Nonlinear surface acoustic waves: realization of solitary pulses and fracture

A laser-based technique for the contact-free generation and detection of strongly nonlinear surface acoustic wave (SAW) pulses with amplitudes limited by the materials strength has been developed. The effects of nonlinear propagation of short elastic surface pulses with finite strength in isotropic solids, such as fused quartz, anisotropic solids, such as silicon, and dispersive media were investigated. Solitary surface wave propagation was observed in layered structures for normal and anomalous dispersion. In addition, a SAW-based method for evaluating the critical fracture stress of anisotropic brittle solids, such as single crystal silicon, is introduced.     

Soliton propagation in tapered silicon core fibers

Numerical simulations are used to investigate soliton-like propagation in tapered silicon core optical fibers. The simulations are based on a realistic tapered structure with nanoscale core dimensions and a decreasing anomalous dispersion profile to compensate for the effects of linear and nonlinear loss. An intensity misfit parameter is used to establish the optimum taper dimensions that preserve the pulse shape while reducing temporal broadening. Soliton formation from Gaussian input pulses is also observed--further evidence of the potential for tapered silicon fibers to find use in a range of signal processing applications.     

高斯光脉冲在非线性增益介质中的孤子特性

本文从理论上分析了高斯光脉冲在非线性增益介质中的传播特性,从而解释高斯光脉冲的压缩及展宽和形成光孤子的机理。用计算机模拟了不同参数的高斯光脉冲在非线性增益介质中的传播过程,并获得了脉宽沿传播方向变化的定量关系。结果表明,以不同能量向增益介质中注入高斯脉冲,有可能产生各阶光孤子,但由于增益的存在,光孤子的传输距离受到限制。     

Impulsive fracture of silicon by elastic surface pulses with shocks

During nonlinear evolution of surface acoustic waves (SAWs) stress increases with propagation, and may cause fracture of brittle materials. This effect was used to evaluate the strength of crystalline silicon with respect to impulsive load in the nanosecond time scale without using seed cracks. Short SAW pulses propagating in the [11(macro)2] direction on the Si(111) plane induce fracture at significantly lower SAW amplitudes than the mirror symmetric wave propagating in the [112(macro)] direction. This effect is explained by the differences in elastic nonlinearity of the two propagation directions.     

Observation of solitary elastic surface pulses

The formation of solitary elastic surface pulses from laser-generated pulselike initial conditions is reported. The nonlinearity of the medium is compensated by both normal dispersion and anomalous dispersion, which were realized by coating isotropic fused silica by a metal and titanium nitride film, respectively. As an anisotropic material, silicon covered with an oxide layer was studied. The experimental results agree with numerical simulations carried out with a nonlocal evolution equation, which describes nonlinear propagation of surface acoustic waves in a dispersive medium.     

Nonlinear propagation delay and pulse distortion resulting from dual frequency band transmit pulse complexes

A method of acoustic imaging is discussed that potentially can improve the diagnostic capabilities of medical ultrasound. The method, given the name second order ultrasound field imaging, is achieved by the processing of the received signals from transmitted dual frequency band pulse complexes with at least partly overlapping high frequency (HF) and low frequency (LF) pulses. The transmitted HF pulses are used for image reconstruction whereas the transmitted LF pulses are used to manipulate the elastic properties of the medium observed by the HF imaging pulses. In the present paper, nonlinear propagation effects observed by a HF imaging pulse due to the presence of a LF manipulation pulse is discussed. When using dual frequency band transmit pulse complexes with a large separation in center frequency (e.g., 1:10), these nonlinear propagation effects are manifested as a nonlinear HF propagation delay and a HF pulse distortion different from conventional harmonic distortion. In addition, with different transmit foci for the HF and LF pulses, nonlinear aberration will occur.     

Slow-light switching in nonlinear Bragg-grating couplers

We study propagation and switching of slow-light pulses in nonlinear couplers with phase-shifted Bragg gratings. We demonstrate that power-controlled nonlinear self-action of light can be used to compensate for dispersion-induced broadening of pulses through the formation of gap solitons, to control pulse switching in the coupler, and to tune the propagation velocity.     

Solitary waves in a binary nonlinear waveguide array

Based on the coupled-mode theory, the propagation of light pulses is studied analytically for a system of an infinite number of tunnel-coupled parallel equidistant waveguides of optically nonlinear materials; in the considered system, waveguides with a positive refractive index alternate with waveguides with a negative refractive index. Partial solutions to a system of nonlinear equations describing the evolution of these pulses are found in the case in which fields in adjacent waveguides differ only in the phase factor. For a solitary wave formed by coupled wave packets localized each in its own waveguide, these solutions describe the stationary propagation in a definite direction. It is shown that the coupling strength between waveguides has an effect on the propagation rate of the obtained stationary pulses.     

脉冲在时域二次折射率介质中的传播

从空域与时域的相似性出发，把克尔介质近似为时域二次折射率介质，从而得到了脉冲在该介质中的解析形式，并给出了相应的时域传输矩阵。     

Nonlinear pulse propagation: a time-transformation approach

We present a time-transformation approach for studying the propagation of optical pulses inside a nonlinear medium. Unlike the conventional way of solving for the slowly varying amplitude of an optical pulse, our new approach maps directly the input electric field to the output one, without making the slowly varying envelope approximation. Conceptually, the time-transformation approach shows that the effect of propagation through a nonlinear medium is to change the relative spacing and duration of various temporal slices of the pulse. These temporal changes manifest as self-phase modulation in the spectral domain and self-steepening in the temporal domain. Our approach agrees with the generalized nonlinear Schr?dinger equation for 100 fs pulses and the finite-difference time-domain solution of Maxwell's equations for two-cycle pulses, while producing results 20 and 50 times faster, respectively.     

Localization of optical pulses in guided wave structures with only fourth order dispersion

Inspired by the recent realization of pure-quartic solitons (Blanco-Redondo et al. (2016) [1]), in the present work we study the localization of optical pulses in a similar system, i.e., a silicon photonic crystal air-suspended structure with a hexagonal lattice. The propagation of ultrashort pulses in such a system is well described by a generalized nonlinear Schrödinger (NLS) equation, which in certain conditions works with near-zero group-velocity dispersion and third order dispersion. In this case, the NLS equation has only the fourth order dispersion term. In the present model, we introduce a quasiperiodic linear coefficient that is responsible to induce the localization. The existence of Anderson localization has been confirmed by numerical simulations even when the system presents a small defocusing nonlinearity.     

单模光纤中超短脉冲的前向四波混频

给出了一组在单模光纤中超短脉冲前向四波混频的耦合波方程。利用这组方程所作的数值研究表明：在低转换和脉冲的走离远小于脉冲宽度的条件下,越短脉冲前向四波混凝的转换效率对相位失配的关系与连续波四波混频情况基本相同,不存在使增益为零的Δｋ（ｋ为不考虑非线性折射率时模的波数）的取值区间,蛤峰值条件应该是Δｋ＝０（ｋ为计及非线性折射率时模的波数）,而不是Δｋ＝０;窄脉冲的转换效率略低且峰值位置与Δｋ＝０稍有偏     

Propagation of bright femtosecond pulses in a nonlinear optical fibre with the third- and fourth-order dispersions

We solve the generalized nonlinear Schr\"{o}dinger equation describing the propagation of femtosecond pulses in a nonlinear optical fibre with higher-order dispersions by using the direct approach to perturbation for bright solitons, and discuss the combined effects of the third- and fourth-order dispersions on velocity, temporal intensity distribution and peak intensity of femtosecond pulses. It is noticeable that the combined effects of the third- and fourth-order dispersions on an initial propagated soliton can partially compensate each other, which seems to be significant for the stability controlling of soliton propagation features.     

Nonlinear compression of giant surface acoustic wave pulses

The nonlinear propagation of very high-amplitude surface acoustic wave (SAW) pulses in polycrystalline aluminum and copper was studied. A nonlinear compression and an increase of the SAW pulse amplitude have been observed. SAW pulses were numerically simulated with a nonlinear evolution equation including local and nonlocal nonlinear terms.     

Wave processes in media with hysteretic nonlinearity: Part 2

Nonlinear processes caused by the propagation of low-frequency and high-frequency acoustic pulses in an unbounded medium and the propagation of continuous waves in a ring resonator are theoretically studied on the basis of two hysteretic equations of state for media with imperfect elasticity. The profiles and parameters of pulses, the resonance curve and the Q factor of the resonator, and the ratio of the nonlinear resonance frequency shift to the nonlinear damping decrement are determined. For nonlinear wave processes in such media, the distinctive features that allow one to choose an appropriate hysteretic equation of state for analytically describing the experimental data are revealed.     

An improved nonlinear optical pulse propagation equation

A new equation for self-focusing of extremely focused short-duration intense pulses is derived using a method that treats diffraction and dispersion to all orders with nonlinearity present, and self-consistently determines the nonlinear derivative terms present in the propagation equation. It generalizes both the previous formulation of linear optical pulse propagation to the nonlinear regime, and the cw nonlinear regime propagation to the pulsed regime by including temporal characteristics of the pulse. We apply the new equation and propagate a tightly focused picosecond pulse in silica and explicitly show the effects of spatial-derivative nonlinear coupling terms.     

Influence of nonlinear dispersion on modulation instability of coherent and partially coherent ultrashort pulses in metamaterials

The combination of dispersive magnetic permeability with nonlinear polarization leads to a series of nonlinear dispersion terms in the propagation equations for ultrashort pulses in metamaterials. Here we present an investigation of modulation instability (MI) of both coherent and partially coherent ultrashort pulses in metamaterials to identify the role of nonlinear dispersion in pulse propagation. The Wigner–Moyal equation for partially coherent ultrashort pulses and the nonlinear dispersion relation for MI in metamaterials are derived. Combining the standard MI theory with the unique properties of the metamaterial, the influence of the controllable first-order nonlinear dispersion, namely self-steepening, and the second-order nonlinear dispersion on both coherent and partially coherent MI, in both negative-index and positive-index regions of the metamaterial for all physically possible cases is analyzed in detail. For the first time to our knowledge, we demonstrate that the role of the second-order nonlinear dispersion in MI is equivalent to that of group-velocity dispersion (GVD) to some extent, and thus due to the role of the second-order nonlinear dispersion, MI may appear in the otherwise impossible cases, such as in the normal GVD regime. PACS 42.25.Kb; 42.65.Sf; 78.20.Ci     

Femtosecond pulse propagation in silicon waveguides: Variational approach and its advantages

We investigate the propagation characteristics of ultrafast pulses inside silicon waveguides considering frequency chirp associated with each input pulse. Effects of linear losses, two-photon absorption, and free-carrier dynamics are included analytically within the framework of a modified variational formalism and the results are validated by comparing them with full numerical simulations. It is found that an initial chirp helps in maintaining the pulse shape and spectrum in the anomalous-dispersion regime, thereby resulting in soliton-like propagation of ultrashort optical pulses.     

Soliton-like propagation modes of picosecond acoustic pulses in a paramagnetic crystal

The nonlinear propagation of picosecond acoustic pulses at an arbitrary angle to an external magnetic field is studied in an elastically isotropic paramagnetic crystal at low temperatures. Various soliton-like propagation modes arising due to spin-phonon interaction and acoustic anharmonicity are revealed, and the stability of these modes with respect to transverse perturbations is analyzed. In the case of defocusing cubic nonlinearity, the crystal can support the propagation of compression pulses, which undergo defocusing, and rarefaction pulses can propagate in the self-channeling mode. In the case of focusing cubic nonlinearity, only compression pulses can propagate if the conditions of stability with respect to self-focusing are satisfied.     

Generation of RF oscillations in the interaction of an electromagnetic shock with a synchronous backward wave

A new mechanism for the transformation of video pulses into radio pulses during their propagation along a nonlinear transmission line with spatial dispersion—synchronism with a backward wave—is considered. Numerical simulations demonstrate that a substantial advantage of this mechanism over the interaction with a forward wave is the possibility of generating longer radio pulses at higher frequencies.