Soliton Period Research Articles

Soliton Dynamics in a Birefringent Optical Fiber

Long-distance solitons maintain their form and speed. Single mode optical fiber exhibits birefringence as a result of its asymmetric core's effect on the refractive index. The soliton pulse is broadened and chirped as it travels through a birefringent optical fiber due to many features of the fiber. Therefore, it is necessary to strike a balance between the elements influencing the transmission to guarantee minimal data loss. This work uses OptiSysten software to strike a balance between the length, effective area, soliton period, and attenuation effects that affect the performance of the soliton while employing optical fiber as a birefringent optical fiber. Based on this research, a set of values for these parameters that minimizes widening and chirping was determined. The simulation findings are compared to the mathematical and analytical combination of soliton, which is based on the coupled non-linear Schrodinger equation. Although previous works on soliton had demonstrated the impact of GVD and SPM on the transmission, this paper aids comprehension by including additional performance-affecting characteristics.

Soliton–soliton interaction and its influence on soliton amplitude and period

The study of soliton interactions in birefringent fibers has important applications in optical communications. In this paper, the coupled nonlinear Schrödinger equations, which can be used to model the soliton propagation in birefringent fibers, are investigated theoretically. Analytical two-soliton solutions are given by the use of the Hirota method. Their interactions are analyzed, and their amplitude and period are controlled through choosing the corresponding physical parameters. The relevant conclusions have theoretical guiding significance for high-capacity communication.

N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation

[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the interaction solution among period soliton and two line solitons, or the interaction solution for two period solitons or two lump solitons via taking specific constraints from four soliton solutions. Finally, some images of the results are drawn, and their dynamic behavior is analyzed.

Controlled soliton formation in a femtosecond optical parametric oscillator with positive group delay dispersion

Soliton formation in a femtosecond optical parametric pumped by the second harmonic of a Yb: KGW solid-state oscillator was investigated. The intracavity group delay dispersion was positive, and the soliton condition was satisfied by introducing negative nonlinearity from cascaded quadratic nonlinearity (CQN). Controllable CQN was induced by an additional second-harmonic-generating nonlinear crystal inside the same resonator. Close to zero-phase mismatch, high CQN allows higher-order soliton formation, which leads to output power increase, self-phase modulation phase-matched dispersive wave formation, pulse splitting under perturbations of higher orders of nonlinear phase, and stable time/spectral domain oscillations with soliton period. Numerical simulations were employed to aid interpretations of the experimental data.

Soliton-effect optical pulse compression in CMOS-compatible ultra-silicon-rich nitride waveguides

The formation of optical solitons arises from the simultaneous presence of dispersive and nonlinear properties within a propagation medium. Chip-scale devices that support optical solitons harness high field confinement and flexibility in dispersion engineering for significantly smaller footprints and lower operating powers compared to fiber-based equivalents. High-order solitons evolve periodically as they propagate and experience a temporal narrowing at the start of each soliton period. This phenomenon allows strong temporal compression of optical pulses to be achieved. In this paper, soliton-effect temporal compression of optical pulses is demonstrated on a CMOS-compatible ultra-silicon-rich nitride (USRN) waveguide. We achieve 8.7× compression of 2 ps optical pulses using a low pulse energy of ∼16 pJ, representing the largest demonstrated compression on an integrated photonic waveguide to date. The strong temporal compression is confirmed by numerical calculations of the nonlinear Schrödinger equation to be attributed to the USRN waveguide’s large nonlinearity and negligible two-photon absorption at 1550 nm.

Analytic study on the influences of higher-order effects on optical solitons in fiber laser

Requirements of the transmission rate, transmission distance and transmission capacity of optical communication systems are becoming higher and higher, and studies on the higher-order effects such as third order dispersion are inevitable for the development of systems. In this paper, we study the influences of higher-order effects on the optical soliton transmission. The high-order nonlinear Schrödinger equation, which can be used to describe the optical soliton transmission in the fiber laser, is investigated. Analytic soliton solution for this equation is obtained. The comprehensive analysis of the solution is made. Through choosing different values of the high-order effects, we discuss their influences on optical soliton transmission speed, period and pulse width. Results can be used to guide the generation and transmission of optical solitons in experiments.

Dynamics of Internal Envelope Solitons in a Rotating Fluid of a Variable Depth

We consider the dynamics of internal envelope solitons in a two-layer rotating fluid with a linearly varying bottom. It is shown that the most probable frequency of a carrier wave which constitutes the solitary wave is the frequency where the growth rate of modulation instability is maximal. An envelope solitary wave of this frequency can be described by the conventional nonlinear Schrödinger equation. A soliton solution to this equation is presented for the time-like version of the nonlinear Schrödinger equation. When such an envelope soliton enters a coastal zone where the bottom gradually linearly increases, then it experiences an adiabatical transformation. This leads to an increase in soliton amplitude, velocity, and period of a carrier wave, whereas its duration decreases. It is shown that the soliton becomes taller and narrower. At some distance it looks like a breather, a narrow non-stationary solitary wave. The dependences of the soliton parameters on the distance when it moves towards the shoaling are found from the conservation laws and analysed graphically. Estimates for the real ocean are presented.

High Energy All-Fiber Tm-Doped Femtosecond Soliton Laser Mode-Locked by Nonlinear Polarization Rotation

A high-energy thulium-doped all-fiber soliton laser passively mode-locked by nonlinear polarization rotation (NPR) technology is presented, generating 350 fs pulses with spectral width of 11.5 nm at 1890 nm wavelength. Kelly sidebands of the soliton spectrum are well suppressed due to the NPR effect in the fiber laser. The average output power reaches 90 mW, corresponding to the pulse energy up to 7.8 nJ and the pulse peak power of 22.3 kW, leading to the higher order soliton generation. This has been testified by the relationship between the soliton period and the cavity length. Thus, the laser can deliver high-energy ultrashort soliton pulses while the pulse shape is close to one of the fundamental solitons. We believe that this represents one of the best observations of short pulse duration as well as high pulse power coexisting in Tm-doped soliton fiber lasers.

Numerical simulations of fast-axis instability of vector solitons in mode-locked fiber lasers.

We demonstrate the fast-axis instability in mode-locked fiber lasers numerically for the first time. We find that the energy of the fast mode will be transferred to the slow mode when the strong pump strength makes the soliton period short. A nearly linearly polarized vector soliton along the slow-axis could be generated under certain cavity parameters. The final polarization of the vector soliton is related to the initial polarization of the seed pulse. Two regimes of energy exchanging between the slow mode and the fast mode are explored and the direction of the energy flow between two modes depends on the phase difference. The dip-type sidebands are found to be intrinsic characteristics of the mode-locked fiber lasers under high pulse energy.

Nonlinear ultrafast switching based on soliton self-trapping in dual-core photonic crystal fibre

In this paper, we present a systematic numerical study of a novel ultrafast nonlinear switching concept based on soliton self-trapping in dual-core (DC) photonic crystal fibre (PCF). The geometrical parameters of highly-nonlinear (HN) DC microstructure are optimized with regard to desired linear and nonlinear propagation characteristics. The comparable magnitude of fibre coupling length and soliton period is identified as a key condition for presented switching concept. The optimized DC PCF design is subjected to detailed nonlinear numerical study. Complex temporal-spectral-spatial transformations of 100 fs hyperbolic secant pulse at 1550 nm in the DC PCF are studied numerically employing a model based on coupled generalized nonlinear Schrödinger equations solved by a split-step Fourier method. For the optimized DC structure, mutual interplay of solitonic and coupling processes gives rise to nonlinear switching of self-trapped soliton. The output channel (fibre core) for the generated soliton can be controlled via the input pulse energy. For vertical polarization, the optimal soliton switching with extinction ratio contrast of 32.4 dB at 10.75 mm propagation distance is achieved. Even better switching contrast of 34.8 dB can be achieved for horizontal polarization at optimal propagation distance of 10.25 mm. Besides energy-controlled soliton self-trapping switching, the fibre supports also nonlinear polarization switching with soliton switching contrast as high as 37.4 dB. The proposed fibre holds a high application potential allowing efficient ultrafast switching of sub-nanojoule pulses at over-Tb/s data rates requiring only about 1 cm fibre length.

Identifying the mechanisms of pulse formation and evolution in actively mode-locked Erbium fiber lasers with meters and kilometers-long

Abstract We investigated the dynamics of pulse evolution in Erbium-doped fiber ring lasers with cavity lengths varying from 16.4 m to 100.8 km actively mode-locked at repetition rate of 1 GHz. The novelty of this work is to explore the limits of Kuizenga–Siegman theory in ultralong fiber laser and to demonstrate the dynamics of pulse generation and propagation separately. When we vary the length of the Erbium-doped fiber lasers from meters to kilometers long, three operation regimes were identified: mode-locking regime (for cavity lengths with 16.4 m to 1 km), nonlinearity-dominant regime (1 to 10 km) and dispersion and nonlinearity regime that locked the ratio between soliton period and cavity length: Z S / L cav = 1.35 for cavities with 10 to 100 km in a soliton intracavity condition. The variation of pulse widths and the peak powers are analyzed to define the propagation regimes inside the cavities, depending on the cavity length ( L cav ) , dispersion length ( L D ) and nonlinear length ( L NL ) . When Lcav is shorter than LD and LNL, there is neither dispersive nor nonlinear effect during pulse evolution (pulse has duration of approximately 30 ps). In this regime, its final duration is determined by the standard theory of active mode-locking. For Lcav shorter than LD but ~ L NL , the pulse evolution is in nonlinearity-dominant regime where soliton propagation provides a sech2 profile with a TBP transform limited of 0.315. In addition, for cavities longer than 10 km, L cav ~ L D and longer (or much longer) than LNL, the pulse evolution is in the dispersion and nonlinearity dominant regime with its duration depending on the accumulated dispersion. In this regime the soliton effect takes place and the final pulse duration is defined by the cavity length which is approximately the soliton period.

The New Infinite Sequence Complexion Solutions of a Kind of Nonlinear Evolutionary Equations

The method combining the function transformation with the auxiliary equation is presented and the new infinite sequence complexion solutions of a class of nonlinear evolutionary equations are constructed. Step one, according to two function transformations, a class of nonlinear evolutionary equations is changed into two kinds of ordinary differential equations. Step two, using the first integral of the ordinary differential equations, two first order nonlinear ordinary differential equations are obtained. Step three, using function transformation, two first order nonlinear ordinary differential equations are changed to the ordinary differential equation that could be integrated. Step four, the new solutions, Backlund transformation and the nonlinear superposition formula of solutions of the ordinary differential equation that could be integrated are applied to construct the new infinite sequence complexion solutions of a class of nonlinear evolutionary equations. These solutions are consisting of two-soliton solutions, two-period solutions and solutions composed of soliton solutions and period solutions.

Study on fundamental and higher order soliton with and without third-order dispersion near zero dispersion point of single mode fiber

In this work, we study the effect of fundamental and higher order soliton with and without the presence of third-order dispersion (TOD, β3). The effect is studied near the zero dispersion wavelength of 1270 nm with second-order dispersion (β2) value of 0.22 ps2/km for various third-order dispersion parameter sweeps from 0.01 to 0.1 ps3/km. The theme of temporal pulse displacement due to TOD is studied for 10 and 20 soliton periods for fundamental soliton and 10 soliton period for higher order soliton (N = 2). The effective pulse width of 1 ps (FWHM) is displaced from its original position to adjacent position depending upon the TOD value. It is found in both fundamental and higher order soliton, that the displacement in higher for TOD value of 0.1 ps3/km than 0.01 ps3/km. The effect of displaced fundamental soliton pulse is pictured with respect to the transmitted distance (different soliton period) and TOD. The spectral characteristics of higher order soliton is also analyzed which is one of the characteristic mechanisms for supercontinuum generation.

Soliton interactions for coupled nonlinear Schrödinger equations with symbolic computation

Soliton interactions for the coupled nonlinear Schrodinger equations, governing the propagation of envelopes of electromagnetic waves in birefringent optical fibers, are investigated with symbolic computation. Based on the Hirota method, analytic two- and three-soliton solutions for this model are derived. Relevant interaction properties are discussed. Stationary bound vector solitons with the periodic attraction and repulsion are obtained. Soliton intensity could be reduced if the nonlinearity in optical fibers is enlarged, while the soliton period could be prolonged as the group velocity dispersion in the anomalous dispersion regime of optical fibers increases. Through the asymptotic analysis for the two-soliton solutions, interactions between two solitons are proven to be elastic. Besides, parallel soliton transmission systems without soliton interactions are presented. Moreover, interactions between the regular and bound vector solitons are studied. Dual complex structures and triple-soliton bound states are presented. Results could be of certain value to the studies on the soliton control and optical switching technologies.

Ultrafast two-bit all-optical analog-to-digital conversion based on femtosecond soliton sequence sampling

Realization of two-bit all-optical analog-to-digital conversion for an analog signal sampled by a femtosecond soliton sequence is investigated. Two approaches are suggested. The first one is based on filtering the broadened soliton spectrum after evolution over half of the soliton period in a standard single-mode fiber. In the second approach, the pulse is temporally sampled at the specified times after propagating through one soliton period. The sampled soliton sequence must be amplified to achieve an initial peak power of between 0 and 75 kW for the first method and between 0 and 66 kW for the second method. The soliton pulse-width is 50 fs. Based on the resulted peak power, the "0" or "1" bit is generated with reference to the threshold values. Subsequently, the digital gray code is produced at the outputs. The effect of inaccuracy in filter frequency and fiber length are also studied in this paper. The first method is sensitive to variations in the filter frequency, whereas the second method is affected by the fiber length inaccuracy.

Analysis of the nonlinear optical switching in a Sagnac interferometer with non-instantaneous Kerr effect

In this work we present a study of the performance of nonlinear switching in a Sagnac interferometer under the action of a relaxed Kerr nonlinearity, using ultrashort optical pulses. Soliton and quasi-soliton pulses have been used as initial conditions. We include the effect of GVD (Group Velocity Dispersion) and consider that losses are negligible. The transmission, compression factor (C) and extinction ratio [XRatio (tr)] curves versus input energy were analyzed for two lengths of the loop (1Z 0 and 2Z 0) of the Sagnac interferometer, where Z 0 is one soliton period. It was verified that an increase of the response time (τ) of the relaxed Kerr nonlinearity leads to a degradation of the nonlinear switching, transmission, compression factor and extinction ratio curves. For instance, in the quasi-soliton propagation regime with loop of length 1Z 0 and input energy 1.83 pJ, the extinction ratio (XRatio (tr)) decreases from + 8.13 dB, at the instantaneous nonlinear medium, to − 0.83 dB, − 2.50 dB, − 5.95 dB, − 8.63 dB, − 10.11 dB and − 12.10 dB, at the relaxed medium with τ = 1 ps, τ = 2 ps, τ = 5 ps, for τ = 10 ps, τ = 15 ps and τ = 30 ps, respectively. In the soliton propagation regime with loop of length 2Z 0 and time duration of 10 ps, for the input pulse (pump power of 0.34 W), one can observe that for the non-instantaneous nonlinear medium, as τ increases, the transmitted output pulses are delayed to longer times (21.49 ps, 23.9 ps and 25 ps) and the pulse envelope starts presenting broadening effects (14.7 ps and 29 ps) for τ = 2 ps and 5 ps, respectively. In our analysis, for the Sagnac interferometer with ring of length 2 Zo = 5.06 km, the chirp distribution has revealed that the spectral profile of the output pulses are smoother for the non-instantaneous medium with τ = 2 ps and 5 ps. In this sense, these two last situations are more suitable for switching applications in WDM systems. These studies are crucial for the analysis of the behavior of the Sagnac interferometers based in non-instantaneous Kerr response fibers, applied in telecommunication systems, in optical signal processing, optoelectronics instrumentation and in several related fields.

Cascaded higher-order soliton for non-adiabatic pulse compression

Non-adiabatic pulse compression of cascaded higher-order optical soliton is investigated. We demonstrate high degree compression of pulses with soliton orders N=2, 3, 4, and 5 in two or three nonlinear fibers with different second-order dispersion coefficients. Each fiber length is shorter than half of its soliton period. This compression technique has significant advantages over the widely reported adiabatic and higher-order soliton compression.

Solitary pulse propagation and soliton-induced supercontinuum generation in silica glasses containing silver nanoparticles

We study solitary pulse propagation in the normal dispersion region in glasses containing silver nanoparticles with a self-defocusing nonlinearity and predict that, despite high plasmonic loss, pulse propagation without significant distortion over five soliton periods can be achieved in such materials. As an application, we study low-threshold soliton-induced supercontinuum generation and predict more than octave-spanning spectral broadening by femtosecond pulses with an intensity in the range of hundreds of GW/cm(2).

Snake solitons in the cubic–quintic Ginzburg–Landau equation

Comprehensive numerical simulations of pulse solutions of the cubic–quintic Ginzburg–Landau equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons [ C.I. Christov, M.G. Velarde, Dissipative solitons, Physica D 86 (1995) 323] are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied. In this paper, we address the issues of central interest in the area, i.e., the conditions for the occurrence of the five categories of dissipative solitons, as well the dependence of both their shape and their stability on the various parameters of the CGLE, viz. the nonlinearity, dispersion, linear and nonlinear gain, loss and spectral filtering parameters. Our predictions on the variation of the soliton amplitudes, widths and periods with the CGLE parameters agree with simulation results. First, we develop and discuss a variational formalism within which to explore the various classes of dissipative solitons. Given the complex dynamics of the various dissipative solutions, this formulation is, of necessity, significantly generalized overall earlier approaches in several crucial ways. Firstly, the starting formulation for the Lagrangian is recent and not well explored. Also, the trial functions have been generalized considerably over conventional ones to keep the shape relatively simple (and the trial function integrable!) while allowing arbitrary temporal variation of the amplitude, width, position, speed and phase of the pulses. In addition, the resulting Euler–Lagrange equations are treated in a completely novel way. Rather than consider the stable fixed points which correspond to the well-known stationary solitons or plain pulses, we use dynamical systems theory to focus on more complex attractors, viz. periodic, quasiperiodic, and chaotic ones. Periodic evolution of the trial function parameters on stable periodic attractors yield solitons whose amplitudes and widths are non-stationary or time dependent. In particular, pulsating and snake dissipative solitons may be treated in this manner. Detailed results are presented here for the pulsating solitary waves; their regimes of occurrence, bifurcations, and the parameter dependences of the amplitudes, widths, and periods agree with simulation results [1,26].

Simulative demonstration of soliton pulse stability over the nonlinear regime in a birefringent optical fiber

In this paper, the results of numerical analysis are demonstrated for sech pulse (soliton) propagation in a birefringent optical fiber using computer modeling and simulation. Here, the initial pulse is polarized linearly and guided into the fiber at an angle of 45° to its polarization axes. The birefringence-induced time delay of 200 and 440 ps between X and Y polarization components has been reported at a fiber length of 631.72 km (10 soliton periods) by considering linear and nonlinear regimes, respectively. The Kerr nonlinearity, which stabilizes solitons against spreading due to GVD, also stabilizes them against splitting due to birefringence. A similar fact is true for the birefringent walk-off. Above a certain soliton order ( N th), the evolution scenario is qualitatively different and two orthogonally polarized components of the soliton move with a common group velocity despite their different modal indices or polarization mode dispersion (PMD) at a fiber length of 631.72 km (10 soliton periods) and 1264.344 km (20 soliton periods) over a nonlinear regime at θ≠45°. The physical effect responsible for this type of behavior is the cross-phase modulation (XPM) between the two polarization components.