Soliton Power Research Articles

Numerical investigation of turnkey soliton generation in an organically coated microresonator

Kerr soliton frequency-comb generation in microresonators has attracted extensive interest since soliton microcombs offer the potential for integration and can be widely used in many fields, such as spectroscopy, communications, precision metrology, sensing, etc. Here, the mechanism of turnkey soliton generation in a microresonator with an organic material coating is illustrated and investigated in both analytical and numerical ways. In particular, based on the thermal curve under a stable state and soliton power from analytical analysis, the turnkey soliton generation regime is calculated and proved by coupled equations with the split-step Fourier method. In addition, the physical parameters of the hybrid modes in the coated resonators are studied, and a suitable design is given in this paper. This research will be helpful for increasing the accessibility of Kerr solitons and make them easier to integrate.

Existence, symmetry breaking bifurcation and stability of two-dimensional optical solitons supported by fractional diffraction.

We study existence, bifurcation and stability of two-dimensional optical solitons in the framework of fractional nonlinear Schrödinger equation, characterized by its Lévy index, with self-focusing and self-defocusing saturable nonlinearities. We demonstrate that the fractional diffraction system with different Lévy indexes, combined with saturable nonlinearity, supports two-dimensional symmetric, antisymmetric and asymmetric solitons, where the asymmetric solitons emerge by way of symmetry breaking bifurcation. Different scenarios of bifurcations emerge with the change of stability: the branches of asymmetric solitons split off the branches of unstable symmetric solitons with the increase of soliton power and form a supercritical type bifurcation for self-focusing saturable nonlinearity; the branches of asymmetric solitons bifurcates from the branches of unstable antisymmetric solitons for self-defocusing saturable nonlinearity, featuring a convex shape of the bifurcation loops: an antisymmetric soliton loses its stability via a supercritical bifurcation, which is followed by a reverse bifurcation that restores the stability of the symmetric soliton. Furthermore, we found a scheme of restoration or destruction the symmetry of the antisymmetric solitons by controlling the fractional diffraction in the case of self-defocusing saturable nonlinearity.

Influence of reverse saturable absorption effect on conventional and dissipative solitons fiber lasers

We numerically investigate the influence of the reverse saturable absorption effect of real saturable absorbers on conventional and dissipative solitons. The results show that the reverse saturable absorption effect leads to more loss and clamps peak power of both conventional and dissipative solitons, but plays different roles on their properties. When the cavity operates at conventional solitons state, the reverse saturable absorption effect restricts the maximum pulse energy to less than 0.1 nJ, facilitates the formation of multiple solitons, but maintains the time-bandwidth product close to 0.315, indicating the pulses maintain the sech2 shape. While the cavity operates at dissipative solitons state, the reverse saturable absorption effect increases the maximum pulse energy from 11 to 13 nJ and plays a key role in transforming the pulse states, which further facilitates the generation of dissipative soliton resonance pulses. In addition, the reason of the different influences on pulses in two mode-locked regimes is also discussed. Our results reveal the role and promote the rational use of the reverse saturable absorption effect in different mode-locked regimes.

Single- and multi-soliton generation in figure-eight mode-locked fibre laser with two active media

We present a study of generation of a figure-eight mode-locked all-PM fibre laser having two independently pumped active media in each loop of the cavity under varied power level of both pump sources. Controllable and reproducible generation of 1- to 7-picosecond solitons per cavity round trip is demonstrated, as well as the possibility of soliton peak power and energy adjustment in a pre-determined passively mode-locked regime. Salient features are identified of transition among regimes with different soliton count, including those generating Raman solitons. The studied all-fibre laser system makes it possible to reproducibly generate pre-determined soliton molecules with variable energy. Such a fibre-optical system may be widely used as a seed generator of electronically controlled bursts of picosecond solitons with nanosecond inter-pulse delays.

Vortex and cluster solitons in nonlocal nonlinear fractional Schrödinger equation

We discover a series of ring and cluster solitons in the (1+2)-dimensional nonlocal nonlinear fractional Schrödinger equation by iteration algorithm, and verify their robustness by introducing random perturbations during propagations. We obtain the relations between the soliton power, the orbital angular momentum, and the rotation period of phase, which are dependent on the Lévy index α. When the radial number p = 0, the soliton shapes slightly vary with the change of Lévy index. However, when p ≥ 1, the solitons exhibit novel structures, the outer ring (hump) of such solitons decrease as the Lévy index decreases. Our results extend the study of vortex and cluster solitons into fractional systems and deepen the understanding of fractional dimensions.

The relation of Zakharov-Shabat scattering problem to Schrödinger equation with complex potential and approximations for soliton parameters

The relation of Zakharov-Shabat scattering problem to Schr\"{o}dinger equation with complex potential is used to analytically approximate parameters of high power solitons produced in positive Kerr media with chirped parabolic pulses. The soliton parameters are estimated for different types of chirp and intensity distortions. The comparison with numerics is discussed.

On the propagation modes of light bullets in the gradient fibers

An analytical study of the propagation of a spatiotemporal optical soliton in a gradient fiber with the Kerr nonlinearity has been carried out. Two approaches were used, based on the heuristic method of the averaged Lagrangian. In the framework of the first approach, for the envelope of the light signal, a well-known factorized representation is used in the form of two functions that depend on the longitudinal and transverse coordinates, respectively. In the framework of the second approach was used a trial solution in the form of temporal soliton. However, the parameters of this soliton depend on the coordinates. By means of the second approach the approximate solutions are found in the form of stationary and pulsating light bullets. The conditions for their stability are determined. These conditions apply to the aperture and temporal duration of the soliton. I addition, the soliton power should be less than a certain threshould value. If the soliton power is much less than this threshould value, then both analytical approaches are consistent with each other.

Symmetry breaking and restoration of symmetric solitons in partially parity-time-symmetric potentials

We address the symmetry-breaking bifurcation of optical solitons in cubic–quintic media with an imprinted partially parity-time-symmetric potential. An increase in soliton power leads to symmetry breaking, which occurs through a pitchfork bifurcation. In contrast to all previously reported symmetry breaking, restoring bifurcation occurs when soliton power exceeds another critical value. Symmetry-breaking region between symmetry-breaking point and restoration point shrinks with the growth of the strength of quintic nonlinearity. While the base branch of solitons loses their stabilities in the symmetry-breaking region, the stabilities of two branches of bifurcated asymmetric solitons respecting mirror symmetry are opposite. Nonreciprocal propagation of unstable asymmetric solitons is also observed. We thus put forward the first example of restoring bifurcation of symmetric solitons in two dimensions.

The Physical Parameters of EDFA and SOA Optical Amplifiers and Bit Sequence Variations Based Optical Pulse Generators Impact on the Performance of Soliton Transmission Systems

Abstract This study has outlined the effects of physical parameters of erbium doped fiber amplifier (EDFA), semiconductor optical amplifier (SOA) on the performance of amplified soliton transmission systems. Injection current-based SOA, EDFA length is taken into account. It is observed that the optimum soliton power and signal per noise ratio are achieved with 5 m EDFA length and 900 mA injection current-based SOA. As well as the bit sequence variations based user defined bit sequence generator are employed in order to measure the soliton transmission system performance. The signal per noise ratio is enhanced with 4 bit sequence. Soliton peak power, output soliton power, and maximum Q-factor are optimized with 8 bit sequence for soliton propagation length of 150 km and possible transmission data rates of 160 Gb/s. Improvement percentage ratio in soliton peak power by using two amplification techniques a long propagation length is deeply stimulated with optiwave simulation program.

Improvements of Soliton Pulse Energy and Peak Power in Thulium-Doped Fiber Laser

We report on improvements of mode-locked soliton pulse energy and peak power in a thulium-doped fiber laser. At the pump power of 370 mW, conventional soliton can be first generated using nonlinear polarization rotation technology. By increasing the pump power to 550 mW and appropriately adjusting cavity polarization state, the conventional soliton pulse can be converted into the Gaussian pulse. Due to dispersion management, excess accumulation of nonlinear phase shifts in the cavity can be avoided. In this case, the pulse energy and peak power can be increased from 77 pJ to 1.38 nJ and from 106.9 W to 2.67 kW, respectively. These improvements indicate that the Gaussian pulse operation can effectively enhance the pulse energy and peak power of the thulium-doped fiber laser.

One-dimensional solitons in fractional Schrödinger equation with a spatially periodical modulated nonlinearity: nonlinear lattice

The existence and stability of stable bright solitons in one-dimensional (1D) media with a spatially periodical modulated Kerr nonlinearity are demonstrated by means of the linear-stability analysis and in direct numerical simulations. The nonlinear potential landscape can balance the fractional-order diffraction and thus stabilizes the solitons, making the model unique and governed by the recently introduced fractional Schr\"{o}dinger equation with a self-focusing cubic nonlinear lattice. Both 1D fundamental and multihump solitons (in forms of dipole and tripole ones) are found, which occupy one or three cells of the nonlinear lattice respectively, depending on the soliton's power (intensity). We find that the profiles of the predicted soliton families are impacted intensely by the L\'{e}vy index $\alpha$ which denotes the level of fractional Laplacian, so does to their stability. The stabilization of soliton families is possible if $\alpha$ exceeds a threshold value, below which the balance between fractional-order diffraction and the spatially modulated focusing nonlinearity will be broken.

Effects of Order Super Gaussian Pulses on the Performance of High Data Rate Optical Fiber Channel in the Presence of Self Phase Modulation

Abstract The work has simulated different order Gaussian pulses effects on the high data rate fiber communication channel and optical receiver sensitivity with/without self-phase modulation (SPM). The light signal per noise ratio, and total dispersion coefficient after optical fiber communication channel are measured at different order Gaussian pulses. Receiver sensitivity and maximum Q-factor are also measured for an optical receiver at high transmission data rates at different order Gaussian pulses. As well as Soliton peak power is measured for different transmission data rates with/without SPM effects. It is observed that the system performance is degraded over 100 Gb/s data transmission and 50 km fiber distance especially in the presence of SPM effects. It is evident that the system performance efficiency is degraded with high order Gaussian pulses. It is recommended to use first-order Gaussian pulse for upgrade optical communication system performance efficiency.

Ultra high transmission capacity based on optical first order soliton propagation systems

Abstract This study presents the first order optical soliton propagation systems for ultra-high transmission distance that reaches up to 20,000 Km with transmission data rates of 80 Gb/s and its corresponding maximum Q-factor and Soliton peak power. The simulation has been performed for the distance up to 20000 Km at the operating wavelength of 1300 and 1550 nm.

Off-site and on-site vortex solitons in space-fractional photonic lattices.

We address the existence and stability of off-site and on-site vortex solitons with a unit topological charge in space-fractional Kerr lattices. In contrast to the reported ordinary Kerr lattices, vortex solitons in the proposed space-fractional lattices are stable only in the intermediate region of propagation constant, and this region widens rapidly with the increase of a Lévy index. Under the same Lévy index, the stability range of on-site vortices is larger than that of off-site ones. In particular, for on-site vortex solitons, the upper edge of the stability range appears where the maximum of soliton power is located, which provides an effective way to identify the stability range of on-site vortices. Our results extend the study of vortex solitons into space-fractional systems and deepen the understanding of Kerr lattices in fractional dimensions.

Variational approach for breathers in a nonlinear fractional Schrödinger equation

The fractional Schrödinger equation with a Kerr nonlinearity, is reformulated as a variational problem to predict the evolutions of breathers. Here the breather is formed from a soliton when the input power deviates little from the soliton power. By means of a Gaussian trial function, the soliton solution is analytically obtained, and the evolutionary equations for the breather are derived. When the ratio of the input power and the soliton power approaches 1, the predictions for breather evolutions give good agreement with the numerical results. In this case, the predicted analytical breather period is obtained approximately and is also a very good fit. When the soliton at higher powers, its shape is numerically found to exhibit dramatic changes during propagation, and therefore the variation approach fails to predict its evolution.

Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential.

We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time ([Formula: see text])-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of the saturable nonlinearity in such [Formula: see text]-symmetric waveguides. The dependence of the propagation constant on the soliton's power is presented for different strengths of the nonlinearity saturation, S The stability of fundamental, dipole, tripole and quadrupole solitons is investigated by means of the linear-stability analysis and direct numerical simulations of the corresponding (1+1)-dimensional nonlinear Schrödinger-type equation. The results show that the instability of the stationary solutions can be mitigated or completely suppressed, increasing the value of SThis article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.

Universal isocontours for dissipative Kerr solitons.

Dissipative Kerr solitons can be generated within an existence region defined on a space of normalized pumping power versus cavity-pump detuning frequency. The contours of constant soliton power and constant pulse width in this region are studied through measurement and simulation. Such isocontours impart structure to the existence region and improve understanding of soliton locking and stabilization methods. As part of the study, dimensionless, closed-form expressions for soliton power and pulse width are developed (including Raman contributions). They provide isocontours in close agreement with those from the full simulation, and, as universal expressions, can simplify the estimation of soliton properties across a wide range of systems.

Symmetric and asymmetric solitons supported by a 𝒫𝒯-symmetric potential with saturable nonlinearity: bifurcation, stability and dynamics.

The symmetry breaking bifurcation of solitons in an optical waveguide with focusing saturable nonlinearity and parity-time (𝒫𝒯)-symmetric complex-valued external potentials is investigated. As the soliton power increases, it is found that the branches of asymmetric solitons split off from the base branches of 𝒫𝒯-symmetric fundamental soliton. The bifurcation diagrams, consisting essentially of the propagation constants of optical solitons, indicate that symmetric fundamental and multipole solitons, as well as asymmetric solitons can exist. The stabilities and the dynamics characteristics of solitons are comprehensively investigated. We find the different instability scenarios of the symmetric solitons, but the symmetry breaking bifurcation is caused only by the onset of instability of the symmetric fundamental solitons. This result is further confirmed by the numerical examples with the different saturable nonlinearity parameters. In particular, we find that the soliton power and the stability of soliton at the bifurcation points are significantly changed by varying the strength of the saturable nonlinearities. These results provide additional way to control symmetry breaking bifurcations in 𝒫𝒯-symmetric optical waveguide.

Solitons under spatially localized cubic-quintic-septimal nonlinearities

We explore stability regions for solitons in the nonlinear Schrödinger equation with a spatially confined region carrying a combination of self-focusing cubic and septimal terms, with a quintic one of either focusing or defocusing sign. This setting can be implemented in optical waveguides based on colloids of nanoparticles. The solitons’ stability is identified by solving linearized equations for small perturbations, and is found to fully comply with the Vakhitov–Kolokolov criterion. In the limit case of tight confinement of the nonlinearity, results are obtained in an analytical form, approximating the confinement profile by a delta-function. It is found that the confinement greatly increases the largest total power of stable solitons, in the case when the quintic term is defocusing, which suggests a possibility to create tightly confined high-power light beams guided by the spatial modulation of the local nonlinearity strength.

Dissipative solitons characteristics in passively mode-locked Er-doped fiber laser based on black phosphorus as a new saturable absorber

Two-dimensional materials such as graphene or black phosphorus have attracted attention of researches in the field of ultra-fast photonics. In this paper, the structure of the passively mode-locked Er-doped fiber laser based on black phosphorus as a new saturable absorber has studied by modeling and analysis. The dissipative solitons characteristics in passively mode-locked Er-doped fiber laser are obtained in the simulation. The research focuses on analyzing the influence of gain bandwidth and gain saturation energy on the pulse duration, peak power, and single-pulse energy of the dissipative solitons.