Cooperative dynamics of a coupled-oscillator system and the forced free shear layer

A phenomenological model of nonlinear mode competition between instability waves in the forced free shear layer is proposed. The model comprises mutually interacting nonlinear oscillators with distribution in intrinsic frequencies and exhibits “locking-on” behaviour, suppression of broadband fluctuations under forcing and induced subharmonic oscillations.     

High-order subharmonic parametric resonance of nonlinearly coupled micromechanical oscillators

This paper studies parametric resonance of coupled micromechanical oscillators under periodically varying nonlinear coupling forces. Different from most of previous related works in which the periodically varying coupling forces between adjacent oscillators are linearized, our work focuses on new physical phenomena caused by the periodically varying nonlinear coupling. Harmonic balance method (HBM) combined with Newton iteration method is employed to find steady-state periodic solutions. Similar to linearly coupled oscillators studied previously, the present model predicts superharmonic parametric resonance and the lower-order subharmonic parametric resonance. On the other hand, the present analysis shows that periodically varying nonlinear coupling considered in the present model does lead to the appearance of high-order subharmonic parametric resonance when the external excitation frequency is a multiple or nearly a multiple (≥3) of one of the natural frequencies of the oscillator system. This remarkable new phenomenon does not appear in the linearly coupled micromechanical oscillators studied previously, and makes the range of exciting resonance frequencies expanded to infinity. In addition, the effect of a linear damping on parametric resonance is studied in detail, and the conditions for the occurrence of the high-order subharmonics with a linear damping are discussed.     

Investigations on optically controlled millimeter wave Gunn oscillators

There is a growing interest in optically controlled millimeter wave oscillators. In this paper, we have investigated the external-circuit impedances of an optically controlled millimeter wave subharmonic Gunn diode oscillator, which is illuminated by GaAs/GaAlAs laser beam. The variation of the external-circuit impedances looking outward from the Gunn diode with respect to the optical injection plasma density are calculated based on a field analysis method. The results give some useful conclusions for optically controlled millimeter wave Gunn diode oscillator design. Experimentally an optical tuning frequency shift of 7MHz is achieved at W-band.     

An oscillator using high order Lamb wave modes

An oscillator using high order Lamb wave modes is presented. Due to the multimode property of Lamb waves, high frequency oscillators using high order mode Lamb waves can be fabricated. To select the operating mode of the Lamb wave oscillator, a high order mode selector is inserted into the feedback loop. An oscillator using the 13th antisymmetric mode (a₁₃) in Lamb wave is achieved in experiments and the oscillating frequency is 5.30 times higher than that of the a₀ mode excited by the interdigital transducer.     

Dynamical signatures of self-phase-locking in a triply resonant optical parametric oscillator

We report on specific signatures of self-phase-locking in a cw frequency divide-by-three optical parametric oscillator subject to two competing chi(2) nonlinear processes that couple the signal and idler subharmonic waves. The self-phase-locked pair appears as a broad fringe dip within the mode-pair cluster. We have also observed Hopf instabilities of the zero-detuning case at approximately 4 x the pump threshold. These results open the path to experimental investigation of quantum entanglement and phase-locked transverse mode structures in this novel class of parametric oscillators.     

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.     

Solid-state traveling-wave amplifiers and oscillators in the THz range: effect of electron collisions

Due to their high plasma frequencies, drifting semiconductor plasmas interacting with slow electromagnetic waves hold promise for terahertz amplifiers and oscillators. In these devices, the gain and the type of instabilities are influenced by electron collisions. To study the effect of collisions, we developed a two-wave model describing the interaction between drifting solid-state plasmas and electromagnetic waves. This paper analyzes the two-wave dispersion relation for representative examples. As the examples show, convective and absolute instabilities can occur at high and low collision frequencies depending on the relationship between the collision frequency and the coupling coefficient. Surprisingly, an absolute instability occurs when collision-dominated plasmas interact with backward waves. The model can be used to determine the potential of a particular configuration in a solid-state amplifier or oscillator.     

Approach to the quantum evolution for underdamped, critically damped, and overdamped driven harmonic oscillators using unitary transformation

Exact solution of the Schrödinger equation is derived for underdamped, critically damped, and overdamped harmonic oscillators with a driving force. A unitary operator transforming Hamiltonian into a simple form is introduced. The transformed Hamiltonian, represented in terms of a modified frequency ω, is identical with the Hamiltonian of the standard harmonic oscillator for the underdamped oscillator, with the Hamiltonian of a free particle for the critically damped oscillator, and with the Hamiltonian of a system with a harmonic parabolic potential for the overdamped oscillator. The eigenvalues of underdamped oscillator are discrete while those of the critically damped and the overdamped oscillators are continuous.     

Stimulated Cherenkov radiation of a relativistic electron beam moving over a periodically corrugated surface (quasi-optical theory)

The propagation of waves over periodically corrugated surfaces and their excitation by relativistic electron beams are investigated within the framework of a quasi-optical approach. The dispersion equation is derived for normal waves under the assumption of a small (in the scale of the period and wavelength) corrugation depth, based on which two limiting cases are identified. In the first limiting case, the wave frequency is far from the Bragg resonance, and the propagation of waves can be described in terms of the impedance approximation, in which the fundamental spatial harmonic slows down. In the second limiting case realized at frequencies close to the Bragg resonance, the field is represented as two counterpropagating quasi-optical wave beams coupled on a corrugated surface and forming a normal surface wave. When interacting with an electron beam, convective instability, which can be used to realize amplifier regimes, corresponds to the first case, and absolute one, which is applied in surface-wave oscillators, corresponds to the second case. The developed theory is used to determine basic characteristics of amplifier and oscillator schemes: the growth rates, the energy exchange efficiency, and the formation of a self-consistent spatial structure of the radiated field. The practical realization of relativistic submillimeter amplifiers and surface-wave oscillators is shown to hold promise.     

Displaced phase-amplitude variables for waves on finite background

Wave amplification in nonlinear dispersive wave equations may be caused by nonlinear focussing of waves from a certain background. In the model of nonlinear Schrödinger equation we will introduce a transformation to displaced phase-amplitude variables with respect to a background of monochromatic waves. The potential energy in the Hamiltonian then depends essentially on the phase. Looking as a special case to phases that are time independent, the oscillator equation for the signal at each position becomes autonomous, with the change of phase with position as only driving force for a spatial evolution towards extreme waves. This is observed to be the governing process of wave amplification in classes of already known solutions of NLS, namely the Akhmediev-, Ma- and Peregrine-solitons. We investigate the case of the soliton on finite background in detail in this Letter as the solution that descibes the complete spatial evolution of modulational instability from background to extreme waves.     

Two regimes of the parametrically self-exciting ultrasonic standing waves

This paper discusses a nonlinear multi-wave mechanism for the parametrically self-exciting standing waves in a plane-parallel liquid layer driven at one end of the layer. The dependence of this process on the number of parametrically self-exciting waves and the frequency detuning between the frequency "f" of the pump wave and the nearest natural frequency are analyzed. It is found that two regimes with different thresholds are possible. One of them is characterized by self-exciting subharmonic frequencies close to f/2 and the second has a much lower threshold and the presence of a self-exciting subharmonic at a frequency near to the smallest natural frequency. Three dimensionless parameters determining each regime are introduced.     

Multiple conversion and optical limiting in a subharmonic-pumped parametric oscillator

We demonstrate that multiple coexisting frequency-conversion processes can occur in an externally resonant second-harmonic generator under suitable conditions. Besides the generation of signal and idler waves by subharmonic-pumped parametric oscillation, sum-frequency mixing among the resonant subharmonic (1064-nm), signal, and idler waves was observed, leading to additional emission wavelengths around the harmonic wavelength (532 nm). The output waves both exhibit high frequency stability, with as long as 4 h of mode-hop-free parametric oscillation, and are continuously tunable over 2 GHz. Near degeneracy the parametric oscillator operates as an optical limiter for the harmonic wave.     

Travelling waves in chains of pulse-coupled integrate-and-fire oscillators with distributed delays

We analyse travelling waves in a chain of pulse-coupled integrate-and-fire oscillators with nearest-neighbour coupling and delayed interactions. This is achieved by approximating the equations for phase-locking in terms of a singularly perturbed two-point (continuum) boundary value problem. The latter has a solution provided that a self-consistent value for the collective frequency of oscillations can be found. We investigate how the qualitative behaviour of travelling waves depends on the distribution of natural frequencies across the chain and the form of delayed interactions. A linear stability analysis of phase-locked solutions is carried out in terms of perturbations of the firing times of the oscillators. It is shown how travelling waves destabilize when the detuning between oscillators or the strength of the coupling becomes too large.     

Experimental study on subharmonic and ultraharmonic acoustic waves in water-saturated sandy sediment

Experimental observations of the subharmonic and ultraharmonic acoustic waves in water-saturated sandy sediment are reported in this paper. Acoustic pressures of both nonlinear acoustic waves strongly depend on the driving acoustic pressure at a transducer. The first ultraharmonic wave reaches a saturation value as the driving acoustic pressure increases. The acoustic pressure levels of both nonlinear acoustic waves exhibit some fluctuations in comparison with that of the primary acoustic wave as the receiving distance of hydrophone increases in sediment. The subharmonic and the ultraharmonic phenomena in this study show close resemblance to those produced in bubbly water.     

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.     

Amplitude modulation and demodulation of an electromagnetic wave in magnetised acousto-optic diffusive semiconductor plasmas: Hot carrier effects

In communication processes, amplitude modulation is very helpful to save power using a single band transmission. Using the hydrodynamical model of semiconductor plasma analytical investigations are made for the amplitude modulation as well as demodulation of an electromagnetic wave incorporating carrier heating (CH) effects in acousto-optic magnetised semiconductor plasma. The CH effects add new dimensions in the present analysis. Analysis are made under different wave number regions over a wide range of cyclotron frequencies. It is found that incorporation of CH effects modifies the amplitude modulation and demodulation processes effectively. Numerical estimations are made for III–V semiconductor crystal irradiated by pump wave of frequency 1.6×10¹³ s^?1. Complete absorption of the waves takes place in all the possible wavelength regimes when the cyclotron frequency ω_c becomes nearly equal to ω₀, the pump frequency on neglecting the collision term in modulation/ demodulation indices.     

Resonant nonlinear interactions between atmospheric waves in the polar summer mesopause region

Data obtained from the mobile SOUSY VHF radar at And(ya/Norway in summer 1987 have been used to study the nonlinear interactions between planetary waves, tides and gravity waves in the polar mesosphere, and the instability of background atmosphere above the mesopause. It is observed that 35-h planetary wave, diurnal, semidiurnal and terdiurnal tides are the prominent perturbations in the Lomb-Scargle spectra of the zonal wind component. By inspecting the frequency combinations, several triads are identified. By bispectral analysis it is shown that most bispectral peaks stand for quadratic coupling between tidal harmonics or between tide and planetary or gravity wave, and the height dependence of bispectral peaks reflects the variation of wave-wave interactions. Above the mesopause, the occurrence heights of the maximum L-S power spectral peaks corresponding to the prominent wave components tend to increase with their frequencies. This may result from the process in which two low frequency waves interact to generate a high frequency wave. Intensities of the planetary wave and tides increase gradually, arrive at their maxima, and then decay quickly in turn with increasing height. This kind of scene correlates with a "chain" of wave-wave resonant interactions that shifts with height from lower frequency segment to higher frequency segment. By instability analysis, it is observed that above the mesopause, the Richardson number becomes smaller and smaller with height, implying that the turbulent motion grows stronger and stronger and accordingly the background atmosphere more and more instable. It is suggested that the wave-wave sum resonant interaction and the wave dissipation due to instability are two dominant dynamical processes that occur in the mesopause region. The former invokes the energy transfer from lower frequency waves to higher frequency waves. The latter results in the heating of the atmosphere and accelerating of the background flow.     

Effect of viscous electron flow on THz plasma waves in field effect transistors

The instability of plasma waves is influenced by many factors, such as quantum effects and electrical thermal motion. However, in sufficiently small electronic devices, viscous electron flows can be generated from the electronic interactions and govern electronic transport. The strong influence of the viscous electron fluid on plasma wave instability in field effect transistors(FET) was analyzed in this study. The theoretical results show that the instability increment and radiation frequency are functions of the Mach number, and the instability increment. Further, the computer simulative data show that the radiation frequencies increase within a certain range and the instability increment decreases owing to the presence of viscous electron flows. Therefore, it can be concluded that the viscous electron flow FETs exerts considerable influence on the characteristics of the terahertz wave.     

Synchrony-optimized networks of non-identical Kuramoto oscillators

In this Letter we discuss a method for generating synchrony-optimized coupling architectures of Kuramoto oscillators with a heterogeneous distribution of native frequencies. The method allows us to relate the properties of the coupling network to its synchronizability. These relations were previously only established from a linear stability analysis of the identical oscillator case. We further demonstrate that the heterogeneity in the oscillator population produces heterogeneity in the optimal coupling network as well. Two rules for enhancing the synchronizability of a given network by a suitable placement of oscillators are given: (i) native frequencies of adjacent oscillators must be anti-correlated and (ii) frequency magnitudes should positively correlate with the degree of the node they are placed at.     

Absorption of long waves by linear structures

The phenomenon of resonance absorption of long waves by small-size oscillators is studied both analytically and numerically. The phenomenon consists in that the scattering cross section of an oscillator (a monopole, a dipole, etc.) is determined by the wavelength of the absorbed wave and does not depend on the wave size of the oscillator when this size tends to zero. The expression for the optimal excitation amplitude is derived for a group of oscillators of arbitrary wave size in the framework of the boundary-value problem formulated in the general form in terms of the generalized velocities and generalized forces. Using examples of linear structures (consisting of monopoles equidistantly positioned on the axis), the possibility of obtaining the maximal absorption cross section for sound absorption by such structures with a small wave size is investigated. Examples of linear structures providing unbounded logarithmic, linear, or quadratic growth of the total absorption cross section with an increase in the number of monopoles comprising them are considered for the case of the wave size of the absorbing structures being as small as desired. Characteristic features of the cooperative and individual strategies of absorbing oscillators are described. The results are applicable to waves of various physical natures.