Propagation In Optical Fibers Research Articles

Conservation laws of the complex short pulse equation and coupled complex short pulse equations

In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases. Based on the linearizing operator and adjoint linearizing operator for the two real systems, adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair (SA) method. Relationships between the nonlinear self-adjointness method and the SA method are investigated.

Extraction of some optical solutions to the (2+1)-dimensional Kundu–Mukherjee–Naskar equation by two efficient approaches

The Kundu–Mukherjee–Naskar (KMN) model is considered for describing the pulse propagation in optical fibres and communication systems. Two efficient approaches via the exp (−φ(ξ))-expansion and the improved F-expansion schemes are applied to the KMN model and in order to convert the KMN equation to an ODE, we test the complex wave conversions and present some optical soliton solutions, which are expressed in terms of hyperbolic, rational and trigonometric functions. We create three dimensional and two-dimensional images to explain the underlying optical wave properties of the KMN equation and compare our solutions with the ones in the literature. Our example shows that the two adopted methods provide an efficient mathematical tool for constructing new optical wave solutions to nonlinear partial differential equations arising in fibre optic communication systems.

Self-steepening, Raman scattering and self-phase modulation-interactions via the perturbed Chen–Lee–Liu equation with an extra dispersion. Modulation insability and spectral analysis

It is worth mentioning that the perturbed Chen–Lee–Liu equation (PCLLE) exhibits the effects of self-steepening (SS), Raman scattering (RS) and self-phase modulation (SPM). Our attention is focused, here, to inspect the challenge between these phenomena may lead to a dominant one among them. On the other hand, we investigate the dominant phenomena produced due to these interactions. Furthermore, the structure of the configuration of pulses propagation in optical fibers are depicted. These phenomena are illustrated, here, via studying the PCLLE with an extra dispersion. This equation is formulated and the exact solutions of this new equation are found by using the unified method (UM). The importance of the UM stems from the fact that, in the applications, we have found that the UM is of low time cost in symbolic computation. So, we think that it prevails the known methods in the literature. On the other hand, the solutions for the complex envelope field equations, found in the literature, are always considered with real wave amplitude. Here, a transformation based on using complex wave amplitude is introduced. Indeed, in this case, solutions describe the waves that result from soliton- periodic wave collision, which may reveal novel phenomena. The solutions obtained are evaluated numerically and represented in graphs. It is shown that pulses compression occurs which may be due to self-phase modulation. Also, dispersive shock wave can be produced which may be argued to the presence of the extra dispersion and self-sdteepening. It is worthy to mention that, self-steepening arises for a small value of the related coefficient. The results obtained, here, are novel. The modulation instability is analyzed and it is found that it triggers at a critical values of SS and RS coefficients. At this stage, shock wave may occur. It is observed that the spectrum shows soliton with periodic waves background.

Continuous limit and location-manageable discrete loop rogue wave solutions for the semi-discrete complex short pulse equation

This paper focuses on the semi-discrete complex short pulse equation which may describe the ultra-short pulse propagation in optical fiber. First, we study the continuous limit of the semi-discrete complex short pulse equation and establish a certain connection with a continuous complex short pulse equation. Then the discrete generalized (p,N−p)-fold Darboux transformation is constructed to generate three kinds of location-manageable discrete localized wave solutions including loop rogue wave, loop periodic wave, and their mixed collision loop structures. With the help of the hodograph transformation, we find a class of implicit solutions of semi-discrete complex short pulse equation, and some specific parameters are added to the analytical expressions so that we can theoretically manage these loop structures where we want them to appear. These unique structures may help researchers better grasp the characteristics of location-manageable loop localized wave solutions and explain many physical phenomena in nonlinear optics.

The closed-form soliton solutions of the time-fraction Phi-four and (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff model using the recent approach

The Phi-four (PF) model is a variation of the familiar Klein–Fock–Gordon​ (KFG) model. Quantum effects, ultra-short pulse propagation in optical fibers, character of de-Broglie waves, wave-particle duality, composite particles of spineless relativistic, etc. are investigated through the PF model. The interface of Riemann waves in two spatial dimensions is explained by the Calogero–Bogoyavlenskii–Schiff (CBS) model. Many physical phenomena such as, the magneto-sound waves in plasmas, tsunami and tidal in rivers, and the internal waves in oceans can be describe through the Riemann wave. This article investigates the unique and wide-ranging analytic soliton solutions to the above-stated models in the sense of the fractional conformable derivative by using the auxiliary equation technique in terms of exponential, trigonometric, hyperbolic, and rational functions. To analyze the underlying wave structures and to examine the active behavior of the obtained solutions, three-dimensional (3D) and contour graphs are plotted using the Wolfram Mathematica program. The attained solutions demonstrate that the method is compatible, effective, and scientifically efficient.

Recent Development of Mid-Infrared Supercontinuum Generation in Fluoroindate Glass Fibers

Supercontinuum (SC) generation that leads to the emission of broadband radiation has been extensively studied. In particular, SC sources encompassing the wavelength range of 2–5 μm have attracted considerable interest in the last decade, and a continuous increase in the output power and spectrum width has been observed. To enable broadband and high-power SC generation, suitable nonlinear media combined with appropriate pump sources must be used, maintaining the output as spectrally flat. This paper briefly reviews the current state-of-the-art SC sources restricted to those based on fluoroindate fibers, including systems pumped with femtosecond, picosecond, and nanosecond pulses. First, the concept of SC generation in optical fibers is briefly presented. This is followed by an examination of indium fluoride optical fibers, with an emphasis on their material and waveguide properties. Furthermore, the advances in SC generation in fluoroindate fibers, including the latest results on high-power (Watt-level) continuum generation adopting different pump schemes, are also explored. A record time-averaged output power of 11.8 W with a spectrum spanning from ~1.9 to 4.9 µm has been demonstrated, which is certainly not the power limit of this technology. Finally, potential future directions of research are discussed at the end of this paper.

Optimal system of Lie subalgebra for symmetry reductions, group invariant solutions and exact solutions to the coupled Hirota–Maccari system driving pulse propagation in optical fiber

In this paper, Lie symmetry analysis has been proposed by utilizing the Lie group of continuous point transformation for obtaining the new exact soliton solutions of the (2+1)-dimensional Hirota–Maccari system. Lie infinitesimals and possible geometric vector fields are obtained by applying the third-order prolongation on this system. Also, their commutative product and adjoint relations have been presented in Tables 1 and 2. By considering the resulting symmetries, one-dimensional optimal system of Lie subalgebra is obtained. Meanwhile, the Hirota–Maccari system is reduced to a system of ordinary differential equations with the help of optimal subalgebras. Furthermore, the simplest equation method has been used to obtain the abundant exact soliton solutions of the reduced system. At last, conservation laws of Hirota–Maccari system have been extracted by utilizing the generalized “new conservation theorem” invoked by Ibragimov.

Optical solitons with Kudryashov’s sextic power-law nonlinearity

Objective –The main objective of this paper is to investigate analytic soliton solutions of a nonlinear Schrödinger equation (NLSE), including Kudryashov’s sextic power-law nonlinearity by introducing different approaches of two efficient analytical methods. The considered equation has been recently introduced by N. A. Kudryashov to describe pulse propagation in optical fibers. The refractive index in the equation comprises six terms, each of the terms containing a power-law component. Methods –Applying a wave transformation to the considered NLSE and splitting up the real and imaginary parts, the NLSE is converted to the nonlinear ordinary differential equations (NLODEs). Then, the solutions of NLODEs are considered as suggested in the proposed method and suggested solutions that include some unknown parameters are substituted into the NLODE. An algebraic equations system is acquired by collecting the same power of the unknown function and equating all coefficients to zero. The unknown parameters in the system, and so the solutions of the NLSE, are found by solving the system. In the proposed first method, the modified extended tanh method is enhanced by proposing more solutions. The proposed second method, a different version of auxiliary methods, can remarkably reduce calculations to easily get solutions for the NLSEs with higher-order or power-law nonlinearity. Results –The two proposed methods are successfully applied to the considered NLSE and the abundant solutions of the NLSE are attained. Besides, 2D, 3D and contour graphs are demonstrated in figures for the physical illustrations of the gained solutions. Conclusion –Obtaining the solutions of NLSEs with higher-order or power-law nonlinearity has crucial importance but still challenging work. So, we propose different approaches of two efficient analytical methods, namely, enhanced modified extended tanh expansion method and an auxiliary function method. The derived results imply that the used methods are very efficient, reliable and powerful such that they can be easily implemented to many nonlinear NLSEs with higher-orders or higher power-law nonlinearities that describe real-life phenomena.

Spectral element modeling of ultrasonic guided wave propagation in optical fibers

Recent advancements in fiber optic methods have enabled their use for guided wave sensing. It opens up new possibilities for Structural Health Monitoring. The aim of this paper is to provide insight for the physics related to guided wave propagation and coupling between the optical fiber and solid structure. For this purpose, a new approach for non-matching interface based on Lagrange multipliers and the time domain spectral element method was developed. A parallelized code has been implemented in order to simulate the guided wave propagation in the structure, its coupling into the optical fiber and the propagation in the fiber in a computationally efficient way. The paper presents four studies showing the efficacy of the modeling approach. The paper first shows the improvement in the computation speed through the use of parallelization and a more efficient implementation. Then the results of the simulation of wave propagation in the fiber are compared with results from previous simulation studies using commercially available software. The third study shows that the spectral element method is able to capture the directional sensitivity of optical fiber based sensors. Lastly, the simulation is used for detection of simulated damage using the spectral element method based simulation. The results indicate that indeed the spectral element implementation is able to recreate the wave coupling phenomena, capture the physics of the system including directional sensitivity and reflections from damage.

Optical solitons of the model with generalized anti-cubic nonlinearity

The mathematical model for description of pulse propagation in optical fiber for the generalized anti-cubic nonlinearity with arbitrary refractive index is considered. The Cauchy problem for this partial differential equation cannot be solved by the inverse scattering transform and the analytical solutions of this mathematical model are found taking into account the traveling wave reduction. First integral of nonlinear ordinary differential equation is presented. Analytical solutions in the form of periodic and solitary waves are found using some transformations. Partial cases of the mathematical model for the generalized anti-cubic nonlinearity are studied.

Temporal Talbot effect of optical dark pulse trains.

The temporal Talbot effect describes the periodic self-imaging of an optical pulse train along dispersive propagation. This is well studied in the context of bright pulse trains, where identical or multiplied pulse trains with uniform bright waveforms can be created. However, the temporal self-imaging has remained unexplored in the dark pulse regime. Here, we disclose such a phenomenon for optical dark pulse trains, and discuss the comparison with their bright pulse counterparts. It is found that the dark pulse train also revives itself at the Talbot length. For higher-order fractional self-imaging, a mixed pattern of bright and dark pulses is observed, as a result of the interference between the Talbot pulses and the background. Such unconventional behaviors are theoretically predicted and experimentally demonstrated by using programmable spectral shaping as well as by optical fiber propagation.

Engineering the high-frequency components of coherent supercontinuum generation in hybrid optical fibers with yttrium aluminum garnet core

Coherent supercontinuum (SC) generation in optical fibers has spurred extensive research interest and found many applications. Here, we report a hybrid optical crystal fiber with an yttrium aluminum garnet (YAG) core. The optimized fiber features broad and flat near-zero normal dispersion and three wavelengths where the dispersion slope is zero. Through numerical modeling, we in detail investigate the influence of the pump wavelengths near the three wavelengths on the spectral broadening. The spectral broadening shows asymmetric towards the high-frequency region. The longer the pump wavelength, the more is the short wavelength components of the generated SC. Thus, the high-frequency components of the SC spectra can be engineered in the fiber. Interestingly, the occurrence of optical wave breaking (OWB) in the low-frequency region is prior to that in the high-frequency region when the pump wavelength is at 1660 nm. The broadest spectrum could be obtained when the pump wavelength is near the middle wavelength where the dispersion slope is zero. The result provides a new strategy for fiber design and broadband SC generation, which is different from the viewpoint that the broadest spectrum can be obtained when the pump wavelength near the local maximum dispersion. Combined with high nonlinearity and flat dispersion, the hybrid fiber allows octave-spanning SC generation with the pump power low to 1 kW at 1100 nm. This provides the potentials for high-power, broadband, and coherent SC generation at 1064 nm where the dispersion slope is near zero.

The soliton analysis for optical fibers models

Optical fibers have a major role in the industry and daily life. To simulate the pulse propagation in optical fibers, numerous models are seen in the literature. In this work, the Kundu-Mukherjee-Naskar (KMN) model and the anti-cubic Schrödinger equation are considered. To solve these models, ansatz-based methods are considered and also, the problem about the determination of transformation is replied so that it is not clear in the literature. The results of the proposed models will play a key role in applications in nonlinear optics, fluid dynamics, quantum mechanics and various other branches of science.

Optical solitons and single traveling wave solutions of Biswas-Arshed equation in birefringent fibers with the beta-time derivative

<abstract><p>This article describes the construction of optical solitons and single traveling wave solutions of Biswas-Arshed equation with the beta time derivative. By using the polynomial complete discriminant system method, a series of traveling wave solutions are constructed, including the rational function solutions, Jacobian elliptic function solutions, hyperbolic function solutions, trigonometric function solutions and inverse trigonometric function solutions. The conclusions of this paper comprise some new and different solutions that cannot be found in existing literature. Using the mathematic software Maple, the 3D and 2D graphs of the obtained traveling wave solutions were also developed. It is worth noting that these traveling wave solutions may motivate us to explore new phenomena which may be appear in optical fiber propagation theory.</p></abstract>

Abundant optical solitons of the (2 + 1)-dimensional Biswas-Milovice equation arising in optical fiber

In this study, we aim to investigate the (2 + 1)-dimensional Biswas-Milovice equation that describes the pulse propagation in optical fiber. With the help of the Exp-function based method and He’s frequency formulation, eleven sets of the optical solitons such as bright soliton, dark soliton, bright-dark soliton, kinky bright-dark soliton and periodic soliton solutions are obtained. The behaviors of the results are presented through the 3-D plot and 2-D curve. The findings of this paper are expected to opened up new horizons for the study of the soliton theory in optics.

Specialty optical fiber modeling, fabrication, and characterization: introduction

In this introduction, we provide an overview of the papers that were accepted for publication in the feature issue on specialty optical fiber modeling, fabrication, and characterization. A total of 22 papers were published in JOSA B. This feature issue presents cutting-edge research on specialty optical fibers and highlights recent developments in a new generation of optical fibers.

A generalized Kundu--Eckhaus equation with an extra-dispersion: pulses configuration

Raman effect is due to self-phase modulation (SPM), which is embedded in Kundu--Eckhaus equation KEE. Here, the objective of this work is to present a generalized KEE by accounting for an extra dispersion which may be induced by Raman scattering. Also, attention is focused to study the effects of the extra dispersion.Which are investigated via obtaining the exact solutions of the new model equation. These solutions are found by the unified method and by introducing a new transformation that ispects soliton- periodic wave collision. We aim to show that a variety of shapes of optical pulses OPs propagation in optical fibers occurs. Waves of multiple geometric structures are observed. Among these waves, hybrid lumps, soliton, cascade, complex chirped, hybrid w-shaped, rhombus (diamond) waves and soliton self phase modulation.The characteristics of the pulses; intensity, frequency, wavelength, polarization, and spectral content are identified. The results found here are of great interest in experimenting the effects of the induced dispersion on pulses configurations. Further, the colliding dynamics are inspected and as it is observed that no rogue or sharp waves formation hold, so the collision is elastic.

Abundant exact soliton solutions to the Fokas system

In the current work, we consider the Fokas system that describes the nonlinear pulse propagation in monomode optical fibers. By employing the Exp-function method, we succeed in constructing six families(eleven sets) of the exact soliton solutions. And the behaviors of the real, imaginary and absolute parts of the solutions are described through the 3-D contours. It reveals that the Exp-function method is an effective method to construct abundant exact solutions for the partial differential equations arising in optics.

Soliton interaction of a generalized nonlinear Schrödinger equation in an optical fiber

Under investigation in this work is a generalized nonlinear Schrödinger (NLS) equation with high-order dispersion and quintic nonlinear terms, which can describe a subpicosecond pulse propagation in optical fibers. By developing Hirota method, the bilinear form and analytical one- and two-soliton solutions are derived. Based on the analytical solutions, we give the corresponding soliton patterns to analyse dynamics of the pulse solitons. It shows that high order dispersion term may change the periodicity of propagation. The interaction of two pulse solitons is an elastic collision. By choosing suitable parameter values, we can obtain the two parallel solitons. It can be applied to improve transmission quality and capacity of information in optical fiber.

Dynamics of optical solitons in higher-order Sasa–Satsuma equation

Higher order and multidimensional generalizations of the nonlinear Schrödinger equation are useful in a variety of applications. A generalized (3+1)-dimensional nonlinear Sasa–Satsuma equation is studied via the improved generalized Riccati equation mapping method and its Bäcklund transformation and the extended hyperbolic function method. This nonlinear model can be use to describe the physical processes of wave propagation in optical fibers. We explicitly retrieved varieties of optical solitons like bright, dark, singular, combined bright–dark and combined singular-bright to this multidimensional generalized nonlinear model. Other solutions, such as periodic, rational, and exponential solutions of different structures, are also produced as a result of the evolution of this improved technique. Furthermore, the graphs in two and three dimensions are provided to visualize the structure of the solutions acquired by choosing certain parameter values.