Order Soliton Research Articles

電子線小角散乱法を用いた磁気微細構造解析

Quantitative reciprocal-space analyses of magnetic fine structures in magnetic artificial lattices of patterned elements and chiral helimagnets have been performed by means of small-angle electron scattering (SAES) technique. Lorentz deflection due to magnetic moments and Bragg diffraction due to lattice periodicity are simultaneously recorded at an angle of the order of 1×10−6 rad using long-distance camera length more than 100 m. The present SAES technique,together with TEM real-space imaging method such as in-situ Lorentz microscopy, is very powerful in analyzing electromagnetic fields in nano-scaled materials. The existence of both chiral helimagnetic order and chiral soliton lattice in a chiral helimagnet CrNb3S6 has been successfully verified using the present methods.

Effect of Ramam gain on the characteristic of soliton propagation

Using the nonlinear Schrödinger equation (NLSE) including Raman gain effect but ignoring fiber loss situation, the linear operator and nonlinear operator specific expression are obtained based on MATLAB fractional Fourier numerical algorithm. They are applied to the NLSE including Raman gain, and the evolutions of soliton pulse are simulated in optical fiber through changing parameters. The result shows that soliton propagation stability is destroyed compared with the case considering no Raman gain, leading to the rapid attenuation of optical soliton. The influence degree depends on input soliton pulse peak power. The effects of Raman gain on ground state soliton and high order soliton are not the same.

Soliton compression to few-cycle pulses with a high quality factor by engineering cascaded quadratic nonlinearities

We propose an efficient approach to improve few-cycle soliton compression with cascaded quadratic nonlinearities by using an engineered multi-section structure of the nonlinear crystal. By exploiting engineering of the cascaded quadratic nonlinearities, in each section soliton compression with a low effective order is realized, and high-quality few-cycle pulses with large compression factors are feasible. Each subsequent section is designed so that the compressed pulse exiting the previous section experiences an overall effective self-defocusing cubic nonlinearity corresponding to a modest soliton order, which is kept larger than unity to ensure further compression. This is done by increasing the cascaded quadratic nonlinearity in the new section with an engineered reduced residual phase mismatch. The low soliton orders in each section ensure excellent pulse quality and high efficiency. Numerical results show that compressed pulses with less than three-cycle duration can be achieved even when the compression factor is very large, and in contrast to standard soliton compression, these compressed pulses have minimal pedestal and high quality factor.

Numerical investigation on frequency-shifting-induced spectral compression of femtosecond solitons in highly nonlinear fiber

We present a numerical investigation on nonlinear propagation of femtosecond pulses in anomalously dispersive highly nonlinear fiber (HNLF) with positive third-order dispersion (TOD). Soliton self-frequency shift (SSFS) in the HNLF is shown to enable efficient spectral compression of ultrashort pulse whose parameters satisfy 0.8≤N≤1.3 for the soliton order N. A spectral-compression factor up to 2.5 can be achieved for 60-fs, 1550-nm fundamental solitons red-shifted to 1609nm in the HNLF. We show that the fiber TOD has significant influence on the SSFS-induced spectral-compression performance. Using HNLF with larger TOD parameter, greater spectral-compression factor can be obtained. We also find that the impact of initial pulse chirp on output spectral width is negligible, indicating SSFS-based spectral-compression method is efficient for both chirped pulses and transform-limited pulses.

Pulse Compression And Pedestal Suppression For The High-Order Solitons

A pulse compression and pedestal suppression method for high-order solitons is presented in this paper. With the existing analytic solutions, the second- and third-order solitons are compressed, and the optimum lengths for them are obtained. Without the soliton broadening, the pedestals of the solitons from different outputs can be suppressed with the choices of corresponding parameters. Unlike other pedestal suppression methods, the energy of the pedestal is transferred to the peak of the soliton, and the output intensity of the high-order compressed solitons increases during the pedestal suppression. As the soliton order increases, results show that the optimum length for the pedestal suppression increases, and the pulse width decreases.

Supercontinuum broadening in all-normal dispersion photonic crystal fiber by means of soliton compression in standard single-mode fiber

Using standard single-mode fiber as high-order soliton compressor for broadening supercontinuum in an 80m long all-normal dispersion photonic crystal fiber is investigated experimentally and numerically. An analytical formula for calculating proper fiber input power to generate the broadest supercontinuum is derived. The numerical results show that the formula is more accurate in high power level corresponding to the soliton order which is larger than two. The measured supercontinuum −20dB bandwidth is broadened from 84.2nm to 277.1nm by using a 20m long standard single-mode fiber without enhancing fiber input power. Numerical calculations of the amplitude noise in the output spectra show that using soliton compression effect can efficiently broaden the spectral bandwidth and not generate obvious noises.

Mid-IR soliton compression in silicon optical fibers and fiber tapers

Numerical simulations are used to investigate soliton compression in silicon core optical fibers at 2.3 μm in the mid-infrared waveguide regime. Compression in both standard silicon fibers and fiber tapers is compared to establish the relative compression ratios for a range of input pulse conditions. The results show that tapered fibers can be used to obtain higher levels of compression for moderate soliton orders and thus lower input powers.

Incoherent Soliton Turbulence in Nonlocal Nonlinear Media

The long-term behavior of a modulationally unstable nonintegrable system is known to be characterized by the soliton turbulence self-organization process: It is thermodynamically advantageous for the system to generate a large-scale coherent soliton in order to reach the ("most disordered") equilibrium state. We show that this universal process of self-organization breaks down in the presence of a highly nonlocal nonlinear response. A wave turbulence approach based on a Vlasov-like kinetic equation reveals the existence of an incoherent soliton turbulence process: It is advantageous for the system to self-organize into a large-scale, spatially localized, incoherent soliton structure.

Pedestal free pulse compression of chirped optical solitons

We consider the evolution of nonlinear optical pulses in inhomogeneous optical media wherein the pulse propagation is governed by the nonlinear Schrödinger equation with varying dispersion. We adopt the Painlevé analysis in order to obtain the condition for the soliton pulse propagation. We find that there exist two dispersion profiles satisfying this criterion, namely, the constant dispersion and exponentially dispersion decreasing profiles. In the exponentially varying dispersion media, we explain the existence and the formation of chirped optical soliton through the equation for the chirp parameter that results from variational analysis. For further elucidation, we provide the phase-plane diagram in terms of the normalized chirp and intensity (peak power), which explains the physical mechanism of linearly chirped soliton pulse compression in the exponentially dispersion decreasing media. In addition, we discuss the generation of exact chirped higher order solitons using the Bäcklund transformation method. As a special case, we find an oscillatory two-soliton breather pulse, which, at decreasing intervals, evolves into a familiar hyperbolic secant shape whose amplitude is twice that of a fundamental soliton. We highlight on the point that the crux of this work in realizing a compact pulse compressor could possibly result in a myriad of applications in modern optical fiber communications systems.

IMPLEMENTATION OF OVERLAPPING SOLITON PAIR TO REDUCE TIME DELAY IN FEMTOSECOND PULSE PROPAGATION OVER SHORT STANDARD SINGLE MODE FIBER

Propagation of 50 femtosecond soliton pulse over short Standard Single Mode Fiber (SSMF) is reported by using soliton pair as the input pulse. The attraction of two solitons to propagate as one pulse is intended. The time deviation and average amplitude of propagating pulses are compared for several soliton orders and initial inter-pulse delays. It is discovered that by considering overlapping soliton pair as the input pulse, under special conditions, better propagation characteristic and lower time delay is experienced over short SSMF in comparison to the fundamental soliton.

Evolution of hyperbolic-secant optical pulses towards wave breaking in quintic nonlinear fibers

Evolutions of the frequency chirps, shapes, and spectra of initial hyperbolic-secant pulses towards wave breaking are numerically investigated in the normal dispersion regimes of optical fibers with quintic nonlinearity and the developing chirps and the characteristic distances of wave breaking are analytically processed approximately. The results show that quite different mathematical expressions from those of initial Gaussian pulses are obtained. Moreover, the wave breaking here will be more intense for more oscillation peaks will appear in the pulse wings and the breaking process will last longer distance before rectangle-shaped pulses form at last. However, the quintic nonlinearity plays a similar role to the case of initial Gaussian pulses in developing chirps and bringing forward or retarding the wave breaking. The wave breaking distance will also decrease with increase of the quintic nonlinearity and the soliton order.

Self-referenceable frequency comb from a gigahertz diode-pumped solid-state laser

We present carrier envelope offset (CEO) frequency detection of a diode-pumped Yb:KGW (ytterbium-doped potassium gadolinium tungstate) laser with a repetition rate of 1 GHz. The SESAM-soliton-modelocked laser delivers 2.2-W average power in 290-fs pulses. This corresponds to a peak power of 6.7 kW and the optical-to-optical efficiency is 38%. With a passive pulse compression the duration is reduced to 100 fs at an average power of 1.1 W. Coherent supercontinuum (SC) generation in a highly nonlinear photonic crystal fiber (PCF) is achieved without additional amplification. Furthermore we have demonstrated that pulse compression towards lower soliton orders of approximately 10 was required for coherent SC generation and CEO detection. Additional numerical simulations further confirm these experimental results.

Spatial solitons with the odd and even symmetries in (2+1)-dimensional spatially inhomogeneous cubic-quintic nonlinear media with transverse W-shaped modulation

We firstly investigate analytical spatial soliton solutions with the odd and even symmetries in (2+1)-dimensional spatially inhomogeneous cubic-quintic nonlinear media considering transverse W-shaped modulation. The power of localized states increases one by one along the line y = x when the soliton order number n increases. The stability analysis and numerical calculations show that stable fundamental solitons exist while higher order solitons are unstable in three nonlinear media, i.e. the defocusing cubic and focusing quintic nonlinear medium, focusing cubic and defocusing quintic nonlinear medium, and focusing cubic and focusing quintic nonlinear medium. While all solitons (even fundamental solitons) are unstable and ultimately decay into noise in the defocusing cubic and defocusing quintic nonlinear medium.

Propagation of femtosecond soliton pulses in standard single mode fiber

Propagation of 50 fs soliton pulse over standard single mode fiber (SSMF) is reported by using soliton pair as the input pulse. The attraction of two solitons to propagate as one pulse is purposed. The time delay and average amplitude of propagating pulses are compared for several soliton orders and initial inter-pulse delays. It is discovered that by using this technique under special conditions, better propagation characteristic is experienced by colliding 50 fs soliton pair in comparison to a 50 fs fundamental soliton.

Collapse in the nonlocal nonlinear Schrödinger equation

We discuss spatial dynamics and collapse scenarios of localized waves governed by the nonlinear Schrödinger equation with nonlocal nonlinearity. Firstly, we prove that for arbitrary nonsingular attractive nonlocal nonlinear interaction in arbitrary dimension collapse does not occur. Then we study in detail the effect of singular nonlocal kernels in arbitrary dimension using both Lyapunoff's method and virial identities. We find that in the one-dimensional case, i.e. for n = 1, collapse cannot happen for nonlocal nonlinearity. On the other hand, for spatial dimension n ⩾ 2 and singular kernel ∼1/rα, no collapse takes place if α < 2, whereas collapse is possible if α ⩾ 2. Self-similar solutions allow us to find an expression for the critical distance (or time) at which collapse should occur in the particular case of ∼1/r2 kernels for n = 3. Moreover, different evolution scenarios for the three-dimensional physically relevant case of Bose–Einstein condensates are studied numerically for both the ground state soliton and higher order toroidal states with, and without, an additional local repulsive nonlinear interaction. In particular, we show that the presence of local repulsive nonlinearity can prevent collapse in those cases.

Dynamics of Raman soliton during supercontinuum generation near the zero-dispersion wavelength of optical fibers

We observe unique dynamics of Raman soliton during supercontinuum process when an input pulse experiences initially normal group-velocity dispersion with a negative dispersion slope. In this situation, the blue components of the spectrum form a Raman soliton that moves faster than the input pulse and eventually decelerates because of Raman-induced frequency downshifting. In the time domain, the soliton trajectory bends and becomes vertical when the Raman shift ceases to occur as the spectrum of Raman soliton approaches the zero dispersion point. Parts of the red components of the pulse spectrum are captured by the Raman soliton through cross-phase modulation and they travel with it. The influence of soliton order, input chirp and dispersion slope on the dynamics of Raman soliton is discussed thoroughly.

Spatial solitons in photonic lattices with large-scale defects**Project supported by the National Natural Science Foundation of China (Grant No. 10704067) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6100381).

We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several families of soliton solutions, including flat-topped, dipole-like, and multipole-like solitons, can be supported by the defected lattices with different heights of defects. The width of existence domain of solitons is determined solely by the saturable parameter. The existence domains of various types of solitons can be shifted by the variations of defect size, lattice depth and soliton order. Solitons in the model are stable in a wide parameter window, provided that the propagation constant exceeds a critical value, which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium. We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.

Higher-order soliton-effect pulse compression in a nonlinear left-handed transmission line

This work introduces a method of pulse compression based on a higher-order soliton effect in a left-handed nonlinear (LH-NL) transmission line with series nonlinear capacitances. A circuit simulation of the LH-NL transmission line which is based on a finite-difference method shows that if a higher-order soliton is replaced by a fundamental soliton launched into the line, the self-phase modulation (SPM) will dominate the group velocity dispersion (GVD). As a result, the pulse compression is realized in a specific length dependent on the soliton order.

Investigations on optical timing jitter in dispersion managed higher order soliton system

The timing jitter in higher order dispersion managed soliton over 4,000 km link length has been investigated. The performance of the system under varied conditions of pulse shape, chirp factor, data rate amplifier spacing has been explored. The higher order soliton of gaussian shape in comparison to super-gaussian have shown reduction in timing jitter. Its results have been fitted in trend lines to form an empirical relationship with distance. The plots at varied chirp factor of gaussian and super gaussian shaped soliton for the system have been provided which show identical behaviour. However, fluctuations in timing jitter can be reduced by a proper chirp factor for the both. The timing jitter for gaussian shape soliton at data rates 20 and 10 Gbps has been plotted which indicates its early growth in the former data rate case. Further, varied amplifier spacing for the same 4,000 km link length in the system indicated that reasonably smaller amplifier spacing can reduce dispersion management induced timing jitter.

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.