Wave processes in media with hysteretic nonlinearity. Part I

Two phenomenological models of hysteretic equations of state for media with imperfect elasticity are described and compared. On the basis of these equations, a theoretical study of nonlinear effects caused by the acoustic wave propagation in an unbounded medium is performed. The profiles, parameters, and spectra of waves are determined. The distinctive features of nonlinear wave processes in such media are revealed, so that these features can be used to choose the appropriate hysteretic equation of state for analytically describing the experimental data.     

Nonlinear acoustic effects in a resonator with saturation of hysteretic loss

Nonlinear wave processes in an acoustic rod resonator with hysteretic nonlinearity under harmonic excitation are studied. The characteristics of longitudinal nonlinear modes of the resonator with hard and soft boundaries (amplitude-dependent loss, shifts of resonance frequencies, and amplitudes of the second and third harmonics) are determined. The comparison of the theoretical and experimental dependences of nonlinear acoustic effects in a resonator that is made of annealed polycrystalline copper is used to determine the parameters of the hysteretic nonlinearity.     

Experimental study of nonlinear acoustical effects in limestone

Results of an experimental and theoretical study of nonlinear acoustic effects (amplitude-dependent loss, resonance frequency shift, second and third harmonic generation, and sound by sound damping) in a limestone bar resonator are reported. The observed effects are analytically described in the framework of phenomenological equations of state with allowance for the low-frequency hysteretic nonlinearity and the high-frequency dissipative nonlinearity. Experimental and analytical dependences of nonlinear effects are compared to find the parameters of the hysteretic and dissipative nonlinearities of the limestone sample studied.     

Propagation of weak ultrasonic pulses in an intense low-frequency wave field in a granite resonator

Results of an experimental study of nonlinear attenuation and carrier frequency phase delay of weak ultrasonic pulses under the effect of an intense low-frequency wave in a bar resonator made from Karelian granite are presented. The effects observed in the experiment are analytically described in terms of the phenomenological equation of state containing hysteretic and dissipative nonlinearities. A frequency dependence of nonlinearity is revealed, and the effective values of nonlinear parameters of granite are estimated for the frequency range from 150 kHz to 1 MHz.     

Propagation of unipolar strain pulses in media with hysteretic nonlinearity

A theoretical study of the propagation of unipolar strain pulses in a solid medium with an arbitrary power-law hysteretic nonlinearity is carried out. Exact analytical expressions are derived for describing the propagation and evolution of initially sine-shaped and triangular pulses in such media. The solutions found are analyzed both numerically and graphically.     

Interaction of acoustic waves in microinhomogeneous media with hysteretic nonlinearity and relaxation

The propagation of a weak high-frequency pulse in the field of an intense standing low-frequency pump wave excited in an acoustic resonator with quadratic hysteretic nonlinearity and relaxation is theoretically investigated. The nonlinear damping coefficient and the carrier phase delay of the weak high-frequency pulse propagating under the action of an intense low-frequency wave are determined.     

Superluminal propagation in resonant dissipative media

We analyse the superluminal propagation of optical narrow-band pulses at resonances in dissipative media. We find that, for a broad class of optical systems holding this type of lossy faster-than-light transmission capability, the output waveform is an attenuated, time-advanced version of the input which can be interpreted as the result of the interference of two scaled replicas of the input having a positive relative delay. This analysis is shown to apply, among other scenarios, both in the propagation in a passive bulk medium at an electronic resonance and in a dielectric waveguide coupled to a lossy micro-ring resonator.     

激光大气成丝中的非线性光频转换

超快强激光在光学介质（如空气）中传播时由于克尔自聚焦效应和等离体散焦效应动态平 衡会发生一种独特的非线性激光成丝现象。激光成丝过程会诱导一些独特的物理现象,如非线性 光频转换产生超连续光谱、等离子体诱导高压放电、锥形辐射等,在大气传感、天气控制等研究 领域具有重要的应用前景。本文针对飞秒激光大气成丝过程中与传输介质相互作用所诱导的非线 性发光过程,介绍了激光大气成丝所产生的超连续光谱（白光）激光、谐波产生和太赫兹波辐射 三种非线性光频转换现象,并着重探讨了太赫兹波辐射的物理机理、研究现状和应用前景。     

Nonlinear wave processes in porous waterlike media containing a system of capillaries partially filled with a viscous liquid

A nonlinear dynamic state equation of waterlike porous material that contains a system of cylindrical capillaries partially filled with viscous liquid was received. It is shown that an acoustic nonlinearity of such media contains the relaxation elastic and inelastic components due to the nonlinear dependence of the capillary and viscous pressure in fluid on the capillary diameter. For the medium, theoretical study of such nonlinear phenomena as generation of the second harmonic and a difference frequency wave, self-demodulation of high-frequency pulses as well as the change in the propagation velocity and absorption coefficient of a test wave being under an action of static loading have been carried out. The frequency dependences of medium nonlinearity parameters for these processes were determined.     

Resonant bar simulations in media with localized damage

As a rule, problems of wave propagation in finite media with non-uniform spatial distribution of material properties can only be tackled by numerical models. In addition, the modeling of damage features in a material requires the introduction of locally non-linear and--more important--non-unique equations of state. Using a multiscale approach, we have implemented a non-linear hysteretic stress-strain relation based on the Preisach-Mayergoyz (PM) model, into a numerical elastodynamic finite integration technique program, which has originally been developed for linearly elastic wave propagation in inhomogeneous media. The simulation results show qualitatively good agreement with data of non-linear resonant bar experiments in homogeneously non-linear and hysteretic media. When the PM density distribution of hysteretic units at the mesoscopic level is not uniform and/or confined to a finite area in stress-stress space, the response at high amplitude excitation tend to deviate from the quasi-analytical results obtained in the case of a uniform PM-space density. Localized microdamage features in an intact medium can be modeled by conceiving finite zones with pronounced hysteretic stress-strain relations within a "linear" surrounding. Forward calculations reveal a significant influence of the amplitude dependent resonance behavior on the location (edge versus center of a bar), the extend (width of the zone) and the degree (density of hysteretic units) of damage.     

Locking of the longitudinal modes of an SBS-laser oscillator by optical feedback

The use of a nonlinear mirror on the basis of the stimulated Brillouin scattering (SBS) as part of a resonator in a laser oscillator leads to the generation of bandwidth due to the shift in frequency that is connected with the reflection at the SBS-mirror. Another effect of the nonlinear SBS-reflection is a passive Q-switch, which leads to a generation of pulses with durations of approximately 100 ns. An almost perfect locking of the longitudinal modes is observed if an additional external resonator is applied and certain resonance criteria are obeyed. This locking of the longitudinal modes surfaces as a splitting of the Q-switch pulses into trains of pulses with subnanosecond duration. PACS 42.60.Fc; 42.60.Gd; 42.65.Es     

Entangled photon states generation and regeneration using a nonlinear fiber ring resonator

We propose a simple system of the entangled photon states generation and regeneration using a standard diode laser, a Mach Zehnder Interferometer (MZI) and a fiber optic ring resonator (FORR). Light from the diode laser is launched into an MZI and circulated in the FOOR, without any optical pumping components included in the system. The nonlinear light pulses are generated by a Kerr nonlinear effects type, while the resonance peaks are formed by the four-wave mixing of light pulses in the FORR. The entangled photons can be performed by using the polarization control device, and then detected by the avalanche photo-detectors, where the entangled photon visibility is plotted and seen. Similarly, the entangled photon states can be easily formed by using the appropriated coupling ratios into a fiber coupler, then into a ring resonator, i.e. without an MZI. The use of the entangled photons generation based on a fiber optic scheme for quantum teleportation, quantum key distribution via optical wireless link, and the system of the entangled photon states recovery by using a fiber ring resonator incorporating an erbium-doped fiber (EDF) have been investigated and discussed. The feasibility of dense coding using multi-entangled photons generation based on the fiber optic scheme and the effect of the entangled state walk-off along the optical fiber are also discussed, respectively.     

Self-similar evolution of parabolic pulses in a laser

Self-similar propagation of ultrashort, parabolic pulses in a laser resonator is observed theoretically and experimentally. This constitutes a new type of pulse shaping in mode-locked lasers: in contrast to the well-known static (solitonlike) and breathing (dispersion-managed soliton) pulse evolutions, asymptotic solutions to the nonlinear wave equation that governs pulse propagation in most of the laser cavity are observed. Stable self-similar pulses exist with energies much greater than can be tolerated in solitonlike pulse shaping, and this has implications for practical lasers.     

Formation of a high-frequency subpulse upon propagation of a femtosecond pulse in a medium with a saturable potential

On the basis of computer simulation of propagation of femtosecond light pulses in terms of the one-dimensional nonstationary nonlinear Maxwell equations with a saturable restoring force, the possibility of formation of a sequence of subpulses with different carrier frequencies is shown. The formation of frequency-modulated pulses with an asymmetric distribution of spectral components with respect to the center of a local line is demonstrated. Appearance of such pulses indicates that a hysteretic dependence of the frequency of the corresponding local line on the amplitude of an external signal can be realized.     

具有像散的克尔透镜锁模腔的研究

从非线性薛定谔方程出发,经严格计算求得了在具有像散情况下,偏振垂直于传播方向的光束在克尔介质中传输的一般特性,所用的计算方法可应用于高斯光束及克尔透镜锁模腔的研究,并能对高功率情形进行计算。研究表明,在有其他锁模启动机制下,不一定要用［ｄω／ｄｐ］ｐ＝０＜０作为克尔透镜锁模的必要条件。对于光脉冲的压缩来说,椭圆形光阑将优于圆形光阑。     

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。     

Wave processes in microinhomogeneous elastic media with hysteretic nonlinearity and relaxation

The nonlinear propagation of an initially harmonic acoustic wave in a microinhomogeneous medium containing defects with quadratic hysteretic nonlinearity and relaxation is studied by the perturbation method. The frequency dependences of the effective nonlinearity parameters are determined for the self-action of the quasi-harmonic acoustic wave and the higher harmonic generation processes.