Effect Of Third-order Dispersion Research Articles

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.

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.

Delayed feedback control on wave dynamics in a nonlinear optical cavity with third-order chromatic dispersion

By taking into account third-order dispersion effects in the presence of feedback, we investigate the stability and nonlinear dynamic movements of waves created in microcavities and fiber cavities from numerical simulations of the extended Lugiato–Lefever equation. The current analysis emphasizes that third-order scattering, feedback strength, and feedback local and global components allow for the numerical observation of dissipative bound states of solitons and chaos with extended and antisymmetric interaction domains. In this regard, we demonstrate how the symmetry of the localized structural interactions is broken by the radiation that results from third-order dispersion.

Higher-order rogue-wave fission in the presence of self-steepening and Raman self-frequency shift

Using the generalized nonlinear Schr\"odinger equation, we investigate how the effect of self-steepening and Raman-induced self-frequency shift impact higher-order rogue-wave solutions. We observe that each effect breaks apart the higher-order rogue wave, reducing it to its constituent fundamental parts, in a similar manner to how a higher-order soliton undergoes fission. Applying a local inverse-scattering technique, we show that under the effect of self-frequency shift, the emergence of a rogue wave significantly influences the surrounding wave background, triggering solitons, breathers, and new rogue waves. We demonstrate that under the combined effect of third-order dispersion, self-steepening, and Raman-induced self-frequency shift, the disintegrated elements of higher-order rogue waves become fundamental solitons, creating an asymmetrical spectral profile that generates both red- and blue-shifted frequency components. We also show the intermediary processes of the fission steps prior to soliton transformation which can only be observed in the presence of weak perturbations. These observations reveal the mechanisms that create a large number of solitons in the process of modulation instability-induced supercontinuum generation from a continuous-wave background in optical fibers.

Soliton-sinc optical pulse propagation in the presence of high-order effects.

We investigate the propagation dynamics of the soliton-sinc, a kind of novel hybrid pulse, in the presence of higher-order effects with emphasis on the third-order dispersion (TOD) and Raman effects. At variance with the fundamental sech soliton, the traits of the band-limited soliton-sinc pulse can effectively manipulate the radiation process of dispersive waves (DWs) induced by the TOD. The energy enhancement and the radiated frequency tunability strongly depend on the band-limited parameter. A modified phase-matching condition is proposed for predicting the resonant frequency of the DWs emitted by soliton-sinc pulses, which is verified by the numerically calculated results. In addition, Raman-induced frequency shift (RIFS) of the soliton sinc pulse increases exponentially with a decrease of the band-limited parameter. Finally, we further discuss the simultaneous contribution of the Raman and TOD effects to the generation of the DWs emitted from the soliton-sinc pulses. The Raman effect can then either reduce or amplify the radiated DWs depending on the sign of the TOD. These results show that soliton-sinc optical pulses should be relevant for practical applications such as broadband supercontinuum spectra generation as well as nonlinear frequency conversion.

Soliton stabilization in microresonators with high order dispersion via pump phase modulation

We theoretically and numerically investigate the effects of third-order dispersion on microresonator solitons in anomalous dispersion with an extended normalized Lugiato–Lefever equation. The temporal position drift of solitons in the microresonator induced by the third-order dispersion is observed. The soliton temporal location stabilization is realized via pump phase modulation. Moreover, the final stable cavity soliton temporal position is deviated to the maxima of the pump phase modulation field profile which is the stable position of the solitons without high-order dispersion. We also study the effectiveness of the pump phase modulation in different modulation parameters. The research method sheds light on the cavity soliton stabilization, on-chip ultrashort pulse formation and optical information processing.

Design and development of coherent-OOFDM techniques in wavelength division multiplexing optical network for long-haul communication

Abstract Today, communication is a crucial factor and requires a high data rate for transmission with in an error-free environment, so optical communication has emerged as a best solution to high-speed transmission systems due to its higher bandwidth and higher data rates. Fiber optic transmission integrating with some modern processing and modulator techniques are applied in various areas that need transfer of data from one point to another through reducing an optical affect. Coherent optical orthogonal frequency division multiplexing is a popular technique in optical communication today because of the excessive spectral efficiency, immune to interference, tolerance of the fiber dispersion and it is long-haul application. It employs the OFDM modulation method, which is a type of multicarrier modulation in which data statistics are distributed over a large number of low-cost subcarriers and is a solution to inter-symbol interference. Inter-symbol interference is generated by chromatic dispersion in high-speed optical transmission systems, and it is a severe issue in long-haul systems in the case of higher data rates transmission. The use of standard dispersion compensating devices, such as dispersion compensating fiber, does not completely compensate for high order dispersion, which includes third-order and high dispersion effects and also increase the loses of the system because it is a fiber in itself. This study proposes introducing the concept of coherent optical orthogonal frequency division multiplexing techniques in to the wave division optical network in the case of multiple users, high data rate transmission and long-haul and ultra-long-haul optical link to reduce the optical transmission on related issues and to improve the performance of optical network. The performance of the proposed network can be evaluated by using different parameters such as signal to noise ratio, bit error rate, optical signal to noise ratio, Quality factor and eye-diagram at different distance transmission up to 8000 km by using Optisystem software.

Optical soliton solutions of (1 + 1)- and (2 + 1)-dimensional generalized Sasa–Satsuma equations using new Kudryashov method

In this paper, we aim to derive new soliton solutions of (1+1)- and (2+1)-dimensional generalized Sasa–Satsuma equations via the new Kudryashov method. In optical fiber transmission systems, the Sasa–Satsuma equation describes the effects of third-order dispersion, self-steepening and stimulated Raman scattering in the propagation of ultrafast pulses. The considered equations are encountered in various physical applications such as ultra-short and femto-second pulse propagation in optical fibers and dynamics of deep water waves. So, investigation of the novel solutions of the equations is one of the important topics. We have successfully extracted some soliton solutions for the considered equation. The various graphs of the obtained solutions have been depicted in the figures by selecting appropriate parameters. The singular and bright soliton solutions have been revealed in the figures. All acquired solutions have been confirmed to satisfy the considered equations. The results show that the approach may be used to find exact solutions to various nonlinear evolution equations. The new solutions and the paper results may enrich the understanding of the wave propagation in the optical fibers and may shed light on new studies.

Switchable property of dissipative soliton and dispersion-management soliton in fiber laser

We numerically and experimentally demonstrated that the central wavelength of the output pulses in an Er-doped mode-locked fiber laser can be switched from ∼1561 to ∼1531 nm, while these two pulses exhibit dispersion-management soliton and dissipative soliton, respectively. The switch capability of our fiber laser with different pulse waveforms can be attributed to combining the double-hump gain spectrum of Er-doped fiber and third-order dispersion (TOD) effect. By considering the TOD effect, the two wavelengths can be operated in different dispersion regime. The transient switch dynamics of these different type of solitons are also observed by time stretched technique. These findings provide a good foundation for comprehensively studying pulse formation dynamics in laser cavities, and benefit for design dual-wavelength fiber lasers.

Cnoidal waves and dark solitons with linear third-order dispersion and self-steepening effect

The present paper investigates the conditions needed for the generation and propagation of cnoidal waves in the form of dark solitons under the influence of self-steepening effect and linear third-order dispersion. This kind of optical pulses could be obtained in single-mode waveguides due to the precise balance between higher orders of nonlinear and dispersive phenomena. As a basic equation, it is used the nonlinear amplitude equation (NAE). It is found a new analytical solution of this equation in the form of a cnoidal wave (Jacobi elliptic sine function). In the article it is presented that the solution can be reduced to dark soliton at specific values of the modulus of ellipticity κ.

Symmetrical reversal transmission of Airy pulses in dispersion-managed fiber systems.

Based on the dispersion management technology, the transmission characteristics of Airy pulses in optical fiber systems are studied theoretically and numerically. The results show that the group velocity dispersion and third-order dispersion that change periodically along the transmission direction of the optical fiber can prolong the transmission of pulses. Under the action of periodically varying group velocity dispersion, the symmetrical reversal of the Airy pulse can be realized which the shape of the pulse keeps invariable and the tail converses after the inversion. When the periodic third-order dispersion effect is also considered, the periodically symmetrical reversal of the Airy pulse happens and the pulse can be regenerated periodically at the certain transmission distance. Adjusting the parameters of the third-order dispersion, the inversion position and the period can be manipulated. In addition, it is found that the tight focusing of the Airy pulse is also controllable.

Bright solitons under the influence of third-order dispersion and self-steepening effect

Bright solitons under the influence of third-order dispersion and self-steepening effect

Dark soliton solutions for a variable coefficient higher-order Schrödinger equation in the dispersion decreasing fibers

Under investigation in this paper is a variable coefficient higher-order Schrödinger equation with the effects of third-order dispersion, self-steepening and stimulated Raman scattering, which describes the propagation of ultrashort optical pulses in the dispersion decreasing fibers. Via the symbolic computation and Hirota method, the bilinear forms, dark one- and two-soliton solutions are derived. Propagation and interaction for the dark solitons are illustrated graphically: the shape of the dark solitons is affected by the third-order dispersion, self-steepening and stimulated Raman scattering, while the amplitude and velocity of those are influenced by the gain coefficient Γ. With the increase of the parameter Γ, the amplitude of the dark soliton pulse increases, and the velocity of that changes exponentially in the same propagation distance. For the elastic interaction, the anti-bell- and two parabolic-shape dark solitons are discussed respectively, where the amplitudes and shapes remain unchanged after interaction except for certain phase shifts.

Cubic–quartic optical solitons in birefringent fibers with Sasa–Satsuma equation

Objective:The paper recovers cubic–quartic optical solitons with the Sasa–Satsuma equation that includes a combination of third-order dispersion and fourth-order dispersion effects to address cubic–quartic vector solitons for the first time. Methods:Two integration schemes are applied to catch out the solitons to the newly structured model. They are G′/G–expansion scheme and modified Kudryashov’s approach. These pave way for a full spectrum of vector solitons. The recovered vector solitons are enumerated after a revisiting the mathematical strategies. Results:The mathematical approaches retrieve the dark, bright and singular vector solitons to the model. These solitons are presented by virtue of the certain restrictions. Rational and singular periodic solutions are also emerged with the mathematical schemes. Conclusion:Cubic–quartic vector solitons are yielded for such a model in this work for the first time. This would naturally lead to further ventures in this area. The newly structured model would be to address to recover the conservation laws. Other natural extensions to the model would be to consider with DWDM topology that would also lead to soliton solutions and their respective conservation laws.

Study of Optical Soliton of Nonlinear Optical Fibers by Nonlinear Schrodinger Equation

This paper is mainly concerned with obtaining the pure optical cubic of solitons in nonlinear optical fibers and formulating them by relying on the nonlinear Schrodinger equation (NLSE). This method is effective for extracting optical solitons. We discuss the model responsible for controlling the motion of the soliton with a third-order dispersion effect. This is done without the need for external capabilities to support the visual movement of the soliton. The cubic optical soliton of this model is obtained by relying on the nonlinearity of Kerr law of and without chromatic dispersion. Soliton wave solutions are precisely extracted and constructed using different Csch, Tanh-Coth and exponential functions as well as fiber-optic solitary wave solutions which include complex soliton mixed solutions, singular, multiple, dark and bright solutions. The terms of integration and constraints for the resulting solutions are presented and discussed and we find the solitary and periodic waves solutions of the nonlinear Schrödinger equations.

Dispersion Characteristic of Spatiotemporal Sharply Autofocused Vector Airy-Circular Airy Gaussian Vortex Wave Packets

The spatiotemporal vector Airy-Circular Airy Gaussian vortex wave packet is constructed by solving the (3 + 1)D Schrodinger equation in free space. The wave packet can simultaneously autofocus in space and time by setting the appropriate initial pulse velocityυand the initial position of the main lobeT0. This kind of wave packet has low intensity before focusing, but the intensity at focus is about 80 times of the initial plane intensity. Our results may have potential applications in particle manipulation, laser processing, and other fields. Furthermore, the influence of the third-order dispersion coefficient on the evolution trajectory, the focus position, and the main peak intensity at the focus of the focusing pulse vector field is analyzed. The results show that the change of the initial velocity, the initial position, and the third-order dispersion coefficient can accurately control the evolution trajectory and the focus position, while the main peak intensity at the focus can only be controlled by adjusting the third-order dispersion coefficient. This means that the pulse vector light field can be manipulated precisely for precise processing by adjusting the third-order dispersion effect.

Propagation of the pure-cubic optical solitons and stability analysis in the absence of chromatic dispersion.

The main concentration of this article is to extract pure-cubic optical solitons in nonlinear optical fiber modeled by nonlinear Schrödinger equation (NLSE). The governing model is discussed the with the effect of third-order dispersion, Kerr law of nonlinearity and without chromatic dispersion. We extract the solutions in different forms like, Jacobi’s elliptic, hyperbolic, periodic, exponential function solutions including a class of solitary wave solutions such that bright, dark, singular, kink-shape, multiple-optical soliton, and mixed complex soliton solutions. Recently developed integration tools known as varPhi ^6-model expansion method, generalized exponential rational function method (GERFM) and generalized Kudryashov method are applied to analyze the governing model. The studied model is also discussed by the concept of modulation instability (MI) analysis. The constraints conditions are explicitly presented for the resulting solutions and singular periodic wave solutions are recovered. Furthermore, for explaining the solutions in physical phenomena, the three dimensional, two dimensional, and their related contours graphs are plotted under the selection of appropriate parameters. The accomplished results show that the applied computational system is direct, productive, reliable and can be carried out in more complicated phenomena. The results show that the studied equation theoretically has extremely rich pure-cubic optical structures of nonlinear fiber relevance.

Origin, bifurcation structure and stability of localized states in Kerr dispersive optical cavities

Abstract Localized coherent structures can form in externally driven dispersive optical cavities with a Kerr-type non-linearity. Such systems are described by the Lugiato–Lefever (LL) equation, which supports a large variety of dynamical states. Here, we review our current knowledge of the formation, stability and bifurcation structure of localized structures in the one-dimensional LL equation. We do so by focusing on two main regimes of operation: anomalous and normal second-order dispersion. In the anomalous regime, localized patterns are organized in a homoclinic snaking scenario, which is eventually destroyed, leading to a foliated snaking bifurcation structure. In the normal regime, localized structures undergo a different type of bifurcation structure, known as collapsed snaking. The effects of third-order dispersion and various dynamical regimes are also described.

Giant anomalous self-steepening and temporal soliton compression in silicon photonic crystal waveguides

Self-steepening (SS) is enhanced by slow-light effects in photonic crystal waveguides (PhCWs), with coefficients as large as hundreds of femtoseconds, and it plays an important role in temporally compressed solitons with narrow widths. Here, we investigate the soliton evolution in silicon PhCWs through experiments and numerical simulations; the simulated results agree well with the experimental measurements and help in revealing the physical mechanism of high-order soliton evolution. The dual opposite effects of giant anomalous SS on temporal soliton compression are demonstrated for the first time, i.e., the SS weakens or improves the compression competing with the effects of third-order dispersion (TOD) through two different physical mechanisms. It is also found that SS flattens or steepens the pulse leading edge depending on the strength of the positive TOD perturbation. These results promote the understanding of high-order solitons and can help with the design of suitable dispersion engineered silicon waveguides for superior on-chip temporal pulse compression for optical interconnects, data processing, and microwave photonics.