Harmonic and subharmonic acoustic wave generation in finite structures

The generation of harmonic and subharmonic vibrations is considered in a finite monodimensional structure, as it is produced by the nonlinear acoustic characteristics of the medium. The equation of motion is considered, where a general function of the displacement and its derivatives acts as the forcing term for (sub)harmonic generation and a series of 'selection rules' is found, depending on the sample constrains. The localization of the nonlinear term is also considered that mimics the presence of defects or cracks in the structure, together with the spatial distribution of subharmonic modes. Experimental evidence is given relative to the power law dependence of the harmonic modes vs. the fundamental mode displacement amplitude, and subharmonic mode distribution with hysteretic effects is also reported in a cylindrical sample of piezoelectric material.     

Quantum dynamics of intracavity third-subharmonic generation

The quantum dynamics of the mean number of photons and quantum entropy of interacting modes, as well as the Wigner function of the stationary state of the fundamental mode and the third subharmonic mode has been investigated for the intracavity third-subharmonic generation. It is shown that the quantum dynamics of the system depends strongly on the nonlinear coupling coefficient between the modes. It is also demonstrated that, in the steady-state limit, depending on the intermodal coupling coefficient, the fundamental mode can be either in a pure coherent state, or in a squeezed state, or in a pure vacuum state. The third subharmonic mode in the subthreshold regime of generation of this mode is in the vacuum state. The Wigner function is squeezed over three sides of an equilateral triangle (squeezed vacuum). The quantum entropy of this state is nonzero. It is also shown that the third subharmonic mode, depending on the nonlinear coupling coefficient in the steady-state limit, can be localized in the three-component state with the same probability of detecting a field in each coherent component of the state and with the presence of quantummechanical interference between the state components. The mean number of photons in this state is smaller than unity. Depending on the nonlinear coupling coefficient, the third subharmonic mode can also be localized in the three-component state, which is a statistical mixture of three squeezed states.     

Subharmonic imaging of contrast agents

Ultrasound contrast agents promise to improve the sensitivity and specificity of diagnostic ultrasound imaging. It is of great importance to adapt ultrasound equipment for optimal use with contrast agents e.g., by exploiting the nonlinear properties of the contrast microbubbles. Harmonic imaging is one technique that has been extensively studied and is commercially available. However, harmonic imaging is associated with problems, due to second harmonic generation and accumulation within the tissue itself. Given the lack of subharmonic generation in tissue, one alternative is the creation of subharmonic images by transmitting at the fundamental frequency (fo) and receiving at the subharmonic (fo/2). Subharmonic imaging should have a much better lateral resolution and may be suitable for scanning deep-lying structures owing to the higher transmit frequency and the much smaller attenuation of scattered subharmonic signals. In this paper, we will review different aspects of subharmonic imaging including implementation, in-vitro gray-scale imaging and subharmonic aided pressure estimation.     

Quantum coherence and entangled states in intracavity third subharmonic generation process

The dynamics of correlation of photon number fluctuations of interacting modes for the process of intracavity third subharmonic generation is investigated. It is shown that the entangled field states by the variables of photon number can be obtained in this system. The quantum dynamics of the photons number, the quantum entropy and the Wigner function of the stationary states of the fundamental mode and the third subharmonic mode have also been studied. It is found that the dynamics of these quantities depends highly on the value of the coupling coefficient of the interacting modes. It is shown that at long interaction times and for the large values of the coupling coefficient of the modes, the mode of the third subharmonic is localized in the three-component state with the same probability of detection of the mode in each component of the state. The quantum entropy of the state is less than the maximal entropy of the three-component state ln3, which points out the presence of quantum mechanical interference between the components of the state of third subharmonic mode.     

Quantum dynamics of interacting modes in the process of intracavity subharmonic generation

The dynamics of correlation between fluctuations of the number of photons of interacting modes is investigated for the process of intracavity subharmonic generation. It is demonstrated that this correlation strongly depends on the nonlinear mode coupling coefficient. For small values of the coupling coefficient, the correlation between fluctuations of the number of photons is small. With an increase in the coupling coefficient, the correlation increases (the state of subsystems becomes entangled) and, starting from a particular value of the coupling coefficient, starts to decrease with further increase in the coupling coefficient, gradually approaching zero (entanglement of subsystem states decreases). The quantum dynamics of the number of photons, quantum entropy, and Wigner function of the stationary state of the fundamental and subharmonic modes is investigated. It is demonstrated that the dynamics of these quantities also strongly depends on the coupling coefficient of the interacting modes. We show that, for large values of the mode coupling coefficient and long interaction times, the subharmonic mode becomes localized in a two-component state with equal probabilities of finding it in each component. Quantum entropy of this state is smaller than maximum entropy of the two-component state equal to ln2, which suggests that quantum-mechanical interference takes place between the subharmonic mode components.     

Soliton excitation in the pass band of the transmission line based on modulation

We numerically investigate the excitation of soliton waves in the nonlinear electrical transmission line formed by many cells. When the periodic driving voltage with frequency in the pass band closing to the cutoff frequency is applied to the endpoint of the whole line, the soliton wave can be generated. The numerical results show that the soliton wave generation mainly depends on the self modulation associated with the nonlinear effect. In this study, the lower subharmonic component is also observed in the frequency spectrum. To further understand this phenomenon, we study the dependence of the subharmonic power spectrum and frequency on the forcing amplitude and frequency numerically, and find that the subharmonic frequency increases with the gradual growth of the driving amplitude.     

Experimental studies of nonlinear phenomena in ferromagnetic metals

In this paper we report the first observation of microwave subharmonic generation in ferromagnetic metals. The nonlinear phenomena described here might be of use in determining the temperature dependence of the exchange parameters of metals and alloys.     

基于次谐波调制光注入半导体激光器获取窄线宽微波信号的实验研究

实验研究了处于单周期振荡的光注入半导体激光器在频率等于单周期振荡频率一半的1/2次谐波调制下所产生的微波信号的特性.实验结果显示:在合适的注入条件下,处于单周期(P1)振荡的光注入半导体激光器可输出频率可达26.5 GHz、光谱具有单边带结构的光生微波信号,但微波信号的线宽比较宽(MHz量级);通过采用频率为单周期振荡频率一半的次谐波信号调制光注入半导体激光器,可将微波线宽从十几MHz压缩到几十k Hz.进一步分析了次谐波调制信号的功率以及频率对微波信号的相位噪声的影响,并在由次谐波调制信号的功率和频率构成的参数空间绘制出了能实现次谐波频率锁定的分布区域.     

Evaluation of correlation between chemical dosimetry and subharmonic spectrum analysis to examine the acoustic cavitation

Currently several therapeutic applications of ultrasound in cancer treatment are under progress which uses cavitation phenomena to deliver their effects. There are several methods to evaluate cavitation activity such as chemical dosimetry and measurement of subharmonic signals. In this study, the cavitation activity induced by the ultrasound irradiation on exposure parameters has been measured by terephthalic acid chemical dosimetry and subharmonic analysis. Experiments were performed in the near 1 MHz fields in the progressive wave mode and effect of duty cycles changes with 2 W/cm² intensity (I_SATA) and acoustic intensity changes in continuous mode on both fluorescence intensity and subharmonic intensity were measured. The dependence between fluorescence intensity of terephthalic acid chemical dosimetry and subharmonic intensity analysis were analyzed by Pearson correlation (p-value < 0.05). It has been shown that the subharmonic intensity and the fluorescence intensity for continuous mode is higher than for pulsing mode (p-value < 0.05). Also results show that there is a significant difference between the subharmonic intensity and the fluorescence intensity with sonication intensity (p-value < 0.05). A significant correlation between the fluorescence intensity and subharmonic intensity at different duty cycles (R = 0.997, p-value < 0.05) and different intensities (R = 0.985, p-value < 0.05) were shown. The subharmonic intensity (μW/cm²) significantly correlated with the fluorescence intensity (count) (R = 0.901; p < 0.05) and the fluorescence intensity due to chemical dosimetry could be estimated with subharmonic intensity due to subharmonic spectrum analysis. It is concluded that there is dependence between terephthalic acid chemical dosimetry and subharmonic spectrum analysis to examine the acoustic cavitation activity.     

Nonlinear properties of the lattice network-based nonlinear CRLH transmission lines

The nonlinear properties of lattice network-based(LNB) composite right-/left-handed transmission lines(CRLH TLs)with nonlinear capacitors are experimentally investigated.Harmonic generation,subharmonic generation,and parametric excitation are clearly observed in an unbalanced LNB CRLH TL separately.While the balanced design of the novel nonlinear TL shows that the subharmonic generation and parametric processes can be suppressed,and almost the same power level of the higher harmonics can be achieved over a wide bandwidth range,which are difficult to find in conventional CRLH TLs.     

Subharmonic behavior of phospholipid-coated ultrasound contrast agent microbubbles

Coated microbubbles, unlike tissue are able to scatter sound subharmonically. Therefore, the subharmonic behavior of coated microbubbles can be used to enhance the contrast in ultrasound contrast imaging. Theoretically, a threshold amplitude of the driving pressure can be calculated above which subharmonic oscillations of microbubbles are initiated. Interestingly, earlier experimental studies on coated microbubbles demonstrated that the threshold for these bubbles is much lower than predicted by the traditional linear viscoelastic shell models. This paper presents an experimental study on the subharmonic behavior of differently sized individual phospholipid coated microbubbles. The radial subharmonic response of the microbubbles was recorded with the Brandaris ultra high-speed camera as a function of both the amplitude and the frequency of the driving pulse. Threshold pressures for subharmonic generation as low as 5 kPa were found near a driving frequency equal to twice the resonance frequency of the bubble. An explanation for this low threshold pressure is provided by the shell buckling model proposed by Marmottant et al. [J. Acoust. Soc. Am. 118, 3499-3505 (2005)]. It is shown that the change in the elasticity of the bubble shell as a function of bubble radius as proposed in this model, enhances the subharmonic behavior of the microbubbles.     

Enhanced second-harmonic generation from resonant GaAs gratings

We theoretically study second harmonic generation in nonlinear, GaAs gratings. We find large enhancement of conversion efficiency when the pump field excites the guided mode resonances of the grating. Under these circumstances the spectrum near the pump wavelength displays sharp resonances characterized by dramatic enhancements of local fields and favorable conditions for second-harmonic generation, even in regimes of strong linear absorption at the harmonic wavelength. In particular, in a GaAs grating pumped at 1064?nm, we predict second-harmonic conversion efficiencies approximately 5 orders of magnitude larger than conversion rates achievable in either bulk or etalon structures of the same material.     

The viscoelasticity of lipid shell and the hysteresis of subharmonic in liquid containing microbubbles

The viscoelasticity and subharmonic generation of a kind of lipid ultrasound contrast agent are investigated. Based on the measurement of the sound attenuation spectrum, the viscoelasticity of the lipid shell is estimated by use of an optimization method. Shear modulus G_S=10MPa and shear viscosity \mu _S=1.49N\cdotS/m² are obtained. The nonlinear oscillation of the encapsulated microbubble is studied with Church's model theoretically and experimentally. Especially, the dependence of subharmonic on the incident acoustic pressure is studied. The results reveal that the development of the subharmonic undergoes three stages, i.e. occurrence, growth and saturation, and that hysteresis appears in descending ramp insonation.     

Single quantum path control by a fundamental chirped pulse combined with a subharmonic control pulse

In this paper, we study the issue of single quantum path control and its role in attosecond pulse generation. By carrying out the time-dependent Schrödinger equation analysis for the harmonic emission from a single He atom irradiated by the two-color laser field, consisting of a short 800 fundamental chirped pulse and a subharmonic 800–2400 nm control pulse, we find that the most favorable condition for attosecond generation is at the fundamental chirp parameter β = 4.55 together with the zero-phase 2000 nm control pulse, in which the single quantum path (short quantum path) is selected to contribute to the harmonic spectrum exhibiting an ultrabroad supercontinuum of a 337 eV bandwidth. Finally, an isolated attosecond pulse as short as 39 as is thus generated directly.     

Nonclassical light generation in quasi-phase-matched parametric self-frequency conversion

We present a quantum theory of the parametric self-conversion of the laser radiation frequency in active nonlinear crystals with a regular domain structure. Such crystals feature simultaneous lasing and quasi-phase-matched parametric conversion of the laser radiation frequency. These processes are described using the Heisenberg-Langevin equations in two regimes of the subharmonic generation: super-and subthreshold. The spectral properties of the quadrature components of the laser frequency and its subharmonic and the photon statistics have been studied as dependent on the pump power, crystal length, and reflectance of the laser cavity output mirror. Using the obtained analytical expressions, these characteristics are calculated for a active nonlinear Nd:Mg:LiNbO₃ crystal with a regular domain structure. In the subthreshold regime, the maximum decrease in the spectral density of fluctuations in the subharmonic quadrature component relative to the standard quantum limit may reach 90%; in the above-threshold regime, these fluctuations are virtually not suppressed. A decrease in the spectral density of fluctuations of the laser frequency quadrature does not exceed 10%. In the subthreshold excitation regime, the subharmonic photons obey a super-Poisson statistics; in the above-threshold regime, the photon statistics is Poisson-like.     

Numerical Analysis of Weakly Relativistic Large Orbit Gyrotron with Permanent Magnet System

High-harmonic gyro-devices with axis-encircling electron beams known as large orbit gyrotrons (LOG) represent an appealing alternative to the conventional gyrotrons. In this paper we investigate the feasibility of such device operating with low current and low energy electron beams formed by a novel electron gun with a permanent magnet system. The results from the numerical experiments indicate the possibility to excite TE₄₁ mode at fourth harmonic of the cyclotron frequency. Simulations predict generation of microwave radiation with frequency 104 GHz and output power near 1 kW.     

Electric convection in a nematic liquid crystal in a varying electric field

The emergence of electric convection in a nematic liquid crystal under the action of a varying electric field is analyzed in the 1D approximation. A new mode of external field variation with subharmonic oscillations is proposed. The behavior of several classes of synchronous perturbations and subharmonic oscillations is analyzed; the evolution of the fields of the director and of the volume charge is studied. Parametric instability regions are specified and the critical frequencies of transitions between response modes are determined. Stability maps for a nematic liquid crystal are plotted on the frequency-amplitude plane.     

Optical vortex solitons in parametric wave mixing

We analyze two-component spatial optical vortex solitons supported by parametric wave mixing processes in a nonlinear bulk medium. We study two distinct cases of such localized waves, namely, parametric vortex solitons due to phase-matched second-harmonic generation in an optical medium with competing quadratic and cubic nonlinear response, and vortex solitons in the presence of third-harmonic generation in a cubic medium. We find, analytically and numerically, the structure of two-component vortex solitons, and also investigate modulational instability of their plane-wave background. In particular, we predict and analyze in detail novel types of vortex solitons, a "halo-vortex," consisting of a two-component vortex core surrounded by a bright ring of its harmonic field, and a "ring-vortex" soliton which is a vortex in a harmonic field that guides a ring-like localized mode of the fundamental-frequency field.     

Excitation threshold for subharmonic generation from contrast microbubbles

Six models of contrast microbubbles are investigated to determine the excitation threshold for subharmonic generation. The models are applied to a commercial contrast agent; its characteristic parameters according to each model are determined using experimentally measured ultrasound attenuation. In contrast to the classical perturbative result, the minimum threshold for subharmonic generation is not always predicted at excitation with twice the resonance frequency; instead it occurs over a range of frequencies from resonance to twice the resonance frequency. The quantitative variation of the threshold with frequency depends on the model and the bubble radius. All models are transformed into a common interfacial rheological form, where the encapsulation is represented by two radius dependent surface properties-effective surface tension and surface dilatational viscosity. Variation of the effective surface tension with radius, specifically having an upper limit (resulting from strain softening or rupture of the encapsulation during expansion), plays a critical role. Without the upper limit, the predicted threshold is extremely large, especially near the resonance frequency. Having a lower limit on surface tension (e.g., zero surface tension in the buckled state) increases the threshold value at twice the resonance frequency, in some cases shifting the minimum threshold toward resonance.