Oscillation dependence of two-wave mixing gain for unidirectional ring resonator in photorefractive materials

Dependence of the coupling strength of two-wave mixing gain in photorefractive materials for the single unidirectional ring resonator on oscillation conditions has been analyzed in the strong nonlinear regime. In this regime, difference between the frequency of the pump beam and oscillating beam is proportional to the cavity-length detuning, which can be explained in terms of the photorefractive phase-shift. This phase-shift results due to slightly non-degenerate two-wave mixing that compensates for cavity detuning and satisfies the round-trip phase condition for the steady-state oscillation. The presence of such a phase-shift allows the possibility of the nonreciprocal steady-state energy transfer between the pump and oscillating beams. If the gain due to the beam coupling is large enough to overcome the cavity losses then the signal beam is amplified in the presence of material absorption. Such amplification is responsible for the oscillations. For the single unidirectional ring resonator, the effects of cavity-length detuning, energy coupling coefficient, crystal thickness of the material, reflectivity of the cavity mirrors and material's absorption coefficient on the frequency and intensity of oscillations have also been studied in detail. It has been found that for the smaller value of absorption coefficient (α) of the photorefractive crystal, the unidirectional ring resonator can oscillate at almost any cavity-length detuning (ΔΓ) whereas for the larger value of α oscillation occurs only when the cavity-length detuning is limited to small region (around ΔΓ=0). But reverse of the case is found for energy coupling coefficient (γ₀).     

Dependence of gain and phase-shift on crystal parameters and pump intensity in unidirectional photorefractive ring resonators

The steady-state amplification of light beam during two-wave mixing in photorefractive materials has been analysed in the strong nonlinear regime. The oscillation conditions for unidirectional ring resonator have been studied. The signal beam can be amplified in the presence of material absorption, provided the gain due to the beam coupling is large enough to overcome the cavity losses. Such amplification is responsible for the oscillations. The gain bandwidth is only a few Hz. In spite of such an extremely narrow bandwidth, unidirectional oscillation can be observed easily at any cavity length in ring resonators by using photorefractive crystals as the medium and this can be explained in terms of the photorefractive phase-shift. The presence of such a phase-shift allows the possibility of the non-reciprocal steady-state transfer of energy between the two light beams. Dependence of gain bandwidth on coupling constant, absorption coefficient of the material’s cavity length (crystal length) and modulation ratio have also been studied.      

圆孔非线性声阻抗三维时域仿真与特性分析

为研究有限振幅声波作用下圆孔的非线性声学特性,提出了基于三维时域计算流体动力学(CFD)仿真的圆孔非线性声阻抗提取方法,通过求解层流方程来模拟声信号在圆孔及上下游的传播,以及采用横向周期性边界条件来考虑高穿孔率时圆孔之间相互作用的影响。研究了不同幅值声波作用下孔径、厚度和穿孔率对声阻抗的影响规律,通过对质点振速幅值、频率和板厚等组成的无量纲参量进行非线性回归分析,得到了圆孔非线性声阻抗的拟合公式,并将其转换为可考虑多频声波影响的时域模型。最后结合声阻抗时域模型和有限差分方法计算了直通穿孔管消声器在小振幅和有限振幅声波作用下的传递损失,通过与实验测量结果的比较,验证了拟合公式的准确性和实用性。     

Modified model for four-wave mixing-based wavelength conversion in silicon micro-ring resonators

A modified model for wavelength conversion based on the four-wave mixing (FWM) in a silicon micro-ring resonator is presented. Unlike previous contributions, the nonlinear phase shifts caused by self-phase modulation and cross-phase modulation are also taken into account in the present theoretical analysis besides the linear propagation loss and the nonlinear losses caused by two-photon absorption and free-carrier absorption. Analysis shows that the nonlinear phase shifts will cause different red shifts for the pump and signal (or converted) resonant wavelengths, and consequently an additional wavelength difference between the signal transmission dip and the efficiency peak, which will increase/decrease the conversion efficiency of the signal channel far from/near the pump. The conversion efficiency and the conversion peak width of each signal channel are both affected by the micro-ring radius and coupling coefficient. A broader conversion peak width can be obtained by using a micro-ring resonator with a smaller Q factor.     

Increased heating by diagnostic ultrasound due to nonlinear propagation

The heating of tissues by the absorption of ultrasound is an important safety consideration in the use of diagnostic ultrasound. This paper shows that models of ultrasonic heating for this situation need to take account of nonlinear propagation. Measurements were made of the temperature rise in a sample of tissue-mimicking gel, caused by the application of 3.6-MHz focused ultrasonic beams for 3 min. The propagation path to the focus was in water, to mimic the situation where the fetus is scanned through the full bladder. The effect of nonlinear propagation was seen by changing the pressure amplitude of the pulse, while altering the pulsing regime to preserve a constant spatial-peak temporal-average intensity of 1 W cm-2. When nonlinear distortion was present, an enhancement in the temperature rise was observed, which correlated with the value of the shock parameter. The enhancement ratio was typically up to a factor of 3, and the maximum temperature rise observed was 2 degrees C. This enhanced heating was seen both at the surface of the tissue-mimicking gel and after propagation through 23 mm of the material. Under conditions of nonlinear propagation, the maximum heating usually occurs in the prefocal region, rather than at the focus.     

Investigation on an evanescent wave fiber-optic absorption sensor based on fiber loop cavity ring-down spectroscopy

An improved ring-down measurement principle for optical waveguides is presented. Fiber loop ring-down spectroscopy allows for measurement of minute optical losses in high-finesse fiber-optic cavities and immunity to the fluctuation of laser source. The evanescent wave absorption losses dependent on the absorption and the refractive index of ambient solution have been theoretically analyzed. The complex refractive index is introduced into our model and extinction coefficient can be calculated accurately through finite element analysis by setting the boundaries of the fiber and the ambient conditions. Using this method, the refractive index of environment can be taken into consideration. Our principle is validated by the highly-sensitive measurement of evanescent wave absorption loss. By chemically processing the surface of sensing segment along an extending ring-down cavity, the concentration of small volume Diethyl Sulphoxide solution where the etched fiber immersed into has been successfully measured and discussed.     

Propagation of fast ion-acoustic waves in multi-dimensions

By using a perturbation method, it is shown that the nonlinear fast ion-acoustic wave of a small but finite amplitude in a collisionless plasma consisting of hot and isothermal electrons and cold ions is governed by a nonlinear equation in which, in general, the coefficients of nonlinear and dispersive terms are not constant but depend on the form of the wave-front and the lowest order term contains mean curvature of the wave-front as its coefficient.     

Vibro-acoustic radiation of rigid bodies oscillating at large amplitude and low Mach number: Modelling and experiments

The acoustic radiation of vibrating bodies can usually be considered as a linear phenomenon as in most cases the vibration amplitudes of oscillating bodies are small compared to their dimension. However, in case of large amplitude and small Mach number, the large displacement amplitude of a vibrating body gives rise to geometric nonlinear acoustic effects. In this paper it is shown that the nonlinearity causes an asymmetry in the time signal of the radiated pressure as observed at a fixed position, resulting in harmonic distortion of the radiated sound field. These nonlinear effects can be analysed by the finite element method, using a linear fluid behaviour in combination with a moving mesh approach. This approach is implemented and used to predict the nonlinear sound radiation of lithographic stages oscillating at large amplitude and low Mach number. Acoustic experiments prove the validity of the analysis technique for the geometrical nonlinear phenomena. In addition the structural response of a nearby body excited by the nonlinear acoustic radiation of the stage is calculated and verified experimentally.     

Generation of a forward-traveling phase-conjugate wave in germanium

In this communication, we report the generation of a picosecond forward-traveling phase-conjugate wave at 1.06 μm in thin germanium samples by degenerate four-wave mixing. At this wavelength, the conjugate wave is produced by diffraction of the pump from an absorption grating produced by direct absorption of pump and signal pulses. We measure and discuss the transient effects caused by the finite duration of the nonlinear material response.     

Nonlinear characterization with burst excitation of 1-3 piezocomposite transducers

Ultrasonic transducers made with 1-3 connectivity piezocomposites are frequently used in Medical applications and nondestructive testing. When the transducer is used for special applications as, for instance air-coupled transmission, it is necessary to compensate for the high difference of acoustic impedance between transducer and medium using high amplitude pulses to generate high acoustic signal. Thus, the nonlinear behavior of the transducer must be taken into account in similar application conditions. The newly developed method, which performs the nonlinear characterization with burst signal excitation near the thickness resonance frequency, is based on the measure of the current as well as the vibration velocity of the piezocomposite transducer. The current of the stationary response is measured before the end of the burst signal excitation. Burst excitation enables us to measure the nonlinear characterization without producing overheating in the transducers. The amplitude level dependence of mechanical losses tandelta(m) and the stiffness increases |Deltac/c(0)| have been studied, as well as the velocity dependence of a point of the transducer, measured with a laser vibrometer. In this method, the power level applied to the transducers can be higher than other nonlinear measurement methods, providing measurements of high accuracy.     

Travelling Waves in a Chain¶of Coupled Nonlinear Oscillators

In a chain of nonlinear oscillators, linearly coupled to their nearest neighbors, all travelling waves of small amplitude are found as solutions of finite dimensional reversible dynamical systems. The coupling constant and the inverse wave speed form the parameter space. The groundstate consists of a one-parameter family of periodic waves. It is realized in a certain parameter region containing all cases of light coupling. Beyond the border of this region the complexity of wave-forms increases via a succession of bifurcations. In this paper we give an appropriate formulation of this problem, prove the basic facts about the reduction to finite dimensions, show the existence of the ground states and discuss the first bifurcation by determining a normal form for the reduced system. Finally we show the existence of nanopterons, which are localized waves with a noncancelling periodic tail at infinity whose amplitude is exponentially small in the bifurcation parameter. Received: 10 September 1999 / Accepted: 15 December 1999     

Dissipative Vortex Solitons in Defocusing Media with Spatially Inhomogeneous Nonlinear Absorption

In this paper, by solving a complex nonlinear Schr¨odinger equation, radially symmetric dissipative vortex solitons are obtained analytically and are tested numerically. We find that spatially inhomogeneous nonlinear absorption gives rise to the stability of dissipative vortex solitons in self-defocusing nonlinear medium in the presence of constant linear gain. Numerical simulation reveals the interaction effect among linear gain and nonlinear loss in the azimuthal modulation instabilities of these vortices suppression. Apart from the uniform linear gain indeed affects the stability of vortex in this media, another noticeable feature of current setup is that the steep spatial modulation of the nonlinear absorption can suppress sidelobes effectively and support stable vortex solitons in situations with uniform linear gain.Under appropriate conditions, the vortex solitons can propagate stably and feature no symmetry breaking, although the beams exhibit radical compression and amplification as they propagate.     

Shear waves in a resonator with cubic nonlinearity

Shear waves with finite amplitude in a one-dimensional resonator in the form of a layer of a rubber-like medium with a rigid plate of finite mass at the upper surface of the layer are investigated. The lower boundary of the layer oscillates according to a harmonic law with a preset acceleration. The equation of motion for particles in a resonator is determined using a model of a medium with a single relaxation time and cubical dependence of the shear modulus on deformation. The amplitude and form of shear waves in a resonator are calculated numerically by the finite difference method at shifted grids. Resonance curves are obtained at different acceleration amplitudes at the lower boundary of a layer. It is demonstrated that, as the oscillation amplitude in the resonator grows, the value of the resonance frequency increases and the shape of the resonance curve becomes asymmetrical. At sufficiently large amplitudes, a bistability region is observed. Measurements were conducted with a resonator, where a layer with the thickness of 15 mm was manufactured of a rubber-like polymer called plastisol. The shear modulus of the polymer at small deformations and the nonlinearity coefficient were determined according to the experimental dependence of mechanical stress on shear deformation. Oscillation amplitudes in the resonator attained values when the maximum shear deformations in the layer were 0.4–0.6, which provided an opportunity to observe nonlinear effects. Measured dependences of the resonance frequency on the oscillation amplitude corresponded to the calculated ones that were obtained at a smaller value of the nonlinear coefficient.     

Numerical investigation of coexisting high and low amplitude responses and safe basin erosion for a coupled linear oscillator and nonlinear absorber system

Over the last half century, numerous nonlinear variants of the tuned mass damper have been developed in order to improve attenuation characteristics. In the present study, the performance of a linear oscillator and an absorber with a strongly nonlinear cubic stiffness is evaluated by using numerical methods. This configuration has been of recent interest due to its capability of wide-band energy absorption. However, high amplitude solutions, which would amplify the response of the system, have been shown to often coexist with the low amplitude solutions. The present research is focused on numerically determining the relative strength of the coexisting solutions. Erosion profiles are presented, quantifying the integrity of the system, i.e. the likelihood of converging to a safe, low amplitude response, and providing an indication of the structural safety of a practical absorber system. The results indicate that the high amplitude solutions not only exist but significantly influence the response of the system within the range of expected operating conditions, particularly at excitation frequencies lower than the natural frequency of the linear oscillator. The erosion profiles indicate a 20–40% increase in system integrity for the case of zero damping compared to a small amount of damping, no significant integrity change when adding a small linear stiffness component to the nonlinear absorber, and no significant change in integrity between the midpoint and extreme of the bi-stable range. Additional higher-period solutions are also discovered and evidence of a chaotic response is presented.     

Effects of dust size distribution on nonlinear waves in a dusty plasma

For two-dimensional unmagnetized dusty plasmas with many different dust grain species, a Kadomtsev--Petviashvili (KP) equation, a modified KP (mKP) equation and a coupled KP(cKP) equation for small, but finite amplitude dust-acoustic solitary waves are obtained for different physical conditions respectively. The influence of an arbitrary dust size distribution described by a polynomial expressed function on the properties of dust-acoustic solitary waves is investigated numerically. How dust size distribution affects the sign and the magnitude of nonlinear coefficient A(D) of KP (mKP) equation is also discussed in detail. It is noted that whether a compressive or a rarefactive solitary wave exists depends on the dust size distribution in some dusty plasmas.     

Nonlinear model order reduction of jointed structures for dynamic analysis

Assembled structures generally show weak nonlinearity, thus it is rather commonplace to assume that their modes are both linear and uncoupled. At small to modest amplitude, the linearity assumption remains correct in terms of stiffness but, on the contrary, the dissipation in joints is strongly amplitude-dependent. Besides, the modes of any large structure may be LOCALLY collinear in the localized region of a joint. As a result the projection of the structure on normal modes is not appropriate since the corresponding generalized coordinates may be strongly coupled. Instead of using this global basis, the present paper deals with the use of a local basis to reduce the size of the problem without losing the nonlinear physics. Under an appropriate set of assumptions, the method keeps the dynamic properties of joints, even for large amplitude, which include coupling effects, nonlinear damping and softening effects. The formulation enables us to take into account FE models of any realistic geometry. It also gives a straightforward process for experimental identification. The formulation is detailed and investigated on a jointed structure.     

Anisotropic optical absorption in quantum well wires induced by high-frequency laser fields

The subband structure and optical properties of a cylindrical quantum well wire under intense non-resonant laser field are investigated by taking into account the correct dressing effect for the confinement potential. The energy levels and wave functions are calculated within the effective mass- approximation using a finite element method. It is found that the absorption coefficient and the saturation intensity are strongly affected by the laser amplitude and frequency as well as by the incident light polarization. As a key result, a large anisotropy in the linear and nonlinear optical absorptions for very intense laser field is predicted. These effects can be useful for the design of polarization sensitive devices.     

Validity of linear acoustics for prediction of waveforms caused by sonically moving laser beams

The question is raised as to whether the analysis of the generation of sound by a laser beam moving over a water surface at the sound speed c for an interminable time period requires consideration of nonlinear effects. A principal consideration in this regard is whether the linear acoustics theory predicts a pressure waveform that is bounded in the asymptotic limit when the laser irradiation time is arbitrarily large. It is shown that a bounded asymptotic limit exists when the upper boundary condition corresponds (as is more nearly appropriate) to that of a pressure release surface, but not when it corresponds to that of a rigid surface. The asymptotic solution to the appropriate inhomogeneous wave equation is given exactly for the former case, and it is shown that the highest asymptotic amplitudes, given specified laser power and beam radius a, occur in the limit of a very small light absorption coefficient mu. In this limit, the peak amplitude is independent of mu and occurs at a depth of 0.88/mu. An approximate solution for the pressure waveform at intermediate times establishes that the characteristic time for buildup to the asymptotic limit is of the order of 2.5/(c mu 2a). If this time is substantially shorter than the time that a plane-wave pulse with the asymptotic waveform would take to develop a shock wave, then accumulative nonlinear effects are of minor importance.     

Numerical analysis of ultrasonic transmission and absorption of oblique plane waves through the human skull.

Ultrasonic transmission and absorption of oblique plane waves through the human skull are analyzed numerically for frequencies ranging from 1/2 to 1 MHz. These frequencies are optimum for noninvasive ultrasound therapy of brain disorders where numerical predictions of skull transmission are used to set the phase and amplitude of source elements in the phased array focusing system. The idealized model of the skull is a three-layer solid with ivory outer and inner layers and a middle marrow layer. Each layer is modeled as a flat, homogeneous, isotropic, linear solid with effective complex wave speeds to account for focused energy losses due to material damping and scattering. The model is used to predict the amplitude and phase of the transmitted wave and volumetric absorption. Results are reported for three different skull thicknesses: 3 mm, 6 mm, and 9 mm. Thickness resonances are observed in the transmitted wave for 3 mm skulls at all frequencies and for the 6 mm skulls below 0.75 MHz. Otherwise, the transmission is dominated by the direct wave. Skull phase errors due to shear waves are shown to minimally degrade the power at the focus for angles of incidence up to 20 degrees from normal even for low material damping. The location of the peak volumetric absorption occurs either in the outer ivory or middle marrow layer and shown to vary due to wave interference.     

Nonlinear thickness dependence of two-photon absorptance in Al2O3 films

Linear and nonlinear absorptance in Al₂O₃ films of different optical thicknesses are investigated using an ArF laser calorimeter. While the linear absorptance at 193 nm shows the expected linear increase, nonlinear absorptance increases quadratically with increasing film thickness. Thus, it cannot be described by a constant nonlinear absorption coefficient β. The experimental findings are explained by a simple phenomenological approach using excited states with a finite interaction length longer than the actual film thickness. a new material constant Γ is introduced, which describes the nonlinear absorptance behavior correctly. Received: 19 May 2000 / Accepted: 22 May 2000 / Published online: 13 July 2000