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A dense wavelength division multiplexing (DWDM) system improves the capacity of an optical communication system. On the other hand, nonlinear effects are critical issues that limit the performance of the DWDM system. The nonlinear effects of self-phase modulation, cross-phase modulation, and four-wave mixing affect optical communication's capacity. This paper focuses on mitigating the nonlinear effect of cross-phase modulation in the DWDM system with a suitable technique. [ABSTRACT FROM AUTHOR]

In this paper, the proficiency of nonlinearity compensation studied on the polarization division multiplexing 0.3 return-to-zero quadrature phase-shift keying (PDM-0.3RZ-QAM) coherent optical system. The considerable nonlinear effect is the self-phase modulation (SPM) in the presence of chromatic dispersion. The nonlinearity mitigation technique based on the digital backpropagation (DBP) algorithm is implemented on the receiver side. The performance of the system was investigated in different terms as the optical signal-noise ratio, bit error rate, and the maximum transmission distance. The results demonstrated that the penalties were decreased by 3 dB. The maximum achievable distance was extended to 2000 km. [ABSTRACT FROM AUTHOR]

In this study, we aimed to obtain optical soliton solutions of the perturbed Fokas–Lenells equation having the parabolic law of self-phase modulation in the presence of spatio-temporal dispersion. The Fokas–Lenells equation is significant in nonlinear optics, particularly for modeling femto-second pulse propagation. By implementing the enhanced Kudryashov method, we derive dark, bright, and kink optical solitons for the investigated model. Visualizing the obtained results supported by 3D and 2D simulations and examining the effects of the parameters within the model on the soliton behavior constitute the other branches of the study. Considering that the interaction of various self-phase modulation forms with the chromatic dispersion term is different and its effects on soliton behavior are different, the parabolic law nonlinearity form is examined in the study and the results obtained are aimed at contributing to studies on both the model and nonlinear optics. [ABSTRACT FROM AUTHOR]

A degenerated four‐wave‐mixing (FWM) process in single‐crystal (CH3NH3)PbBr3 (MAPbBr3) is reported, where 150‐fs laser pulses at 1.33 µm are employed as the pump. Two pump photons interact with a single crystal, producing another two photons with higher and lower energies, respectively. One of the FWM‐generation sidebands is tuned from ∼1.23 to 1.21 µm and the other from ∼1.43 to 1.48 µm for the center wavelength, as the pump fluence is increased from 2.6 to 11.69 mJ cm−2. The self‐phase modulation induced by the strong pump pulses through the optical Kerr effect is responsible for the tuning dynamics. Transient spectroscopy not only verifies the FWM scheme for the interacting waves but also reveals the interference dynamics between the FWM‐generated sidebands and the probe pulse. In particular, the angular dependence of the FWM generation supplies direct evidence for the phase‐matching geometry. Using experimental data, a nonlinear refractive index coefficient of 1.19 × 10−14 cm2 W−1 at 1.33 µm for single‐crystal MAPbBr3 is determined. [ABSTRACT FROM AUTHOR]

Recently, dense wavelength division multiplexing passive optical networks (DWDM-PONs) have become a considerable choice for 5G and beyond fronthaul implementations. Formerly, we have proposed a full-duplex bidirectional DWDM-PON architecture convenient for those implementations and analyzed the combined dual impact of four-wave mixing (FWM) and stimulated Raman scattering (SRS) nonlinear impairments on the proposed architecture. Meanwhile, a detailed literature analysis showed us that the combined quadruple impact of self phase modulation (SPM), cross phase modulation (XPM), FWM and SRS on the performance of bidirectional DWDM-PONs have never been researched up to now. In this paper, quadruple impact of SPM, XPM, FWM and SRS on the performance of both uplink channels (ULCs) and downlink channels (DLCs) of the formerly proposed DWDM-PON has been analyzed with simulations. Simulations have been performed in O-band region for ULCs and in C-band region for DLCs of 2 × 15- and 2 × 63-channel DWDM-PONs having 12.5 GHz, 25 GHz, 50 GHz, 100 GHz equally-spaced channels. The quadruple impact of optical nonlinear impairments on the DWDM-PON performance has been analyzed with signal-to-crosstalk ratio (SXR) simulations performed under varying channel input powers and channel lengths. Results show that under the quadruple nonlinear impact reliable bidirectional transmission with an SXR over 23 dB can be achieved for channel input powers below 0.58 mW and 0.16 mW in 2 × 15- and 2 × 63-channel DWDM-PONs, respectively, for all channel spacing values and 25 km transmission lengths. Moreover, results also imply that variations in channel lengths do not significantly affect SXR at both ULCs and DLCs of 2 × 15- and 2 × 63-channel DWDM-PONs for lengths exceeding 50 km. The thorough analysis presented in the paper will give a new insight for analysis of conventional and next generation PONs. [ABSTRACT FROM AUTHOR]

On-chip light generation in the mid-infrared (mid-IR) region of the electromagnetic spectrum is gaining considerable attention due to its various potential applications in free-space communication, mid-IR spectroscopy, sensing, and thermal Imaging. In this work, we have designed a dispersion-engineered silicon nitride (SiN)-coated tellurium oxide (TeO2) hybrid waveguide on silica (SiO2) substrate with barium fluoride (BaF2) as cladding for nonlinear applications. Strong modal confinement, broad dispersion characteristic, and high nonlinearity were achieved in the proposed hybrid waveguide design, which are important features for obtaining desired nonlinear applications. Through numerical simulations, we found that the dispersion curve is nearly flat within the dispersion range of −40.60 ps/nm/km to 33.15 ps/nm/km for a spectral bandwidth of 1.55–4.25 µm with a zero-dispersion wavelength (ZDW) around 1.80 µm, which is suitable for generating nonlinear effects such as four-wave mixing, self-phase modulation, and Raman scattering. Such types of on-chip hybrid waveguide devices can be pumped using a commercially available fiber laser operating at a wavelength of 2 µm. The design of the hybrid waveguide was optimized to achieve very low modal confinement loss ranging from 0.1 × 10−4 to 35 dB/cm, with a spectral bandwidth of 1.5–4 µm. Additionally, a high nonlinear coefficient value of 1372 W−1 km−1 was achieved at a pumping wavelength of 1.5 µm in hybrid waveguide. The results of such hybrid waveguides can be helpful to experimentalists working in this field for developing nonlinear hybrid waveguide devices. These nonlinear hybrid waveguide devices have potential nonlinear applications, including four-wave mixing, Raman scattering, and supercontinuum spectrum spanning the near-IR to mid-IR. Further, the on-chip hybrid waveguide structure can be significantly help to expand the functionality of future photonics integrated circuits. [ABSTRACT FROM AUTHOR]

Logic gates are an extremely important structural component for logical operations and high-speed data transmission now-a-days. Initially, logic gates were functioning with electrical signals; however, for wide bandwidth and high-speed transmission, they can also work with optical signals. Data are processed by digital logic gates in a variety of ways, and we explored data analysis for logic design in a number of potential ways. We examine all the many facets of digital signal processing. With optical signals, data are sent incredibly quickly in a nearly dispersion-free condition. We go over the different facets of logic design here. [ABSTRACT FROM AUTHOR]

Abstract We report the numerical and experimental studies of the two-dimensional Brillouin gain spectrum (BGS) distribution deformation induced by the self-phase modulation in the Brillouin optical time domain reflectometry (BOTDR) with a 20.6 km sensing distance. The BGS distribution deformation is investigated by analyzing the evolution of the point spread function along the fiber in the two-dimensional model of the BOTDR. In the simulation and experimental results, the specific deformation degree of the BGS distribution induced by the self-phase modulation is related to the pump pulse profile, pump pulse peak power, BGS demodulation method, and detected scattered light component. By comprehensively analyzing the evolution of the point spread function induced by the self-phase modulation and using the image deconvolution, a typical BOTDR sensor with a 25 ns pump pulse reaches the 20 cm spatial resolution over the 20.6 km sensing fiber.

Concatenation model assist in optimising the setup for controlling and manipulating the soliton dynamics. Solitons are self-reinforcing solitary waves that maintain their shape and energy over long distances, also have applications in optics and physics. A thorough analysis of the concatenation model, which incorporates a power law nonlinearity, is presented in this work. This investigation also comprises the phenomena of nonlinear chromatic dispersion, which affects optical fibres and other dispersive media that modulates the chromatic dispersion of the material. When nonlinearities like as self-phase modulation and cross-phase modulation are present, the chromatic dispersion coefficient becomes a function of optical intensity. By employing the modified auxiliary mapping scheme, new families of optical dromions (solions) like bright dromion, domain wall, singular, periodic, doubly periodic, trigonometric, rational and hyperbolic solutions etc. are extracted for the suggested model. The two classes of M-shaped analytical rational solutions are also acquired and by selecting the appropriate values for the relevant parameters, their dynamics are visualised in figures. Likewise two different kinds of interactions between M-shaped rational solutions and kink waves are also computed. In addition, we evaluate periodic cross-rational solutions, kink cross-rational solutions, homoclinic breather solutions and multiwaves solutions for the governing model. The derived solutions have confirmed the potency and stability of the current techniques. In addition, certain solutions graphs are also provided to show the physical nature of the derived results. [ABSTRACT FROM AUTHOR]

Nonlinear optics (NLO) and its applications have attracted increasing research interest in recent years owing to their contribution to the development of photonic technology. Accordingly, in this study, we investigated the NLO response of pumpkin seed oil using the spatial self-phase modulation (SSPM) method. Significant NLO characteristics have been experimentally studied at 405 nm and 532 nm continuous wave (CW) laser wavelengths, yielding second-order nonlinear refractive index ( n 2 , t h ) values of 6.54 × 10 - 5 cm 2 / W and 2.73 × 10 - 5 cm 2 / W , respectively. The findings suggest that the absorption of the material leads to higher optical nonlinearity at shorter wavelengths owing to higher thermal effects. Furthermore, we implemented a light-controlled-light system based on the spatial cross-phase modulation (SXPM) technique employing pumpkin seed oil. We successfully achieved all-optical switching by designing the 'ON' and 'OFF' modes. The results of this study can be considered for the future development of NLO applications. Moreover, our work investigates the potential of pumpkin seed oil for designing low-cost and high-efficiency NLO devices, and this contribution opens up a novel practical avenue for oil-based optical devices. [ABSTRACT FROM AUTHOR]

In the current work, we investigate the optical solitons and exact solutions for the conformable time fractional generalized Radhakrishnan–Kundu–Lakshmanan (GRKL)equation with the polynomial law of nonlinearity which represent the mathematical model of pulse propagation in a nonlinear medium in optical fibers. The modified extended direct algebraic method is presented to get the exact solutions for this model. Many varieties of traveling wave solutions are established like, solitons (bright, dark, singular, combo singular-dark), combo periodic solutions, periodic solutions, Jacobi elliptic solutions, exponential solutions and Weierstrass elliptic solutions. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order. [ABSTRACT FROM AUTHOR]

This research paper is dedicated to the investigation of the optical soliton solutions with the power law of self-phase modulation (SPM) and the third-order dispersion (TOD), completely neglecting the chromatic dispersion (CD). The aim is focused on two main points. First, obtaining the straddled soliton solution which permits us to have bright and singular soliton by applying the new Kudryashov (nKM) scheme which was recently introduced as a simple, effective, and reliable method. Second, to observe the influences of the TOD, SPM, and inter-modal dispersion (IMD) on pure-cubic optical soliton dynamics in the absence of the CD. [ABSTRACT FROM AUTHOR]

In this work, we use symbolic computation and ansatz function schemes, to investigate the soliton solutions for the nonlinear Schrödinger equation (NLSE) along with Kudryashov's quintuple self-phase modulation system (KQSPMS) including dual-form of nonlocal nonlinearity (DFNLN). We initially determine the ordinary differential (OD) form for this model through a variable transformation. Then we introduce numerous new dynamical soliton types: the M-shaped rational soliton, the M-shaped interaction between one and two stripe solitons, the periodic cross-M-shaped rational (PCMR) soliton, the periodic cross-kink (PCK) soliton, multi-waves, and the homoclinic breather soliton. Secondly, we determine the partial differential (PD) form for this model through a variable transformation. Moreover, a lump soliton, a periodic wave, a rogue wave, a lump interaction with a periodic and kink wave, and three different types of breather soliton will obtain. We'll demonstrate these solutions' unique structure and extremely interesting interaction behavior. We'll also use graphs (3-D and contour plots) to discuss the dynamics of the results after setting the parameters to the proper values. [ABSTRACT FROM AUTHOR]

The applications of ultrafast optics to biomedical microscopy have expanded rapidly in recent years, including interferometric techniques like optical coherence tomography and microscopy (OCT/OCM). The advances of ultra-high resolution OCT and the inclusion of OCT/OCM in multimodal systems combined with multiphoton microscopy have marked a transition from using pseudo-continuous broadband sources, such as superluminescent diodes, to ultrafast supercontinuum optical sources. We report anomalies in the dispersion profiles of low-coherence ultrafast pulses through long and non-identical arms of a Michelson interferometer that are well beyond group delay or third-order dispersions. This chromatic anomaly worsens the observed axial resolution and causes fringe artifacts in the reconstructed tomograms in OCT/OCM using traditional algorithms. We present DISpersion COmpensation Techniques for Evident Chromatic Anomalies (DISCOTECA) as a universal solution to address the problem of chromatic dispersion mismatch in interferometry, especially with ultrafast sources. First, we demonstrate the origin of these artifacts through the self-phase modulation of ultrafast pulses due to focusing elements in the beam path. Next, we present three solution paradigms for DISCOTECA: optical, optoelectronic, and computational, along with quantitative comparisons to traditional methods to highlight the improvements to the dynamic range and axial profile. We explain the piecewise reconstruction of the phase mismatch between the arms of the spectral-domain interferometer using a modified short-term Fourier transform algorithm inspired by spectroscopic OCT. Finally, we present a decision-making guide for evaluating the utility of DISCOTECA in interferometry and for the artifact-free reconstruction of OCT images using an ultrafast supercontinuum source for biomedical applications. [ABSTRACT FROM AUTHOR]

The current paper studies the Lakshmanan-Porsezian-Daniel equation with nonlinear chromatic dispersion and Kerr law of self-phase modulation having generalized temporal evolution. The governing model is analyzed using Lie symmetry. The implicit solution is in terms of Appell hypergeometric function. The parameter constraints of the solutions are also enumerated. [ABSTRACT FROM AUTHOR]

This work carries out the bifurcation analysis of the dispersive concatenation model with Kerr law of self-phase modulation. The dynamical system is first formulated and the phase-plane portraits are analyzed. The corresponding soliton solutins are subsequently recovered from the analysis. [ABSTRACT FROM AUTHOR]

The current paper recovers quiescent optical solitons for the Radhakrishnan-Kundu-Lakshmanan equation with a power law of self-phase modulation and nonlinear chromatic dispersion. The Lie symmetry analysis leads to stationary bright optical soliton solutions for linear and generalized temporal evolution. The parameter constraints for the existence of such solitons are enumerated. [ABSTRACT FROM AUTHOR]

Soliton "molecules", i.e., bound states of two or several solitons, represent a fundamental concept, which manifests itself in various nonlinear systems. They are dynamically similar to chemical molecules, attracting great interest to fundamental studies and offering potential applications (such as multilevel encoding of optical data). Here, the study demonstrates a novel dichromatic soliton‐molecule compounds (DSMC) built as a hybrid bound state of multiple bound soliton pulses carried by two wavelengths in a fiber laser. The DSMCs are maintained by two different binding mechanisms, viz., the self‐phase modulation (SPM) interaction between temporal solitons at the same wavelength, mediated by their tails, and the cross‐phase modulation (XPM) interaction between solitons at different wavelengths. They also exhibit unique temporal and spectral vibration profiles. Both static DSMCs and ones with robust internal vibrations are generated experimentally in the fiber laser, and numerically as solutions of the corresponding dissipative nonlinear model. The findings reported here expand the concept of soliton molecules and further promote their similarity to chemical molecules. [ABSTRACT FROM AUTHOR]

This paper simulates the relative performance of various artificial intelligence (AI) techniques when applied to nonlinear distortion compensation in wavelength division multiplexing (WDM) optical communication systems. These procedures are less complex than state-of-the-art compensation methods and do not necessitate prior knowledge about the properties of data in neighboring WDM channels, which can be practically challenging. In this study, Neural Networks (NNs) were integrated into both the transmitter and receiver sections of 3- and 5-channel WDM systems, and the resulting enhancement in performance (Q-factor) was assessed across varying levels of fiber nonlinearities. While the NN stage enhances the system performance, the improvement decreases as expected with the channel number and γ . Next, two-stage architectures that employ a transmitter side NN together with a classifier at the receiver side were modeled. For the systems examined in this paper simple decision tree structures, boosting, forests, extra trees, and multi-layer perceptron (MLP) classifiers all yielded enhanced system performance compared to simple chromatic dispersion compensation (CDC) with the only exception being Ada boosting which decreased the Q-factor for γ = 14 W - 1 k m - 1 . The outcomes of these investigations show that the most effective performance in highly nonlinear WDM systems is attained by employing two-stage systems, with the incorporation of random forest or extra tree AI methods at the receiver side yielding the highest results. [ABSTRACT FROM AUTHOR]

This paper examines the complex Ginzburg Landau equation, which describes pulse propagation inside a fiber with the triple power law of self-phase modulation. Since the effect of parameter selection has become very important in relevant model studies recently, self-phase modulation has been added to the complex Ginzburg Landau equation, which has been studied in the literature, and it is aimed at investigating the analytical solutions of the presented equation. Adding the triple power law of the self-phase modulation parameter to the model, in addition to existing studies in the literature, emphasizes the innovative aspect and importance of the study. The first aim is to reveal bright and singular solitons using the new Kudryashov method. The new Kudryashov method is a technique that is frequently used in the literature, is effective for generating analytical solutions, provides ease of operation, and can be applied to a wide class of nonlinear partial differential equations. The second goal is to show that the obtained solutions have modulation stability. By using modulation instability analysis, the gain spectrum is formed for different parameter values. Graphic presentations support the findings. Moreover, bright and singular soliton portraits are demonstrated with 3D and 2D graphs. The novelty of the study lies in the fact that the relevant model has not been studied before with an effective method such as the new Kudryashov method, and the modulation instability has been studied for the first time. [ABSTRACT FROM AUTHOR]

The supercontinuum spectrum is generated through a wide range of wavelengths by sending a short and strong pulse to the nonlinear medium and sputtering at the output and is used in optical measurements, spectroscopy, biological imaging optical coherence photography, etc. Integrated photonics is an idea to realize low-cost and microscale communication, sensing, and fast computing methods. In addition, the miniaturization and integration of photonic structures make possible new designs and applications that are inaccessible in their large volumes. Lithium niobate is one of the most widely used and attractive materials in the field of photonics due to its extraordinary electro-optical, acoustic-optical, nonlinear optics, wide transparency window, and relatively high refractive index. In this work, a lithium niobate waveguide is designed by choosing basic solitons as the input pulse and considering various effects such as high-order scattering, self-phase modulation, second harmonic generation, Raman effect, self-downward effect, etc. The proposed waveguide has super-sustainable production. This supercontinuum spectrum is designed in the waveguide, for the 10th order bright soliton at a distance of 35 mm, 4 times the initial width, for the 20th order bright soliton at 9 mm, 4 times the initial width, and for the 30th order bright soliton at 4.5 mm, 5 times the initial pulse width in the frequency domain are created. Such dimensions are suitable for use in photonic integrated circuits. [ABSTRACT FROM AUTHOR]

A single-pump optical parametric amplifier (OPA) is modeled using a p-toluene sulfonate (PTS) filled silicon-based slotted photonic crystal waveguide (SPCW). The PTS-SPCW has CMOS-process compatibility and offers slow-light enhanced nonlinearity of PTS due to extreme optical confinement in SPCW. The adverse effects of two-photon absorption and free carrier absorption are absent in PTS in the standard optical communication window. The coupled nonlinear Schrödinger's equations have been modified to analyze the OPA under slow-light propagation. Performances of the OPA are evaluated in both the high- and low- dispersive zones of the structure. The high dispersive zone exhibits high group indices to the operating waves, leading to a high parametric gain (≈ 31 dB) and high conversion efficiency (≈ 27 dB) utilizing a 350 μ m long PTS-SPCW and a pump power of 65 mW. However, this zone degrades the shape of a ≤ 10 ps pulse due to self-phase and cross-phase modulation. On the other hand, in the low dispersive zone, a similar parametric gain and conversion efficiency (both ≈ 29 dB) are attained utilizing a 1250 μ m long PTS-SPCW and a pump power of 150 mW. Nevertheless, this zone degrades a 5 ps pulse only after a distance of 1500 μ m. The analyses show a 30 nm bandwidth considering a gain above 30 dB. Investigation of the effect of fabrication imperfections shows excellent performance sustainability of the OPA up to a random error of 40 nm. These remarkable performances make this low-powered, small-footprint OPA suitable for achieving tunable optical amplification in photonic integrated circuits. [ABSTRACT FROM AUTHOR]

In this investigation, we explore the phenomenon of spectral broadening in a gas-filled hollow-core capillary induced by ultra-short pulses, with a focus on nonlinear mode coupling at a power lower than the critical power. As the pulse propagates through the capillary, the spectrum primarily broadens due to self-phase modulation, and concurrently, high-order modes are generated through interactions between different modes. Both experimental and numerical results consistently demonstrate that the spectral region near the center of the spectrum remains within the fundamental mode, while the spectral edges propagate in higher-order modes, predominantly in the LP 12 mode generated through nonlinear mode coupling within the gas-filled hollow-core capillary. This observation is relatively weak but is of paramount importance for the design of post-compression systems in gas-filled hollow-core capillaries with a high-quality beam profile when the power starts to reach the critical level. Understanding and then accommodating the dynamics of nonlinear mode coupling are crucial for achieving the desired characteristics and beam quality while optimising the performance of such systems. [ABSTRACT FROM AUTHOR]

We conducted a systematic investigation into the spectral and pulse characteristics of C and L-band Nonlinear Polarization Rotation (NPR) mode-locked fiber lasers effectively employing nonlinear polarization rotation technology. In our experimental setup, we achieved a stable mode-locked state at 1560.076 nm, exhibiting a 3 dB spectral bandwidth of 9.1 nm. As the pump power increased, we observed spectral shifts accompanied by shifts in the first Kelly sideband and the generation of new Kelly sidebands. In this paper, the phenomenon of spectral deviation is elucidated through the interplay of self-phase modulation, group velocity drift, and polarization-dependent isolator (PD-ISO) filter effect, with an analysis of the formation and deviation of Kelly sidebands. Notably, spectral shift persisted even when the pump power exceeded 200 mW. However, continuous pump power escalation led to soliton splitting, resulting in the formation of new soliton beams. Based on the simultaneous generation of spectral shift and pulse splitting, our study contributes to an enhanced understanding of soliton dynamics in ultrafast fiber lasers and lays a foundation for the application of high-repetition-frequency harmonic mode-locked lasers with tunable wavelengths. [ABSTRACT FROM AUTHOR]

The spatial self‐phase modulation (SSPM) of phosphorus‐based nanomaterials is widely studied and developed as passive nonlinear photonic devices for applications in all‐optical switches, logic gates, information converters, etc. In this work, violet phosphorus quantum dots (VP QDs) are prepared and characterized in three different solvents, their SSPM is investigated, and their spatial asymmetric light propagation performances are demonstrated. It is shown that VP QDs prepared in three different solvents exhibit different bandgaps, mainly due to the interaction between the dangling bonds of VP QDs and functional groups in different solvents. The SSPM experiment characterizes the nonlinear optical response of solvent‐dependent VP QDs. It is found that VP QDs exhibit strong nonlinear optical effect and their nonlinear refractive indexes are comparable to other phosphorus‐based 2D materials. Unlike the previously reported principle of spatial asymmetric light propagation (i.e., a cascaded sample based on SSPM composed of nanomaterials with excellent nonlinear refraction and SnS2 with reverse saturation absorption), the spatial asymmetric light propagation performance based on SSPM is demonstrated using a cascaded sample of VP QDs with significantly different nonlinear optical response prepared in two different solvents. [ABSTRACT FROM AUTHOR]

The paper focuses on investigating the time-fractional (3 + 1)-dimensional cubic and quantic nonlinear Schrödinger equation. We adopt the novel Kudryashov method to generate a distinct class of optical solutions for the current conformable fractional derivative problem. Our method explores various solution forms, including dark, wave, mixed dark-bright, and singular solutions. The soliton solutions we construct are visually represented to illustrate the influence of the fractional order derivative. Further, we elucidate the influence of solution parameters on the wave envelope, providing clear interpretations through 2D graphics presentations. The results underscore the efficacy of our approach in discovering exact solutions for nonlinear partial differential equations, especially in cases where alternative methods prove ineffective. The significance of the present paper lies in its contribution to advancing the understanding of the behavior of optical solutions in nonlinear systems, providing valuable insights for both theoretical and practical applications. In the field of nonlinear optics, this equation can describe the propagation of optical pulses in nonlinear media. It helps in understanding the behavior of intense laser beams as they propagate through materials exhibiting nonlinear optical effects such as self-focusing, self-phase modulation, and optical solitons. [ABSTRACT FROM AUTHOR]

In this article, we are interested in two principal topics. First, the bright optical soliton solutions of the third-order (1+1)-nonlinear Schrödinger equation including power law nonlinearity with inter-modal and spatio-temporal dispersions are perused by taking advantage of the new Kudryashov method. Second, the impacts of power law nonlinearity parameters on soliton attitude are investigated for acquired bright soliton form. With the proposed technique, the bright optical soliton solution is acquired, and 3D, contour, and 2D plots are depicted. Then, the impact of power law nonlinearity parameters on the soliton attitude has been successfully demonstrated. As is clear from this perusal power law parameters have an important impact on the soliton attitude, and this impact alters based on the soliton form. As regards our investigation, this form of the equation has not been studied with the power law nonlinearity in the absence of the chromatic dispersion for nonlinear models and the proposed method has not been applied the introduced equation before. It is expected that the consequences which are acquired in this study will shed light on the studies in this field. [ABSTRACT FROM AUTHOR]

This study introduces a novel truncated Mittage–Leffler (M)- proportional derivative (TMPD) and examines its impact on the perturbed nonlinear Schrödinger equation (PNLSE) that includes fourth-order dispersion and cubic-quintic nonlinearity. The TMPD-PNLSE is used to model light signals in nanofibers. In addition to dispersion and Kerr nonlinearity, which are characteristics of the NLSE, the PNLSE also exhibits self-steepening and self-phase modulation effects. The unified method is implemented to derive exact solutions for the model equation. These solutions provide a variety of phenomena; including breathers, geometric chaos, and complex solitons. The solutions also exhibit numerous structures, such as geometric chaos, where undulated M-shaped and M-shaped solitons are embedded. The modulation instability is analyzed, finding that it is triggered when the coefficient of the fourth-order dispersion surpasses a critical value. [ABSTRACT FROM AUTHOR]

This paper deals with a new variant of the Biswas–Milovic equation, referred to as the perturbed Biswas–Milovic equation with parabolic-law nonlinearity in spatio-temporal dispersion. To our best knowledge, the considered equation which models the pulse propagation in optical fiber is studied for the first time, and the abundant optical solitons are successfully obtained utilizing the auxiliary equation method. Utilizing a wave transformation technique on the considered Biswas–Milovic equation, and by distinguishing its real and imaginary components, we have been able to restructure the considered equation into a set of nonlinear ordinary differential equations. The solutions for these ordinary differential equations, suggested by the auxiliary equation method, include certain undetermined parameters. These solutions are then incorporated into the nonlinear ordinary differential equation, leading to the formation of an algebraic equation system by collecting like terms of the unknown function and setting their coefficients to zero. The undetermined parameters, and consequently the solutions to the Biswas–Milovic equation, are derived by resolving this system. 3D, 2D, and contour graphs of the solution functions are plotted and interpreted to understand the physical behavior of the model. Furthermore, we also investigate the impact of the parameters such as the spatio-temporal dispersion and the parabolic nonlinearity on the behavior of the soliton. The new model and findings may contribute to the understanding and characterization of the nonlinear behavior of pulse propagation in optical fibers, which is crucial for the development of optical communication systems. [ABSTRACT FROM AUTHOR]

We have studied the dynamics of various kinds of optical dark solitons like, chirped, chirp-free, M-shaped & wing shaped dark solitons using higher-order nonlinear Schrödinger equation. To obtain the exact analytical solution, we employed mathematical techniques such as the extended rational sinh-cosh and sin-cos methods. Our investigation shows that one can manipulate the shape of both chirp and chirp free dark solitons by properly tuning the magnitude of the self steepening and self phase modulation. The stability of the obtained dark soliton solutions are verified by using linear stability analysis. [ABSTRACT FROM AUTHOR]

We report the numerical and experimental studies of the two-dimensional Brillouin gain spectrum (BGS) distribution deformation induced by the self-phase modulation in the Brillouin optical time domain reflectometry (BOTDR) with a 20.6 km sensing distance. The BGS distribution deformation is investigated by analyzing the evolution of the point spread function along the fiber in the two-dimensional model of the BOTDR. In the simulation and experimental results, the specific deformation degree of the BGS distribution induced by the self-phase modulation is related to the pump pulse profile, pump pulse peak power, BGS demodulation method, and detected scattered light component. By comprehensively analyzing the evolution of the point spread function induced by the self-phase modulation and using the image deconvolution, a typical BOTDR sensor with a 25 ns pump pulse reaches the 20 cm spatial resolution over the 20.6 km sensing fiber. [ABSTRACT FROM AUTHOR]

This paper recovers quiescent optical solitons for the complex Ginzburg–Landau equation, studied with nonlinear chromatic dispersion and three of Kudryashov’s self–phase modulation structures. The enhanced Kudryashov's procedure has made retrieving a full spectrum of solitons possible. [ABSTRACT FROM AUTHOR]

This study aims to investigate cubic-quartic optical solitons with Kudryashov’s law of self-phase modulation. Thus, the combination of third-order dispersion (3OD) and fourth-order dispersion (4OD) is assumed in the model to ensure the smooth existence of solitons. The study is implemented with the aid of two effective integration schemes known as the improved projective Riccati equations method and the soliton ansatz technique. The soliton solutions are derived based on two physical cases targeting the relation between 3OD and 4OD. In case 3OD is equivalent to fourfold frequency times 4OD, only dark and singular soliton profiles are extracted. However, if the former relation is not achieved, various structures of soliton pulses are generated, including kink-dark, singular, W-shaped, bright, dark, kink, and anti-kink solitons. The physical interpretations of retrieved optical solitons are represented by illustrating the wave behaviors with suitable values of model parameters. The results show that the combination of 3OD and 4OD has a significant effect on the dynamics of soliton propagation. [ABSTRACT FROM AUTHOR]

This research work brings forth the understanding of optical cosh-Gaussian dynamics by incorporating the newly formulated Kudryashov equation. The method used is Anderson’s variational approach. We show that an appropriate choice of the trial wavefunction allows highlighting several varieties of stable and unstable solutions corresponding to non-dissipative or dissipative spatiotemporal solitons, propagating without deformation and with deformation. [ABSTRACT FROM AUTHOR]

The current paper extracts the implicit form of quiescent optical solitons that emerge from the nonlinear Schrödinger’s equation with the generalized form of quadratic–cubic nonlinear refractive index change. The work is with linear temporal evolution as well as with generalized temporal evolution. The results are in terms of Appell hypergeometric functions as in the case of the quadratic–cubic form of nonlinear refractive index, reported earlier. Lie symmetry analysis has made this retrieval possible. [ABSTRACT FROM AUTHOR]

This work is on the retrieval of quiescent optical solitons for the complex Ginzburg–Landau equation that is with nonlinear chromatic dispersion and generalized structure of quadratic–cubic form of self–phase modulation. The Lie symmetry is applied to make this retrieval possible. The model is studied with linear temporal evolutions as well as generalized temporal evolution. [ABSTRACT FROM AUTHOR]

The Biswas–Arshed equation (BAE) with space–time dispersion was currently considered in the literature. Optical phenomena embedded in this equation are self-steepening, self-phase modulation and Raman scattering. Here, we consider BAE with gain or loss. It is worth mentioning that the gain or loss has an impact on blowup or decaying solitons propagation in optical fibers, which is novel. Our objective is to find optical soliton solutions of BAE and the aforementioned physical phenomena are investigated in some details. The conditions for the dominance of a phenomenon are predicted. This is physically important to inspect the behavior of solitons prpagation. To this issue, exact solutions of the model equation are derived by using the unified method. The solutions obtained are displayed graphically. Dark soliton, bright soliton, M-shaped soliton, rhombus soliton (which is novel) and chirped soliton with tunneling are observed. The modulation instability is studied and it is found that it triggers when the coefficients of the space–time dispersions are positive. [ABSTRACT FROM AUTHOR]

We presented a concept of converged coexistence (CC) access network and generate, and test model is demonstrated for optimization of channel launch power PTODN in the distribution network which subsequently confirm power budget class of NG-PON2 in this paper. Multiplexing of wavelength and time (TWDM) technology is incorporated for multichannel NG-PON2 configurations for 5G, internet-of-things (IoT) applications, and fiber-to-the-x (FTTX) services. CC NG-PON2 symmetric configuration supporting 2.5 and 10 Gbps channels are analyzed and compared in the sight of channel nonlinear impairments includes Kerr-effect (γ) spanning from self phase modulation (SPM) and cross-phase modulation (CPM), chromatic dispersion (CD), and four wave mixing (FWM) in worst-case scenario. Intensity modulation (IM) technique incorporated before multiplexing the D/S channels by coexisting element (CEx) and coupled to wavelength routed (WR) optical distribution network (ODN). U/S channels are routed using wavelength select (WS) ODN. ODN is implemented using G.652 non zero dispersion shift (NZ-DSF) single-mode (SM) fiber. Multi-channel spectrum envelope propagating in either direction is optimized to PTODN = 3/5/7/9 dBm and 4 dBm, respectively. The theoretical modeling and simulative results confirms the proposed network configuration supports incremental receiver sensitivity (Rxs) as −42.19/−42/−39.75/−37.97 dBm and −35.45/−35.38/−33.45/0.38/−42 dBm for λ1 2.5 Gbps and λ8 10 Gbps TWDM and PtP WDM channels, respectively, for all-class networks supporting splitter configuration ratio of 640 at 50 km mitigating effect of channel nonlinearities like CD, SPM, cross-phase modulation (XPM), and FWM for λ8 10 Gbps channel. [ABSTRACT FROM AUTHOR]

Black phosphorus (BP) has attracted great research interest in nonlinear optics due to its anisotropic photoelectronic properties. As an allotrope of phosphorus, violet phosphorus (VP) has higher stability and desirable wide bandgap than BP, broadening the potential applications of phosphorus in optoelectronics. Herein, the nonlinear optical responses of layered BP and VP over broad spectral range from 405 to 1064 nm are investigated by the spatial self‐phase modulation (SSPM) method. These results show that both BP and VP exhibit excellent broadband SSPM effects. They all have large nonlinear susceptibility value (up to ≈ 10−8 e.s.u.), except for a weaker value at the near‐infrared band. Moreover, the SSPM pattern formation time becomes significantly longer with increasing wavelength. Significantly, an all‐optical switching using a 532 nm beam to control a 1064 nm near‐infrared beam is realized based on the SSPM, which demonstrate that the nonlinear optical response of signal beam (1064 nm) can be improved by adjusting the intensity of controlling beam (532 nm). This study provides a fascinating foundation for future applications of phosphorus allotropes in broadband nonlinear photonics. [ABSTRACT FROM AUTHOR]

Nonlinear Schrödinger equations with cubic nonlinearity are a model of wave propagation in fiber optics and have numerous nonlinear effects in four-wave mixing, ultrashort pulses, second-harmonic generation, self-phase modulation, stimulated raman scattering, etc. In this study, we apply the modified (G ′ / G) -expansion scheme to the Nonlinear Schrödinger equations with cubic nonlinearity in order to obtain numerous new exact complex wave solutions and their Bifurcation analyses. Despite the fact that numerous new exact complex wave solutions and bifurcation analyses had previously been determined for Nonlinear Schrödinger equations with cubic nonlinearity by a number of researchers, this study yielded not only more precise wave solutions but also new exact complex wave solutions and their Bifurcation analyses.Wave propagation in soliton physics, modulus instability in plasma physics, and soliton propagation in optical fibers may be better understood with the acquired information. To examine the nonlinear effects of the Nonlinear Schrödinger equations with cubic nonlinearity, 2D, 3D, contour, and BA diagrams are created. The Hamiltonian function is established to further the analysis of the phase plane's dynamics. The simulations were conducted using Python and MAPLE software tools. Therefore, the modified (G ′ / G) -expansion scheme solution procedure is more straightforward than other conventional methods. [ABSTRACT FROM AUTHOR]

With respect to parity-time symmetry, an anti-parity-time (APT) symmetric system exhibits much easier readout mechanism due to its real frequency splitting. Generally, such systems need to be operated at exceptional points (EPs) to obtain the best performance. However, strict conditions to locate APT symmetric systems at their EPs precisely put restraints on their practical applications. To overcome this problem, we propose a scheme to manipulate EPs in APT symmetric configuration by the Kerr effect. It is demonstrated that operating EPs by self-phase modulation alone will impede frequency splitting caused by external perturbations, while cross-phase modulation can enhance the response to measurable perturbations. We also investigate the thermal effect induced by high light intensity, which could reduce the power to manipulate EPs. This proposed scheme can pave a new way for fabricating devices based on APT symmetry. [ABSTRACT FROM AUTHOR]

In this work a spatial phase modulation and four-wave mixing in graphene tungsten disulfide (WS2) heterostructure have been demonstrated, which is excited by plasmons of nano-plasmonic donate shape rings. For this purpose, a laser writing system was used to fabricate nanohole arrays and cover them with the plasmonic gold thin film via a sputtering machine and WS2 and graphene heterostructure by chemical vapor deposition method. After evaluating the plasmon excitation in this system by the ellipsometric method, the probe laser excitation was set to 980 nm to record spatial phase modulation, and also, four-wave mixing was used. Our results show spatial self-phase modulation (SSPM) and temperature enhancement due to the nonlinear enhancement of two-dimensional structure by heterostructure substances suitable for new-generation optical devices. [ABSTRACT FROM AUTHOR]

Self-focusing and self-phase modulation of focused femtosecond laser pulse were studied in bulk fused silica. Depending on pulse energy magnitude, three different regimes were observed in the experiment: (1) linear regime, when the self-focusing effect is insignificant, characterized by linear spectral broadening; (2) transition regime, when the self-focusing effect notably reduces a laser beam spot in a focal plane without considerable nonlinear absorption and beam collapse, characterized by quick increase in spectral broadening due to self-phase modulation; (3) nonlinear regime, filamentation, characterized by near-to- linear spectral broadening due to self-phase modulation. The slope for the linear and nonlinear regimes was the same within the measurement error bars. The numerical simulation, using the ray transfer matrix method, envisioned the self-phase modulation spectral broadening effect in all these regimes. [ABSTRACT FROM AUTHOR]

This paper employs the Lie symmetry analysis to integrate the concatenation model studied with the Kerr law of self-phase modulation. The reduced ordinary differential equation is integrated using two approaches, which are the extended tanh method and the generalized Arnous' approach. These yielded dark and singular solitons for the model. [ABSTRACT FROM AUTHOR]

The current paper studies gap solitons with parabolic-nonlocal form of self-phase modulation. The soliton solutions for this model are revealed with the successful application of the extended auxiliary equation approach. The parameter constraints ensure the existence of such gap solitons. [ABSTRACT FROM AUTHOR]

This study focuses on investigating analytical soliton solutions within the context of the time-fractional cubic-quintic nonlinear non-paraxial pulse propagation model, an adaptive model with extensive uses in various intricate real phenomena, such as nonlinear optics, fiber optics communication, optical signal processing, laser-tissue interaction in biomedical science, among others. Depending on the strength of the cubic and quintic nonlinear terms, various nonlinear effects, including self-focusing, self-phase modulation, and wave mixing, can be observed. This model is investigated using a powerful analytical technique, the (G ′ / G , 1 / G) -expansion approach, which develops several potential solitons that allow for insight into the laser pulse interactions. This study yields diverse illustrative soliton solutions, including periodic, bell-shaped, kink, singular solitons, etc. some of which have been documented in former literature. Furthermore, we conduct an extensive analysis of these solitons, considering both anomalous and normal group velocity dispersion, and effectively visualize the results through two- and three-dimensional graphs, along with contour plots. The findings in this article could hold significance for researchers engaged in the advancement of optical equipment, biomedical laser devices, mode-locked lasers, and similar technologies. [ABSTRACT FROM AUTHOR]

This manuscript represents some solitary wave solutions to the perturbed nonlinear Schrödinger equation studied for parabolic law of nonlinearity. Self phase modulation and inter-model dispersion are the main causes of perturbation terms. To investigate the model, we adopt two mathematical methods namely the generalized Kudryashov technique and the modified auxiliary equation technique. As a consequence, a collection of different soliton solutions including dark soliton, singular bright soliton, singular kink soliton, kink soliton and other solitary solutions are generated. The derived soliton solutions have the forms of hyperbolic, trigonometric, and exponential functions. This manuscript also includes the graphical representation of the soliton solutions in the form of 2D, 3D and contour plots. The parameter limitations that naturally arise are also addressed. [ABSTRACT FROM AUTHOR]

In this work, the perturbed nonlinear Schrödinger's equation (NLSE) with self-phase modulation (SPM) of Kudryashov's sextic power law which describes the soliton's propagation in optical fiber is investigated. New exact solutions will be introduced including doubly periodic solutions in the form of Weirstrass and hyperbolic functions by using the simple equation method. There have been several different kinds of optical soliton solutions proposed, including dark, bright, kink, and anti-kink soliton solutions. To further understand some of its physical characteristics, the resulting optical soliton solutions are illustrated graphically. [ABSTRACT FROM AUTHOR]