Nonlinear Fiber Research Articles

Near-noiseless and small-footprint phase sensitive optical parametric amplifier using AlGaAs-on-insulator waveguides.

Phase sensitive amplifiers (PSAs) based on optical parametric amplification feature near noiseless amplification, which is of considerable benefit for improving the performance of optical communication systems. Currently, the majority of research on PSAs is carried out on the basis of highly nonlinear fibers or periodically poled lithium niobite waveguides, with the impediments of being susceptible to environmental interference and requiring complex temperature control systems to maintain quasi-phase matching conditions, respectively. Here, a near-noiseless and small-footprint PSA based on dispersion-engineered AlGaAs-on-insulator (AlGaAsOI) waveguides is proposed and demonstrated theoretically. The phase-dependent gain and the phase-to-phase transfer function of the PSA are calculated to analyze its characteristics. Furthermore, we investigate in detail the effects of linear loss, nonlinear coefficient, and pump power on the PSA gain and noise figure (NF) in AlGaAsOI waveguides. The results show that a PSA based on an AlGaAsOI waveguide is feasible with a maximum phase sensitive gain of 33dB, achieving an NF of less than 1dB over a gain bandwidth of 245nm with a gain of >15d B, which completely covers the S+C+L band. This investigation is worthwhile for noiseless PSAs on photonic integrated chips, which are promising for low-noise optical amplification, multifunctional photonic integrated chips, quantum communication, and spectroscopy, and as a reference for low-noise PSAs depending on the third-order nonlinearity, χ (3), of the waveguide material.

Predicting nonlinear multi-pulse propagation in optical fibers via a lightweight convolutional neural network.

The nonlinear evolution of ultrashort pulses in optical fiber has broad applications, but the computational burden of convolutional numerical solutions necessitates rapid modeling methods. Here, a lightweight convolutional neural network is designed to characterize nonlinear multi-pulse propagation in highly nonlinear fiber. With the proposed network, we achieve the forward mapping of multi-pulse propagation using the initial multi-pulse temporal profile as well as the inverse mapping of the initial multi-pulse based on the propagated multi-pulse with the coexistence of group velocity dispersion and self-phase modulation. A multi-pulse comprising various Gaussian pulses in 4-level pulse amplitude modulation is utilized to simulate the evolution of a complex random multi-pulse and investigate the prediction precision of two tasks. The results obtained from the unlearned testing sets demonstrate excellent generalization and prediction performance, with a maximum absolute error of 0.026 and 0.01 in the forward and inverse mapping, respectively. The approach provides considerable potential for modeling and predicting the evolution of an arbitrary complex multi-pulse.

All-optical wavelength and format conversion of DQPSK-to-PAM4 using DLI and pump assisted NOLM

An all-optical wavelength and format conversion scheme of 20 Gbps differential quadrature phase shift keying (DQPSK)-to-4-ary pulse amplitude modulation (PAM4) signals based on the delay line interferometer (DLI) and the pump assisted nonlinear optical loop mirror (NOLM) is proposed and numerically simulated. The input DQPSK signal is converted into two star-16-ary quadrature amplitude modulation (star-16QAM) signals (namely, star-16QAM-I and star-16QAM-Q) using DLI with the time delay of 1-symbol and different linear phase shifts of π/4 and −π/4, respectively. The star-16QAM signals are converted into the on-off keying (OOK) signals (namely, OOK-I and OOK-Q) using the pump assisted NOLM based on the self-phase modulation (SPM) and the cross-phase modulation (XPM) in the highly nonlinear fiber (HNLF). The two OOK signals can be aggregated into different types of PAM4 signals by adjusting their power ratio (PR) and relative phase shift (RPS) flexibly. Error vector magnitude (EVM) and bit error rate (BER) for the input and output optical signals are calculated to verify the scheme performance. Compared to the DQPSK signal with an input optical signal-to-noise ratio (OSNR) of 30 dB, there are about 2.5 dB penalty of receiver OSNR for the converted OOK-I and OOK-Q signals. For the corresponding aggregated equidistant PAM4 and equiamplitude PAM4 signals, they have about 6.3 dB and 12.1 dB penalty of receiver OSNR. The proposed scheme of DQPSK-to-PAM4 can be deployed at the all-optical gateway to bridge the long-hual and short-reach optical networks.

Rhombus-shaped, M-shaped- solitons, 2D-lumps vector and tunneling in perturbed Gerdjikov–Ivanov equation with fourth-order dispersion: Modulation instability and global bifurcation

The Perturbed Gerdjikov–Ivanov Equation (PGIE) describes optical solitons in nonlinear fiber optics and photonic crystal fibers. It was currently studied in the literature. Here, we consider a new complex field equation, the PGIE with fourth-order dispersion. The exact solutions of the aforementioned equation are obtained by implementing the unified method. These solutions are evaluated numerically and they are shown in graphs. Our objectives, here, are to inspect the onset of self- steepening and self-phase modulation and investigate the structures of solitons produced. It is found that these phenomena are launched for high values of the relevant coefficients, and they may be overlapped. Multiple solitons shapes are observed; M-shaped solitons, rhombus shapes, solitons with tunneling, 2D-lumps vector, and solitons- cascade. Further, the analysis of modulation instability (MI) and global bifurcation are carried out. It is established that the MI triggers when the coefficient of Raman scattering exceeds a critical value. It is worth mentioning that two kinds of bifurcations can be studied, namely local and global bifurcations. Here, we are concerned with studying global bifurcation. This is based on constructing the phase portrait via Hamiltonian function.

High-temperature wave thermalization spoils beam self-cleaning in nonlinear multimode GRIN fibers.

In our experiments, we reveal a so-far unnoticed power limitation of beam self-cleaning in graded-index nonlinear multimode optical fibers. As the optical pulse power is progressively increased, we observed that the initial Kerr-induced improvement of the spatial beam quality is eventually lost. Based on a holographic mode decomposition of the output field, we show that beam spoiling is associated with high-temperature wave thermalization, which depletes the fundamental mode in favor of a highly multimode power distribution.

Physical Realizations of Multidimensional Voronoi Constellations in Optical Communication Systems

Multidimensional geometric shaping has been shown to outperform uniform quadrature amplitude modulation (QAM) in optical communication systems but the complexity of symbol decision and bit mapping can often be significant as dimensionality increases. In this paper, a low-complexity geometric shaping method based on multidimensional lattices is investigated both in experiments and simulations. The modulation formats designed based on this method are called Voronoi constellations (VCs) and we study them in 8, 16, and 32 dimensions. We obtain transmission reach improvements of up to 22 and 70% for VCs compared to 4QAM and 16QAM, respectively, in nonlinear long-haul fiber transmission. Moreover, we compare different physical realizations of multidimensional VCs over wavelengths, polarizations, and time slots in both the Gaussian and nonlinear fiber channels. We demonstrate that different physical realizations perform similarly in the fiber-optic back-to-back channel. However, in long-haul transmission systems, spreading the dimensions over time slots can increase the transmission reach up to 4% compared to wavelengths and polarizations. Furthermore, the mutual information and generalized mutual information are estimated and compared to QAM formats at the same spectral efficiencies.

Raman amplification at 2.2 μm in silicon core fibers with prospects for extended mid-infrared source generation

Raman scattering provides a convenient mechanism to generate or amplify light at wavelengths where gain is not otherwise available. When combined with recent advancements in high-power fiber lasers that operate at wavelengths ~2 μm, great opportunities exist for Raman systems that extend operation further into the mid-infrared regime for applications such as gas sensing, spectroscopy, and biomedical analyses. Here, a thulium-doped fiber laser is used to demonstrate Raman emission and amplification from a highly nonlinear silicon core fiber (SCF) platform at wavelengths beyond 2 μm. The SCF has been tapered to obtain a micrometer-sized core diameter (~1.6 μm) over a length of 6 cm, with losses as low as 0.2 dB cm−1. A maximum on-off peak gain of 30.4 dB was obtained using 10 W of peak pump power at 1.99 μm, with simulations indicating that the gain could be increased to up to ~50 dB by extending the SCF length. Simulations also show that by exploiting the large Raman gain and extended mid-infrared transparency of the SCF, cascaded Raman processes could yield tunable systems with practical output powers across the 2–5 μm range.

Distinct exact solutions for the conformable fractional derivative Gerdjikov-Ivanov equation via three credible methods

This paper reveals the conformable fractional space-time perturbed Gerdjikov-Ivanov (GI) equation, which is applied to nonlinear fibre optics together with photonic crystal fibres. The foremost intent of our operation is adopting the unified method, the modified F-expansion method and the modified Kudryashov method to hunt for definite solutions to the equation. In addition, by selecting fairish values, fluctuation behaviours of the solutions are drafted.

Demonstration of optically-assisted reconfigurable average of two 20-Gbaud 4-phase-encoded data channels using nonlinear wave mixing.

Networks can play a key role in high-speed and reconfigurable arithmetic computing. However, two performance bottlenecks may arise when: (i) relying solely on electronics to handle computation for multiple data channels at high data rates, and (ii) the data streams input to a processing node (PN) are transmitted as phase-encoded signals over an optical network. We experimentally demonstrate the operation of optically-assisted reconfigurable average of two 4-phase-encoded data channels at 10- and 20-Gbaud rates. Our input signals are two streams of 2-bit numbers representing a binary floating-point format, and the operation results in 7-phase-encoded output signals represented by 3-bit numbers. The average operation is achieved in three stages: (1) phase encoding and division-using an optical modulator to encode the data streams; (2) summation-using a highly nonlinear fiber (HNLF); and (3) multicast-using a periodically poled lithium niobate (PPLN) waveguide to multicast back the result into the original signal wavelengths. The experimental results validate the concept, and the measured penalties indicate that: (i) the error vector magnitudes (EVMs) of optical signals increase at each stage and reach ∼18-21% for the final multicast results, and (ii) compared to the inputs, the optical signal-to-noise ratio (OSNR) penalty of output is ∼6.7 dB for the 10-Gbaud rate and ∼6.9 dB for the 20-Gbaud rate at a bit error rate (BER) of 3.8e-3.

Molybdenum gallium carbide as saturable absorbers in 1.5-μm passive mode-locked fibre laser

A saturable absorber (SA) is one of the important components in a passive mode-locked fibre laser configuration to attain picosecond- to femtosecond-competent ultrashort pulses for fulfilling the imperatives of industries, particularly engineering and life sciences. The substantiation of a newfound SA in the generation of mode-locked pulses utilising molybdenum gallium carbide (Mo2Ga2C)—a MAX phase nanomaterial—was authenticated in this work. A Mo2Ga2C SA thin film was fabricated via a simple solution with polyvinyl alcohol (PVA) as the hosting medium. Linear absorption, modulation depth, non-saturable absorption, and saturation intensity of the 17.141-μm Mo2Ga2C SA were found to be 8.29%, 19.82%, 9.21% and 2.85 kW/cm2, respectively. The fabricated Mo2Ga2C SA was then implemented into an erbium-doped fibre laser (EDFL) system to realise the eminently stable mode-locked fibre laser at a centre wavelength of 1559.2 nm and rudimentary signal-to-noise ratio (SNR) of 54.8 dB. The pulse repetition rate and pulse width were measured to be 968.72 kHz and 2.028 ps successively. The maximum pulse energy and peak power are 10.219 nJ and 24.12 mW. In corroboration with previous reports, the implementation of Mo2Ga2C as a mode-locker is propitious in validating the impressively stable and ultrafast nonlinear fibre laser system for further multidisciplinary applications, for instance, medical instrumentation, sensing and range finding, communication, and military due to its excellent optical, physical, thermal, and mechanical properties.

Some new wave solutions and modulation instability of a Hamiltonian amplitude equation in optical fibres

The nonlinear Schrödinger equation (NLSE) is one of the most important physical models for explaining the dynamics of optical soliton proliferation in optical fibre theory. Due to an extensive variety of applications for ultrafast signal routing systems and short light pulses in communications, optical soliton propagation in nonlinear fibres is a topic of substantial present interest. To overcome the ill-posedness of the unstable NLSE, a new term Lxt is introduced which leads to the Hamiltonian amplitude equation. In this work, we study exact wave solutions to the nonlinear complex model by utilizing a set of analytical approaches namely as the exp(−ξ(δ)) method, the improved F-expansion technique, and the extended modified auxiliary equation mapping method. Numerous solutions, including singular periodic, multi-periodic, single bell-shaped, and multi-bell-shaped wave frameworks were found. The proposed plan of action is swift, strong, as well as offers the requirements needed to verify the origin of these solutions. Additionally, a dynamics representation of the fascinating behaviour of several solidarity using 2D, 3D, and contour graphs is provided, also we discuss the stability analysis and modulation instability of the proposed model.

Broadband dual-chirp FMCW laser source based on DSB-SC modulation and cascaded FWM.

Based on dual-sideband suppressed-carrier (DSB-SC) modulation and two-stage cascaded four-wave-mixing (FWM), a scheme of broadband dual-chirp frequency-modulated continuous-wave (FMCW) laser source is proposed and experimentally demonstrated. First, via a Mach-Zehnder modulator biased at its null point, an original DSB-SC FMCW signal with 4.0 GHz swept-frequency range and 0.2 GHz/μs sweep rate is generated. Next, the original DSB-SC FMCW signal is sent to a 1 km dispersion compensation fiber for implementing first-stage FWM, a dual-chirp FMCW signal with 12.0 GHz swept-frequency range and 0.6 GHz/μs sweep rate is acquired and used as the pump for second-stage FWM. Finally, via second-stage FWM in a 200 m highly nonlinear fiber, a dual-chirp FMCW signal with a swept-frequency range of 36.0 GHz and sweep rate of 1.8 GHz/μs is generated. Taking the FMCW signal generated at different stages as the emitted signal, we evaluate the ranging resolution through fiber-based distance measurement, and the results demonstrate that the achieved ranging resolutions are 5.31 cm, 2.04 cm, and 1.18 cm, respectively. Through equalizing the optical power of generated FMCW signal over the swept-frequency range, the ranging resolution can be further improved.

A prince for the sleeping beauty - NFT for soliton signal processing

The soliton, the eigen-solution of nonlinear Schrodinger equation (NLSE), has been investigated in many branches of physics. The first prediction of a soliton in optical fiber could be dated back to 1973. Since then, numerous theoretical and experimental works on solitons have been carried out, including soliton communication and soliton generation in fiber lasers. However, due to the constraints of hardware and digital signal processing methods, research on solitons have been stalled for decades. Recently, the nonlinear Fourier transform (NFT) has attracted significant attention in the field of optical fiber communications and soliton-based signal processing, which provides a powerful mathematical framework for analyzing and understanding the behavior of solitons in optical fibers, enabling the development of novel signal processing techniques. The NFT technique has brought the soliton back to life. It has been widely recognized that in nonlinear frequency domain, the nonlinear crosstalk resulting from the Kerr effect is practically negligible, and fiber nonlinearity damage caused by the Kerr effect can be accounted for as a linear transform factor. Moreover, NFT has been demonstrated for the analysis of laser radiation, highlighting its potential in characterizing ultrafast pulses in the nonlinear frequency domain. In this submission, we review the advancements of NFT concerning both in soliton communication and characterization, focusing on practical implementation aspects. With many practical implementation aspects still being open, our mini review is aimed to assist researchers in evaluating the potential, identifying challenges, and envisioning future directions in NFT-based signal processing technologies. And wake up the sleeping beauty – the soliton!

Nondegenerate solitons of the (2+1)-dimensional coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optical fibers

We derive the multi-hump nondegenerate solitons for the (2+1)-dimensional coupled nonlinear Schrödinger equations with propagation distance dependent diffraction, nonlinearity and gain (loss) using the developing Hirota bilinear method, and analyze the dynamical behaviors of these nondegenerate solitons. The results show that the shapes of the nondegenerate solitons are controllable by selecting different wave numbers, varying diffraction and nonlinearity parameters. In addition, when all the variable coefficients are chosen to be constant, the solutions obtained in this study reduce to the shape-preserving nondegenerate solitons. Finally, it is found that the nondegenerate two-soliton solutions can be bounded to form a double-hump two-soliton molecule after making the velocity of one double-hump soliton resonate with that of the other one.

Effect of Rayleigh backscattering on the multiwavelength random fiber laser bandwidth

We investigated the effect of Rayleigh backscattering on the bandwidth of a multiwavelength random fiber laser (MWRFL). This MWRFL is based on an erbium-doped fiber amplifier (EDFA) as the gain medium and a Lyot filter as the wavelength-selective device. A high number and stable lasing line is generated with the assistance of a nonlinear polarization rotation effect induced by highly nonlinear fiber (HNLF) and optimized by a polarization controller. Longer single-mode fiber (SMF) produces wider multiwavelength bandwidth as compared to shorter SMF lengths, as 10 km, 3 km, and 0.1 km obtained 6.24 nm, 5.76 nm, and 2.75 nm wavelength bandwidth, respectively. When the SMF is removed from the setup, no Rayleigh backscattering is provided in the cavity, which led to a narrower multiwavelength bandwidth of 2.69 nm. Subsequently, the alteration of EDFA power, half-wave plate (HWP) angle, and quarter-wave plate (QWP) angles affected the degradation of multiwavelength performance. The best output spectrum is achieved at an EDFA power of 18 dBm, a HWP angle of 60°, and a QWP angle of 105°. The laser stability over a period of 120 min was excellent with a peak power deviation of 1.33 dB.

NIR to MIR ultra-broadband supercontinuum laser source based on all-silica fibers.

We demonstrated an ultra-broadband supercontinuum (SC) laser source with a wavelength range spanning the near-infrared (NIR) to mid-infrared (MIR) region. The SC spectrum was generated in a very short piece of highly nonlinear silica fiber (HNLF) which has a zero-dispersion wavelength (ZDW) of 1.55 µm. The pump source used has a spectral coverage of 1.5∼2.4 µm which covers the ZDW of HNLF, resulting in a dramatic blue and red shift of the spectrum through strong non-linear effects. As the pump laser pulse launched into HNLF, a SC spectrum with broadband range of 0.92∼2.92 µm and maximum average power of 5.09 W was achieved, which sets record coverage of HNLF-based watts magnitude SC laser sources for now, to the best of the authors' knowledge. The setup consists of silica fiber that can be considered easy-to-implement and with a cost-effectiveness scheme for ultra-broadband SC generation that could be easily applied to optical fiber sensing and spectral imaging technology.

Accurate Computation of b-Coefficients in Nonlinear Fourier Transform for the Manakov Equation

In recent years, nonlinear Fourier transform (NFT) has been intensely researched as a scheme for communication over the nonlinear optical fiber and characterizing dynamics in nonlinear optical systems. For the accurate computation of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> -coefficients on discrete eigenvalues, the bidirectional algorithm has been proposed where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> -coefficients are calculated at a cutting point within the temporal window rather than two boundaries. The performance of the bidirectional algorithm depends severely upon the selection criterion of the cutting-point, which has been investigated in nonlinear Schrodinger equation and Korteweg–De Vries equation but not yet in Manakov equation accounting for the dual-polarization signals over optical fiber. In this paper, we propose a cutting-point criterion of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</i> -coefficients for the bidirectional algorithm of Manakov equation and compare it with existing criteria. Numerical results show that, the resulting algorithm has much better accuracy compared with existing criteria, especially for signals containing a large number of eigenvalues with large imaginary parts. The bidirectional algorithm with the proposed criterion is useful for decoding the dual-polarization nonlinear frequency division multiplexing (DP-NFDM) signals for communication and characterization of vector soliton dynamics in Manakov equation described systems.

Discovery of New Exact Wave Solutions to the M-Fractional Complex Three Coupled Maccari’s System by Sardar Sub-Equation Scheme

In this paper, we succeed at discovering the new exact wave solutions to the truncated M-fractional complex three coupled Maccari’s system by utilizing the Sardar sub-equation scheme. The obtained solutions are in the form of trigonometric and hyperbolic forms. These solutions have many applications in nonlinear optics, fiber optics, deep water-waves, plasma physics, mathematical physics, fluid mechanics, hydrodynamics and engineering, where the propagation of nonlinear waves is important. Achieved solutions are verified with the use of Mathematica software. Some of the achieved solutions are also described graphically by 2-dimensional, 3-dimensional and contour plots with the help of Maple software. The gained solutions are helpful for the further development of a concerned model. Finally, this technique is simple, fruitful and reliable to handle nonlinear fractional partial differential equations (NLFPDEs).

On the solitonic wave structures and stability analysis of the stochastic nonlinear Schrödinger equation with the impact of multiplicative noise

The nonlinear Schrödinger equation (NLSE) is a fundamental and significant physical model that plays a crucial role in demonstrating the dynamics of optical solitons in the theory optical fibers. The propagation of solitons in nonlinear optical fibers has garnered substantial interest due to its broad spectrum of applications, particularly in ultrafast signal routing systems and short light pulses for communications. This article focuses on investigating the impact of multiplicative noise on the solutions of this governing model. To achieve this, three distinct methods, namely the enhanced modified extended tanh expansion (METE) method, the generalized Kudryashov (GK) approach and the extended modified auxiliary equation mapping (EMAEM) method are employed to obtain a new variety of stochastic solutions. The perception of how noise intensity impacts the transmission of waves is a fundamental and critical issue in various fields. In the context of this study, an equation describes an exact wave pattern under the condition that s (representing noise intensity) equals zero. In such cases, the observed pattern remains undisturbed and matches the expected theoretical wave pattern. However, as the strength of noise s increases, the observed pattern begins to deviate from the ideal wave pattern and exhibits signs of damage or distortion. Furthermore, the stability analysis for the stochastic NLSE is performed, providing valuable insights into the behavior solutions as the strength of multiplicative noise increases. The validation of computational results through stability analysis enhances the confidence in the findings of the study. All the mathematical calculations, as well as graphical representations, have been meticulously achieved to present a comprehensive and detailed understanding of the impact of multiplicative on soliton propagation in nonlinear optical fibers.

Frequency modes filtering of spectral peaks in optical frequency combs through molecular gas absorption and nonlinear polarization rotation.

Spectral peak generation is a recently reported phenomenon that narrow spectral dips of the optical spectrum turn into sharp peaks as they propagate through nonlinear optical fibers. We demonstrated the nonlinear polarization rotation-based spectral peak mode filtering to increase the signal-to-background ratio (SBR). The spectral peaks with almost constant frequency separation were generated from the femtosecond pulses absorbed by the CH4 gas through the highly nonlinear fiber. The generated spectral peaks were filtered through the polarizing beam splitter by the nonlinear polarization rotation, and the SBR was improved from 9 dB to ∼20 dB. The spectral peak generation phenomenon and the mode filtering were numerically confirmed by solving the coupled nonlinear Schrödinger equations. The demonstrated method can generate strong comb modes with wide frequency spacing which are useful for highly sensitive environmental gas sensing spectroscopy. The wavelengths of the spectral peaks are fixed by the absorption spectra of the used gas cells. Therefore, this method can generate high quality spectral peaks of any wavelengths with wide spectral ranges through proper combinations of gas cells.