Propagation Of Optical Pulses Research Articles

Optical fractional solitonic structures to decoupled nonlinear Schrödinger equation arising in dual-core optical fibers

This paper explores a specific class of equations that model the propagation of optical pulses in dual-core optical fibers. The decoupled nonlinear Schrödinger equation with properties of M fractional derivatives is considered as the governing equation. The proposed model consists of group-velocity mismatch and dispersion, nonlinear refractive index and linear coupling coefficient. Different types of solutions, including mixed, dark, singular, bright-dark, bright, complex and combined solitons are extracted by using the integration methods known as fractional modified Sardar subequation method and modified F-expansion method. Optical soliton propagation in optical fibers is currently a subject of great interest due to the multiple prospects for ultrafast signal routing systems and short light pulses in communications. In nonlinear dispersive media, optical solitons are stretched electromagnetic waves that maintain their intensity due to a balance between the effects of dispersion and nonlinearity. Furthermore, hyperbolic, periodic and exponential solutions are generated. A fractional complex transformation is applied to reduce the governing model into the ordinary differential equation and then by the assistance of balance principle the methods are used, depending upon the balance number. Also, we plot the different graphs with the associated parameter values to visualize the solutions behaviours with different parameter values. The findings of this work will help to identify and clarify some novel soliton solutions and it is expected that the solutions obtained will play a vital role in the fields of physics and engineering.

Analyzing the time-fractional (3 + 1)-dimensional nonlinear Schrödinger equation: a new Kudryashov approach and optical solutions

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.

A generalized nonlinear Schrödinger equation with logarithmic nonlinearity and its Gaussian solitary wave

In the current paper, a generalized nonlinear Schrödinger (gNLS) equation with logarithmic nonlinearity is studied as a model for the propagation of optical pulses. More precisely, after applying a specific hypothesis for the solution of the governing equation, its Gaussian solitary wave is retrieved using the ansatz method. Some numerical simulations in two- and three-dimensional postures are presented to investigate the impact of different physical parameters on Gaussian solitary wave’ dynamics. Results confirm that the physical parameters of the gNLS equation have a key role in controlling the dynamics of the Gaussian solitary wave.

Localized wave solutions to coupled variable-coefficient fourth-order nonlinear Schrödinger equations

This study investigates higher-order localized waves for coupled variable-coefficient fourth-order nonlinear Schrödinger equations, which are used to describe the simultaneous propagation of optical pulses in an inhomogeneous optical fiber. Based on the seed solutions and Lax pair, the Nth-order localized wave solutions are constructed. The interactions of rogue waves with dark–bright solitons are graphically analyzed via numerical simulation. The results are helpful for studying localized wave phenomena in nonlinear optics.

Study on soliton behaviors of the complex nonlinear Fokas–Lenells equation utilizing different methods

In this paper, we study the Fokas–Lenells equation, which is a derivation form of the nonlinear Schrödinger equation and can be used to describe nonlinearity in the propagation of optical pulses. To seek solutions for this nonlinearity, the Logistic method has been proposed in order to drive acceptable and understandable results regarding physical meaning. This method is defined based on the summation of an ordinary differential equation. Moreover, for further study, the Bernoulli [Formula: see text]-expansion method is used by considering hypothetical solutions as a function of the Bernoulli equation. Subsequently, solutions of the Fokas–Lenells equation are successfully acquired, displaying efficient results in hyperbolic, trigonometric, and exponential equations. The importance of these results appears in the definition of the wave function under the consideration of the appropriate coefficients. Hence, computer simulation is used for better understanding of the generated results. The dynamic behaviors of these solutions are demonstrated in 3D graphs, contour maps, and line plots, under applying various parameters, solutions of the waves show different soliton behaviors, including bright-dark, bright, and breather solitons. The results indicate that the exerted methods are novel, reliable, and effective approaches which can be employed in a wide range of nonlinear differential equations. These methods and their begotten results are far from the complexities of mathematical structures and therefore go beyond previous efforts in the literature.

Soliton solutions of the improved perturbed nonlinear Schrödinger equation having parabolic law with non-local nonlinearity in the presence of chromatic and spatio-temporal dispersion terms

This paper was organized to examine the analytical solutions of the improved perturbed parabolic-law nonlinear Schrodinger equation including non-local nonlinearity in the presence of chromatic and spatio-temporal dispersion. This model mostly makes use of studying the propagation of optical pulses in fiber optic communication systems. We performed the Sinh-Gordon equation expansion method so that we produce the analytical solutions of the model under consideration. It was confirmed that the acquired solutions satisfy the main model. Therefore, bright and dark soliton solutions were retrieved; besides, various 3D and 2D graphical illustrations of the solitons were demonstrated via appropriate values of the parameters. Furthermore, this manuscript focused on the parameters’ effect on the acquired solitons behavior.

On the optical soliton solutions to the fractional complex structured (1+1)-dimensional perturbed gerdjikov-ivanov equation

In this work, we examine the complex structured Fractional Perturbed Gerdjikov-Ivanov equation (FPGIE), which describes the propagation of optical pulses with perturbation effects. This model finds applications in optical fibers, especially in photonic crystal fibers. We are discovered novel and unique optical soliton solutions using the modified Extended Direct Algebraic Method (mEDAM), which has never been used with this model previously. As a result, a hierarchy of traveling wave solutions including singular kink, periodic, solitary kink, and rogue-shaped soliton solutions, etc., are derived. Some obtained solutions are discussed graphically based on numerical values of some parameters related to the solution. The results add new and unique soliton types to the model and demonstrate how they interact and impact the system’s overall dynamics.

Impact of Intense Modulation on Soliton Power Propagation across Optical Fiber and Optical Wireless Channels

The optical pulse generator model in Optisystem 20 is utilized to generate an optical soliton pulse. The performance evaluation of highly modulated soliton power transmission is carried out on both optical fiber and optical wireless communication channels. The evaluation considers a flow rate of 40 Gbps and a link distance, which is not specified in the provided context. Among the proposed modulation schemes, which include CPFSK, FSK, and PSK, CPFSK demonstrates superior performance for both communication channels. Increasing the number of bits per symbol enhances the bit error rate (BER) at the fiber or wireless channel, as received by the optical receiver, for different modulation schemes, except for the CPFSK scheme. Thus, it is evident that the CPFSK modulation scheme is more efficient and outperforms other modulation schemes for various communication channels. Hence, it is evident that the CPFSK modulation scheme exhibits superior efficiency and outperforms other modulation schemes for a variety of communication channels.

A gateway to synthesis of all-optical devices of desired functionalities

I propose combining of all-optical devices to produce an all-optical device that exhibits a desired input–output (I/O) characteristic (i.e., a desired functionality). There could be infinite distinct combinations of same/different all-optical devices of same/different parameters resulting in possibility of infinite number of all-optical devices with distinct I/O characteristics, and hence, the proposal presented here opens-up a gateway to synthesis of all-optical devices of desired functionalities. To give a few of examples in support of the proposal, I show certain series and parallel combinations of nonlinear Mach-Zehnder interferometers (NMZIs) to synthesize an (i) ideal optical switch (with step like I/O characteristic), (ii) optical isolator/optical stabilizer (iii) optical pulse generator (iv) optical power filter and (v) optical limiter. The analytical findings are verified using BPM simulations in presence of losses also.

Silicon photonics-based high-energy passively Q-switched laser

Chip-scale, high-energy optical pulse generation is becoming increasingly important as integrated optics expands into space and medical applications where miniaturization is needed. Q-switching of the laser cavity was historically the first technique to generate high-energy pulses, and typically such systems are in the realm of large bench-top solid-state lasers and fibre lasers, especially in the long wavelength range >1.8 µm, thanks to their large energy storage capacity. However, in integrated photonics, the very property of tight mode confinement that enables a small form factor becomes an impediment to high-energy applications owing to small optical mode cross-sections. Here we demonstrate a high-energy silicon photonics-based passively Q-switched laser with a compact footprint using a rare-earth gain-based large-mode-area waveguide. We demonstrate high on-chip output pulse energies of >150 nJ and 250 ns pulse duration in a single transverse fundamental mode in the retina-safe spectral region (1.9 µm), with a slope efficiency of ~40% in a footprint of ~9 mm2. The high-energy pulse generation demonstrated in this work is comparable to or in many cases exceeds that of Q-switched fibre lasers. This bodes well for field applications in medicine and space.

Conditional recurrent neural networks for broad applications in nonlinear optics.

We present a novel implementation of conditional long short-term memory recurrent neural networks that successfully predict the spectral evolution of a pulse in nonlinear periodically-poled waveguides. The developed networks offer large flexibility by allowing the propagation of optical pulses with ranges of energies and temporal widths in waveguides with different poling periods. The results show very high agreement with the traditional numerical models. Moreover, we are able to use a single network to calculate both the real and imaginary parts of the pulse complex envelope, allowing for successfully retrieving the pulse temporal and spectral evolution using the same network.

Quasinormal Modes of Optical Solitons.

Quasinormal modes (QNMs) are essential for understanding the stability and resonances of open systems, with increasing prominence in black hole physics. We present here the first study of QNMs of optical potentials. We show that solitons can support QNMs, deriving a soliton perturbation equation and giving exact analytical expressions for the QNMs of fiber solitons. We discuss the boundary conditions in this intrinsically dispersive system and identify novel signatures of dispersion. From here, we discover a new analogy with black holes and describe a regime in which the soliton is a robust black hole simulator for light-ring phenomena. Our results invite a range of applications, from the description of optical pulse propagation with QNMs to the use of state-of-the-art technology from fiber optics to address questions in black hole physics, such as QNM spectral instabilities and the role of nonlinearities in ringdown.

Generation of width-tunable optical pulse based on Mach–Zehnder modulator in Sagnac loop

Generation of width-tunable optical pulse based on Mach–Zehnder modulator in Sagnac loop

A ∂¯-Dressing Method for the Kundu-Nonlinear Schrödinger Equation

In this paper, we employed the ∂¯-dressing method to investigate the Kundu-nonlinear Schrödinger equation based on the local 2 × 2 matrix ∂¯ problem. The Lax spectrum problem is used to derive a singular spectral problem of time and space associated with a Kundu-NLS equation. The N-solitions of the Kundu-NLS equation were obtained based on the ∂¯ equation by choosing a special spectral transformation matrix, and a gradual analysis of the long-duration behavior of the equation was acquired. Subsequently, the one- and two-soliton solutions of Kundu-NLS equations were obtained explicitly. In optical fiber, due to the wide application of telecommunication and flow control routing systems, people are very interested in the propagation of femtosecond optical pulses, and a high-order, nonlinear Schrödinger equation is needed to build a model. In plasma physics, the soliton equation can predict the modulation instability of light waves in different media.

Propagation of Broad-Band Optical Pulses in Dispersionless Media

Propagation of Broad-Band Optical Pulses in Dispersionless Media

Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media

We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, α 1 α 2 ∈ ( 1 , 2 ] , and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic FNLS equation with only one Lévy index (LI) α = 1 , can be suppressed in the two-LI FNLS system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability (MI) of continuous waves is investigated in the two-LI system too. In particular, the MI may occur in the case of the defocusing nonlinearity when two diffraction coefficients have opposite signs. Using results for the MI, we produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity.

The Study of Soliton Propagation in Optical Fibers

Abstract: In optical fibres, soliton formation results from a balance between the chirps produced by GVD and SPM, which, when functioning separately, both restrict the system's performance. We will analyse the dispersion-induced pulse broadening and the nonlinear optical effects to understand how such a balance is feasible. During an optical pulse's propagation inside an optical fibre, the GVD broadens it, unless the pulse is first chirped correctly. More precisely, whenever β2 and the chirp parameter C have opposing signs, resulting in β2C being negative, a chirped pulse is compressed at early phases of transmission. SPM causes the optical pulse to chirp so that C > 0. The criterion β2C < 0 can be easily met if β2 < 0. Furthermore, since the SPM-induced chirp is power-dependent, it is conceivable that, under some circumstances, SPM and GVD might work together to the point where the SPM-induced chirp is just the proper amount to cancel out the GVD-induced pulse broadening. In this case, an optical pulse propagates as a soliton with no distortion

GHz repetition rate tunable optical pulses generation using a SBS-based coupled optoelectronic oscillator

An optical pulse generator with a tunable repetition rate of GHz is proposed employing a coupled optoelectronic oscillator (COEO). The tunability is achieved with an equivalent tunable RF bandpass filter which is realized through phase modulation and stimulated Brillouin scattering (SBS) in a high nonlinear fiber. An injected seed laser is applied to stabilize the central wavelength of the mode-locked loop. The repetition rate of the generated optical pulses is the frequency difference between the Stokes wave and the seed laser. It is adjusted by changing the wavelength of the pump laser for SBS effect. In the experiments, optical pulse trains with a repetition rate of 7.3 GHz–9.3 GHz are generated, and RF oscillating signals at the corresponding frequency are simultaneously produced. The side-mode suppression ratios (SMSRs) of the generated RF signals are all higher than 50 dB, and the phase noise is lower than −80dBc/Hz @10-kHz offset frequency. The tunable range of the optical pulse rate is limited by the bandwidth of the used RF phase shifter in the oscillating loop.

A study of optical solitons of Manakov model describing optical pulse propagation

A study of optical solitons of Manakov model describing optical pulse propagation

Novel optical waves for the perturbed nonlinear Chen-Lee-Liu equation with variable coefficients using two different similarity techniques

In this paper, a new extension of the perturbed nonlinear Chen-Lee-Liu equation as a variable coefficients model represents optical pulse propagation in a monomode fiber is studied. The direct similarity reduction method is used to transform the Chen-Lee-Liu model with variable coefficients to a nonlinear ordinary differential equation and the Jacobi elliptic expansion method is used to solve the reduced equation and as a result, novel optical solitons, periodic, and singular waves have arisen. Then, to prove the physical existence and importance of the presented variable coefficients Chen-Lee-Liu model, another similarity technique is used to transform the Chen-Lee-Liu model to the generalized derivative Schrödinger equation which has known bright and dark soliton solutions. Finally, a graphical representation of the obtained wave solutions according to different structures of the variable coefficients is presented.