Semilinear coherent oscillator with reflection-type photorefractive gratings

The saturation intensity, oscillation spectrum, and temporal dynamics of oscillation are studied for a semilinear coherent oscillator with two counterpropagating pump waves and a photorefractive crystal with dominating reflection gratings. The instability of the single-frequency oscillation spectrum is revealed, similar to that known for an oscillator with dominating transmission gratings. The experimental manifestation of this transition in the output characteristics of the oscillator is favourably compared with numerical calculations. PACS 42.65.Hw; 05.45.-a; 42.65.Pc; 42.65.Sf     

The role of the polarization of a nonresonance external harmonic field in the dynamics of a nonautonomous spin oscillator

The results of an analysis of the action of a nonresonance external harmonic electromagnetic field on a quantum oscillator whose active medium is a two-level spin system, i.e. spin oscillator are briefly presented. The role of external field polarization in the dynamics of a nonautonomous spin oscillator is demonstrated. For the circular polarization of a nonresonance external field the shift of oscillation frequency of the spin oscillator is observed. For the linear polarization of a nonresonance external field the specific feature of spin oscillator synchronization at the third overtone of external field frequency is observed, along with an oscillation frequency shift.     

Cascade klystron self-excited oscillator with delay

Experiments with a new type of resonance microwave self-excited system with complex dynamics, a cascade klystron self-excited oscillator with delayed feedback, are reported. The new self-excited oscillator features a low starting current and many oscillation bands; in addition, it can readily be switched into complex, including random, oscillation modes.     

Stochastic and chaotic relaxation oscillations

For relaxation oscillators stochastic and chaotic dynamics are investigated. The effect of random perturbations upon the period is computed. For an extended system with additional state variables chaotic behavior can be expected. As an example, the Van der Pol oscillator is changed into a third-order system admitting period doubling and chaos in a certain parameter range. The distinction between chaotic oscillation and oscillation with noise is explored. Return maps, power spectra, and Lyapunov exponents are analyzed for that purpose.     

Ionization of Clusters in Intense Laser Pulses through Collective Electron Dynamics

The motion of electrons and ions in medium-sized rare gas clusters ( approximately 1000 atoms) exposed to intense laser pulses is studied microscopically by means of classical molecular dynamics using a hierarchical tree code. Pulse parameters for optimum ionization are found to be wavelength dependent. This resonant behavior is traced back to a collective electron oscillation inside the charged cluster. It is shown that this dynamics can be well described by a driven and damped harmonic oscillator allowing for a clear discrimination against other energy absorption mechanisms.     

Mixed-mode oscillations and chaos from a simple second-order oscillator under weak periodic perturbation

In this study, we propose a remarkably simple oscillator that exhibits extremely complicated behaviors. The second-order nonautonomous differential equation discussed in this Letter is considered to be one of the simplest dynamics that can produce mixed-mode oscillations (MMOs) and chaos. Our model uses a Bonhoeffer-van der Pol (BVP) oscillator under weak periodic perturbation. The parameter set of the BVP equation is chosen such that a focus and a relaxation oscillation coexist when no perturbation is applied. Under weak periodic perturbation, various types of MMOs and chaos with remarkably complicated waveforms are observed.     

Energy dissipation in gigahertz oscillators from multiwalled carbon nanotubes

Using atomistic models and molecular dynamics simulations, interlayer corrugation and resistant force in a biwalled carbon nanotube are shown to be strongly dependent upon the morphology combination of the bitube. Consequently, energy dissipation in a commensurate (e.g., armchair/armchair or zigzag/zigzag) bitube oscillator is found to be much larger than that in an incommensurate (e.g., zigzag/armchair) oscillator, resulting in a decay of oscillation amplitude within a few nanoseconds in the commensurate bitube and several tens of nanoseconds in the incommensurate bitube.     

On the scenario of transition to the broadband oscillation regime in the prototype of a low-voltage vircator

This study is devoted to experimental investigation of the scenario for a transition from the narrow-band (single-frequency) oscillation regime to the broadband noise-like oscillation in a prototype of a low-voltage oscillator operating with a virtual cathode. The experimental setup and the control instrumentation are considered. Detailed experimental analysis of the dynamics of variation of temporal realizations of the signals generated by the laboratory prototype upon the variation of the chosen control parameters is performed. Analysis of the power spectra, temporal realizations of output signals, phase portraits, and the bifurcation diagram constructed upon a change of the chosen control parameters shows that a transition from the single-frequency oscillation regime to broadband oscillations occurs via a cascade of period-doubling bifurcations (classical Feugenbaum scenario is implemented).     

Noise-induced critical breakdown of phase lockings in a forced van der Pol oscillator

The effect of noise on the period of the van der Pol oscillator forced by a sinusoidal signal is analyzed in detail. The dynamics of the forced nonlinear oscillator with noise is described by the evolution of probability densities by a Markov operator. The oscillator shows a 1 : 1 phase-locked oscillation whose period is equal to the period of the sinusoidal forcing when the forcing is sufficiently strong. Noise modulates the oscillator's period as expected, but we show that this modulation is not uniform; the period of the oscillator changes drastically at a certain strength of noise. Thus this noise-induced breakdown of the phase locking can be considered as a stochastic bifurcation. The breakdown of stochastic phase-locking or the stochastic bifurcation is also analyzed from the viewpoint of the spectra of the Markov operator.     

振幅耦合动态网络中相邻结点间的相同步

研究用适当的量化指标来刻画动态网络的相同步,为此定义了新的量化指标:相邻结点的网络平均锁相值和网络平均相频差.动态网络结点选择的是多旋转中心的Lorenz混沌振子,对Lorenz系统进行柱面坐标变换,用振幅耦合方法构造动态网络.分别对星形网络和小世界网络进行了仿真计算,结果表明随着耦合强度的增大,网络中相邻结点的两个系统之间存在相同步现象,而且相同步行为与定义的量化指标之间存在较准确的对应关系.     

Phase diagrams for semilinear photorefractive coherent oscillator

The sequence of optical phase transitions is considered for a photorefractive coherent oscillator with a conventional mirror and a four-wave mixing phase conjugate mirror. Analogous to phase transitions in solids, the phase diagrams are constructed and defined qualitatively as different states of a whole system (light-induced scattering below the threshold of oscillation, single-frequency oscillation, two-frequency oscillation, and multimode mirrorless oscillation). The attempt of experimental mapping of a phase diagram is presented for a coherent oscillator with Co-doped BaTiO₃. PACS 42.65.Hw; 05.45.-a; 42.65.Pc; 42.65.Sf.     

Experimental Study of Planar Finite Grid Oscillator Arrays

Results of an experimental study on finite grid oscillator arrays and the effects of the edge element loading stubs in such arrays are presented. Three finite grid oscillator arrays, based on the same unit cell, with different number of unit were fabricated on RT/Duroid 5870 substrate and tested in terms of the oscillation frequencies, radiated power and radiation patterns. It is observed that the oscillation frequency of a finite grid array differs from the theoretically prediction based on the infinite array assumption and is strongly affected by the edge element loading stubs. The measurement also indicates that mode-jumping and multi-frequency (spurious) oscillation can exist in grid oscillator arrays.     

Self-organization of temporal structures in a multiequilibrium self-excited oscillator system with frequency control

An analysis is made of the nonlinear dynamics of a model of a self-excited oscillator system with automatic fine tuning of the frequency and possessing more than one equilibrium state. It is shown that, depending on the delay parameters of the control loop and the initial frequency detuning, various periodic and stochastic temporal structures may be formed, accompanied by the generation of various limit cycles and chaotic attractors in phase space. Reasons for the onset of self-modulation are set forth, and the position of the different oscillation regions is established. The main bifurcations are studied together with scenarios for the transformation of the oscillator self-modulation modes as a function of the parameters. Zh. Tekh. Fiz. 67, 1–8 (March 1997)     

Quantum dynamics of a nano-rod under compression

A nano-rod under compression, which is capacitively coupled to a Cooper-pair box, can be modelled in terms of a quartic oscillator linearly interacting with a tunnelling pseudo-spin. We have integrated numerically the quantum dynamics of this system in the partial Wigner representation and calculated the pseudo-spin population difference. Depending on the coupling, we have verified that the quantum tunnelling of the oscillator can lead to a more effective reduction of the Rabi oscillation amplitude of the pseudo-spin. Such findings suggest an experimental set-up that might be able to discriminate between the quantum and the classical motion of a nano-rod.     

Hopping of chaotic dynamics in a doubly resonant parametric oscillator

We study a doubly resonant optical parametric oscillator where the pump can feed two pairs of signal-idler modes. We assume the presence of gain at the pump frequency. We investigate the various oscillation states of interest, namely, when only the first pair oscillates with the other pair having null amplitudes and vice versa. We demonstrate the exchange of dynamics between the mode pairs when the relevant parameters of the cavity, namely, the phase mismatch factors or the decay rates switch because of fluctuations. The exchange of dynamics is shown to be independent of the nature of dynamics, i.e. independent of whether the motion isn-periodic or chaotic. We also investigate the case where both the pairs can exhibit chaotic dynamics though these states are difficult to realize because of fluctuations.     

Energy exchange between vibration modes of a graphene nanoflake oscillator: Molecular dynamics study

We investigated the oscillatory behaviors of a square graphene-nanoflake (GNF) on a rectangular GNF via classical molecular dynamics simulations, and analyzed the energy exchange and the oscillation frequencies for three different modes. The simulation results using a model structure show that the GNF oscillator can be considered as a high frequency oscillator. As its initial velocity increases, its telescoping region increases, then its structural asymmetry along the axis due to own small rotation exerted asymmetric van der Waals (vdW) force on it, and finally, this asymmetric vdW force enhances its rotational motions during its axial translational motions. So the initial kinetic energy of the axial translational motion is changed into the energy of the orthogonal vibrational and the rotational motions. Its resonance frequencies are dependent on the aspect ratio of the bottom rectangular GNF, the difference between the lengths of the GNF oscillator and the bottom rectangular GNF, and the initial velocity.     

Energy features of an adiabatically loaded anharmonic oscillator

An excited anharmonic oscillator is considered under conditions of adiabatic (i.e., slow, as compared to the oscillation period) loading with an external force tending to a constant value at long times. The energy characteristics of the adiabatically loaded anharmonic oscillator, such as the instantaneous energy of the oscillator, the maximum kinetic (oscillation) energy, and the kinetic and potential energies averaged over the period, are analytically calculated as a function of the steady-state force. The analytical results are confirmed by the data of numerical calculations. It is established that the external force gives rise to a redistribution of the average kinetic and potential components of the initial energy of the anharmonic oscillator and that the transferred energy portions at a small external force considerably exceed the average work done by the external force.     

Quantum correlations of pulses of optical parametric oscillator synchronously pumped above threshold

The quantum analysis of radiation from a degenerate optical parametric oscillator synchronously pumped above its oscillation threshold is presented. It is shown that pulses of signal and pump fields at the output of the oscillator have the following properties: quantum fluctuations of the fields are independent in each individual pulse, but correlated in pulses of the pulse train with a temporal step multiple of the pulse period. The number of essentially correlated pulses is on the order of the oscillator cavity finesse. Cross-correlations between the pump and signal pulses are established above the oscillation threshold. These correlations lead to a significant quantum effect in the integral characteristics of the fields. A theoretical analysis revealed that the spectrum of field fluctuations measured using a balanced homodyne detection technique of phase quadratures of the fields with a pulsed local oscillator reveals quantum noise suppression in the vicinity of frequencies that are multiples of the pulse repetition rate.     

Quantum theory of synchronously pumped type I optical parametric oscillators: characterization of the squeezed supermodes

Quantum models for synchronously pumped type I optical parametric oscillators (SPOPO) are presented. The study of the dynamics of SPOPOs, which typically involves millions of coupled signal longitudinal modes, is significantly simplified when one considers the “supermodes", which are independent linear superpositions of all the signal modes diagonalizing the parametric interaction. In terms of these supermodes the SPOPO dynamics becomes that of about a hundred of independent, single mode degenerate OPOs, each of them being a squeezer. One derives a general expression for the squeezing spectrum measured in a balanced homodyne detection experiment, valid for any temporal shape of the local oscillator. Realistic cases are then studied using both analytical and numerical methods: the oscillation threshold is derived, and the spectral and temporal shapes of the squeezed supermodes are characterized.     

有源环形谐振腔辅助滤波的单模光电振荡器

提出并验证了一种有源环形谐振腔辅助滤波的光电振荡器. 它利用有源环形谐振腔提供的高Q光学梳状频率响应特性, 对振荡器中的光信号模式进行选择, 能有效地提高输出信号的边模抑制比, 获得光电振荡器的单模输出. 理论上, 对光电振荡器的起振模式以及有源腔的频率响应进行了分析, 仿真结果表明有源环形谐振腔的辅助滤波有利于光电振荡器的边模抑制和单模输出. 在实验上, 通过对比验证了理论的预期结果, 并最终得到中心频率为20 GHz, 边模抑制比为58.83 dB, 在频偏10 kHz处相位噪声为-97 dBc/Hz的单模信号输出. 该方案保留了已有光电振荡器边模抑制方法的优势, 实现方法上更加简便, 在工作带宽和可调谐性方面具备良好的灵活性.