Faraday patterns in bose-Einstein condensates

Temporal periodic modulation of the interatomic s-wave scattering length in Bose-Einstein condensates is shown to excite subharmonic patterns in the atom density through a parametric resonance. The dominant wavelength of the spatial structures is primarily selected by the excitation frequency but also affected by the depth of the spatial modulation via a nonlinear resonance. These phenomena represent analogues of the Faraday patterns excited in vertically vibrated liquids.     

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.     

Effect of current modulation depth on the response of single-mode quantum-well heterolasers in the region of 1.5 μm

Numerical simulations are used to study the effect of pump current modulation depth on the response of quantum-well GaInAs–GaInAsP heterolasers at different lasing frequencies within the gain band as a function of the excess above threshold. It is shown that the amplitude-frequency characteristics of these laser emitters generally contain two local maxima. The low frequency maximum usually corresponds to a resonance for the 1/2 subharmonic and the high frequency maximum, to the fundamental. As the modulation depth is increased, the fundamental frequency decreases, while the resonance frequency for the 1/2 subharmonic can change monotonically or not. The behavior found here can be used to develop quantum-well heterolasers with specified modulation parameters.     

Superlattice, rhombus, square, and hexagonal standing waves in magnetically driven ferrofluid surface

Standing wave patterns that arise on the surface of ferrofluids by (single frequency) parametric forcing with an ac magnetic field are investigated experimentally. Depending on the frequency and amplitude of the forcing, the system exhibits various patterns including a superlattice and subharmonic rhombuses as well as conventional harmonic hexagons and subharmonic squares. The superlattice arises in a bicritical situation where harmonic and subharmonic modes collide. The rhombic pattern arises due to the nonmonotonic dispersion relation of a ferrofluid.     

Perception of Pitch and Roughness in Vocal Signals with Subharmonics

Pitch and roughness were rated according to the extent of amplitude modulation (AM) and frequency modulation (FM) of a subharmonic [fundamental frequency (F0)/2]. The objective was to determine the identification boundaries for pitch and roughness and to discover how both kinds of modulation affect these boundaries. Another objective was to judge the reliability between subjects when identifying subharmonic-related pitch and roughness. Three procedures were used: ABX comparisons, method of adjustment, and rating of roughness. Results indicated that the crossover point to the lower pitch (associated with the subharmonic) occurred between 10% and 30% modulation, depending on modulation type and F0. Subjects demonstrated highly variable perceptions of pitch and roughness, with poor intersubject reliability.     

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.     

Marangoni instability of a liquid layer with insoluble surfactant under heat flux modulation

We investigate the parametric excitation of Marangoni convection by a periodic flux modulation in a liquid layer with insoluble surfactant absorbed on the nondeformable free surface. The stability analysis of the convective system is performed for arbitrary wave numbers of the disturbances. An interesting feature of the onset of convection is the existence of bifurcating neutral curves with double minima, one of which corresponds to a quasi-periodic solution, and the other one corresponds to a subharmonic solution. The evolution of the subharmonic instability region depending on the amplitude of the external heat flux modulation and the frequency of the modulation is studied. The quasi-periodic neutral curve is close to the oscillatory neutral curve of the nonmodulated problem.     

Fundamental study on subharmonic imaging by irradiation of amplitude-modulated ultrasound waves

The second harmonic and subharmonic components, the frequencies of which are twice and one half the fundamental frequency, are included in echoes from contrast agents. An imaging method, which employs a second harmonic (second harmonic imaging), is widely used in medical diagnoses. On the other hand, subharmonic is expected to provide a higher contrast between biological tissues and blood flow because echo signals are generated only from blood containing the contrast agents. However, the subharmonic component echo signal power from contrast agents is relatively low. This has resulted in little progress in the field of subharmonic imaging. In this study, a new imaging method is proposed using amplitude-modulated waves as transmitted waves combined with the pulse inversion method to enhance subharmonic echo signals. Two optimal frequencies are set, including the modulated waves, F(1) and F(2), so that the subharmonic frequency of F(1) and the second harmonic frequency of F(2) may result in the same value. This allows a more powerful signal at the frequency band because the second harmonic and subharmonic components are integrated. Furthermore, a B-mode ultrasound image of an agar phantom that imitated biological tissue and showed the effectiveness of our method was reconstructed. As a result, the echo power of the subharmonic component was enhanced by approximately 11.8 dB more than the conventional method and the signal to noise ratio showed an improvement of 7.6 dB.     

Rayleigh-Benard convection in a vertically oscillated fluid layer

We report on the first quantitative observations of convection in a fluid layer driven by both heating from below and vertical sinusoidal oscillation. Just above onset, convection patterns are modulated either harmonically or subharmonically to the drive frequency. Single-frequency patterns exhibit nearly solid-body rotations with harmonic and subharmonic states always rotating in opposite directions. Flows with both harmonic and subharmonic responses are found near a codimension-two point, yielding novel coexisting patterns with symmetries not found in either single-frequency states. Predictions from linear stability analysis of the onset Rayleigh and wave numbers compare well with experiment, and phase boundaries for coexisting patterns track single-frequency marginal stability curves.     

Degenerate parametric frequency conversion of phase-modulated femtosecond laser pulses in crystals with a regular and chirped domain structure

A systematic theoretical analysis of the degenerate parametric frequency conversion in a LiNbO₃ crystal with a regular domain structure and a linearly varying domain thickness (chirped crystal) is presented for the pulses of a titanium-sapphire laser with a wavelength of 0.8 μm and durations of 100 and 50 fs in the presence and in the absence of phase modulation. The results are obtained with regard to the difference in the group velocities of interacting pulses and the group velocity dispersion. For an effective frequency conversion of the phase-modulated (PM) pump pulse, it is expedient to employ chirped crystals in which the domain thickness decreases from the entrance to the exit of the crystal. The pump energy is effectively converted into subharmonic energy when the pump carrier frequency decreases with time. It is demonstrated that the efficiency of the energy conversion to a subharmonic of 80% can be realized for PM pumping with a pulse duration of 100 fs in the chirped LiNbO₃ crystal. The efficiency of the parametric frequency conversion depends on the pump intensity as well as on the phase modulation of the pulse and the chirp of the crystal. Note that a variation in one of these parameters causes variations in the remaining parameters needed for the maximum efficiency of the parametric frequency conversion.     

Linear and nonlinear resonance features of an erbium-doped fibre ring laser under cavity-loss modulation

The continuous-wave output of a single-mode erbium-doped fibre ring laser when subjected to cavity-loss modulation is found to exhibit linear as well as nonlinear resonances. At sufficiently low driving amplitude, the system resembles a linear damped oscillator. At higher amplitudes, the dynamical study of these resonances shows that the behaviour of the system exhibits features of a nonlinear damped oscillator under harmonic modulation. These nonlinear dynamical features, including harmonic and subharmonic resonances, have been studied experimentally and analysed with the help of a simple time-domain and frequency-domain information obtained from the output of the laser. All the studies are restricted to the modulation frequency lying in a regime near the relaxation oscillation frequency.     

Convection and Diffusion in Patterns in Oscillated Granular Media

Motions of individual particles within the stripe and square patterns formed in oscillated granular media are studied using numerical simulations. Our event-driven molecular dynamics simulations yield standing wave patterns in good accord with those observed in experiments at the same frequency and acceleration amplitude. The patterns are subharmonic and so return to their initial macroscopic state after two external cycles. However, simulations reveal that individual particles do not return to their initial position. In addition to diffusive motion, an organized flow of particles within the patterns is found; associated with each peak and each valley of the pattern is a pair of counterrotating convection rolls. The diffusion is anisotropic: transport perpendicular to stripes is enhanced over that parallel to stripes. This enhancement is computed as a function of the layer depth, acceleration amplitude, frequency, and coefficient of restitution of the particles, and is attributed to the effect of the advective motion. Velocity distributions, granular temperature, and the dependence of the diffusion coefficient parallel to the stripes on the average granular temperature are studied.     

Modeling subharmonic response from contrast microbubbles as a function of ambient static pressure

Variation of subharmonic response from contrast microbubbles with ambient pressure is numerically investigated for non-invasive monitoring of organ-level blood pressure. Previously, several contrast microbubbles both in vitro and in vivo registered approximately linear (5-15 dB) subharmonic response reduction with 188 mm Hg change in ambient pressure. In contrast, simulated subharmonic response from a single microbubble is seen here to either increase or decrease with ambient pressure. This is shown using the code BUBBLESIM for encapsulated microbubbles, and then the underlying dynamics is investigated using a free bubble model. The ratio of the excitation frequency to the natural frequency of the bubble is the determining parameter--increasing ambient pressure increases natural frequency thereby changing this ratio. For frequency ratio below a lower critical value, increasing ambient pressure monotonically decreases subharmonic response. Above an upper critical value of the same ratio, increasing ambient pressure increases subharmonic response; in between, the subharmonic variation is non-monotonic. The precise values of frequency ratio for these three different trends depend on bubble radius and excitation amplitude. The modeled increase or decrease of subharmonic with ambient pressure, when one happens, is approximately linear only for certain range of excitation levels. Possible reasons for discrepancies between model and previous experiments are discussed.     

Modulation response of dynamic single-mode quantum-well heterolasers in the 1.5 μm range

Numerical modelling is used to study the effect of tuning the laser output over the gain bandwidth on the modulation response of GaInAs–GaInAsP quantum-well heterolasers for different modulation frequencies of the pump current. It is found that the maximum frequency bandwidth of the response band and the greatest feasibility of high speed modulation for transmission of signals in information systems are achieved in the center of the gain band. Raising the dc component of the pump current increases the response bandwidth. For typical parameters of this system (near 1.5 μm) the maximum response bandwidth can approach ≈40 GHz. For certain parameters, the amplitude-frequency characteristics of the heterolasers have two local maxima: one at low frequency corresponding usually to a resonance for the 1/2 subharmonic and one at high frequency, for the fundamental resonance.     

Chaotic motion in an oscillatory boundary layer

The chaotic time oscillations in an incompressible fluid driven into motion by a harmonic time-varying pressure gradient is examined. Special attention is given to centrifugal destabilization of the viscous boundary layer. The basic flow is shown to be linearly unstable. For increasing modulation amplitude, the flow exhibits chaotic oscillations. The energy exchange between subharmonics and superharmonics of the least-stable spanwise wave number is considered. The presence of subharmonic Fourier modes are shown to accelerate the transition to temporally chaotic motion. (c) 1996 American Institute of Physics.     

Stripe patterns in degenerate optical parametric oscillators

We experimentally demonstrate the stripe (or roll) patterns in a broad-aperture degenerate optical parametric oscillator in a plane-mirror minicavity. The stabilization of stripes is achieved by seed injection at a subharmonic frequency. We measure the temporal spectra of the stripe pattern and obtain the 1/f-like noise spectra.     

Performance Evaluation of Subharmonic-to-Harmonic Ratio (SHR) Computation

Subharmonics are an important class of voice signals, relevant for speech, pathological voice, singing, and animal bioacoustics. They arise from special cases of amplitude (AM) or frequency modulation (FM) of the time-domain signal. Surprisingly, to date there is only one open source subharmonics detector available to the scientific community: Sun’s subharmonic-to-harmonic ratio (SHR). Here, this algorithm was subjected to a formal evaluation with two data sets of synthesized and empirical speech samples. Both data sets consisted of electroglottographic (EGG) signals, ie, a physiological correlate of vocal fold oscillation that bypasses vocal tract acoustics. Data Set I contained 2560 synthesized EGG signals with varying degrees of AM and FM, fundamental frequency (fo), periodicity, and signal-to-noise ratio (SNR). Data Set II was made up of 25 EGG samples extracted from the CMU Arctic speech data base. For a “ground truth” of subharmonicity, these samples were manually annotated by a group of five external experts. Analysis of the synthesized data suggested that the SHR metric is relatively robust as long as the subharmonic modulation extent is below 0.35 and 0.7 for the FM and AM scenarios, respectively. In the CMU Arctic speech data samples, the SHR analysis reached a maximum sensitivity of about 87% at a specificity of over 90%, but only for adaptive algorithm parameter settings. In contrast, the algorithm’s default parameter settings could only successfully classify about 9% of all subharmonic instances. The SHR is a useful metric for assessing the degree of subharmonics contained in voice signals, but only at adaptive parameter settings. In particular, the frequency ceiling should be set to five times the highest fo, and the frame length to at least five times the largest fundamental period of the analyzed signal. For subharmonic classification a threshold of SHR  ≥  0.01 is recommended.     

Ion acoustic subharmonic excitation in a plasma

Ion acoustic subharmonic excitation in a plasma, with ion-neutral collision frequency greater than the frequency of excitation, is theoretically investigated. Two-fluid theory with source term is used to describe the system. The system exhibits either subharmonic excitation of orders 1/2 and 1/3, or subharmonic excitation of orders 1/3, 1/4 and 1/5. The resonance frequency range and the amplitude of second harmonic for each case is calculated. A comparison with experimental data can be used to obtain the values of the parameters describing the source term.     

Nonlinear dynamics of convection patterns in a binary mixture subjected to finite-frequency vibration

Nonlinear evolution of two-dimensional convection patterns is considered for an incompressible binary mixture with negative Soret coupling in a horizontal layer subjected to finite-frequency vertical vibration of arbitrary amplitude. A numerical analysis is performed under impermeability conditions on rigid boundaries, which can be implemented in a laboratory experiment. The dependence of flow intensity on vibration amplitude is examined for the first and second resonance regions in the parameter space of thermal vibrational convection. The numerical results agree with the stability boundaries of equilibrium states predicted by linear theory. A qualitative difference in the dynamics of nonlinear oscillation is exposed between the regions corresponding to critical perturbations at the subharmonic and fundamental frequencies. Regular and chaotic dynamics, as well as hysteretic transitions between the fundamental and subharmonic modes, are revealed.     

Rogue waves in a multistable system

Clear evidence of rogue waves in a multistable system is revealed by experiments with an erbium-doped fiber laser driven by harmonic pump modulation. The mechanism for the rogue wave formation lies in the interplay of stochastic processes with multistable deterministic dynamics. Low-frequency noise applied to a diode pump current induces rare jumps to coexisting subharmonic states with high-amplitude pulses perceived as rogue waves. The probability of these events depends on the noise filtered frequency and grows up when the noise amplitude increases. The probability distribution of spike amplitudes confirms the rogue wave character of the observed phenomenon. The results of numerical simulations are in good agreement with experiments.