. Bright, singular, and bright–singular combo cubic–quartic solitons are derived. Also, periodic solutions, combo periodic solutions, exponential solutions and rational solutions are obtained. Moreover, for the physical illustration, some of the obtained solutions are represented graphically.

Cubic–quartic solitons in couplers with optical metamaterials having triple-power law nonlinearity (sequel to polynomial law)

This paper retrieves soliton solutions to couplers in optical metamaterials with triple-power law of nonlinear refractive index and is thus a sequel to previously reported results with polynomial law of nonlinear refractive index. The enhanced Kudryashov’s scheme made this possible. Two kinds of couplers are addressed, namely twin-core and multiple-core. A full spectrum of soliton solutions are displayed.

Cubic–quartic solitons in couplers with optical metamaterials having polynomial law of nonlinearity

This paper is on couplers with optical metamaterials that are manufactured with polynomial nonlinear form that is also known as cubic–quintic–septic nonlinear form. Cubic–quartic solitons are recovered for such a form of waveguide with the enhanced Kudryashov’s approach. Bright and singular solitons are derived from this scheme for twin-core and multiple-core couplers.

Cubic–quartic solitons in couplers with optical metamaterials having quadratic–cubic law of nonlinearity

This paper acquires cubic–quartic solitons in couplers with optical metamaterials that maintain quadratic–cubic nonlinear form. Two integration schemes, namely unified Riccati equation expansion scheme and an addendum to Kudryashov’s approach have made this retrieval possible. Both multiple-core couplers as well as twin-core couplers are considered. A full spectrum of soliton solutions have emerged from these couple of algorithms.

Cubic–quartic solitons in couplers with optical metamaterials having dual-power law of nonlinearity

This work recovers cubic–quartic solitons in couplers with optical metamaterials, a specific form of optical waveguides. The couplers are with multiple core as well as twin-core. The multiple core couplers are studied with nearest neighbor coupling as well as all neighbor coupling. The dual-power nonlinear form of refractive index is taken into consideration. An addendum to the Kudryashov’s algorithm is the integration scheme adopted here. Bright, singular and bright-singular straddled solitons are derived. These solitons are presented along with their existence criteria.

Cubic–quartic solitons in couplers with optical metamaterials having parabolic law nonlinearity

This work retrieves a complete spectrum of solitons to couplers with optical metamaterials that maintain parabolic nonlinear form. The unified Riccati equation expansion along with an addendum to Kudryashov’s integration scheme has made this recovery of solitons possible. The solitons are displayed along with their respective existence criteria.

Cubic–quartic polarized optical solitons and conservation laws for perturbed Fokas–Lenells model

This paper studies polarized cubic–quartic solitons that are modeled by Fokas–Lenells equation in birefringent fibers. Two integration schemes recovered a spectrum of soliton solutions to the model. Subsequently, the bright solitons compute the corresponding conserved quantities from the respective densities that are recovered by the multiplier approach.

Cubic–quartic optical solitons with Bragg gratings having anti-cubic nonlinearity and dispersive reflectivity

This paper recovers cubic–quartic solitons in fiber Bragg gratings with dispersive reflectivity having anti-cubic nonlinear form. Two integration approaches make this retrieval possible. The modified Kudryashov’s integration scheme reveals a first set of solitons while the addendum to this scheme yields the second set of solitons that completes the picture. The existence criteria of such solitons are displayed.