Model of electron beam transformation in a narrow tube

The problem of transformation of an electron beam in a long narrow conducting tube is considered. General wave solutions for the propagation of an arbitrary (including aperiodic) modulation of a homogeneous beam are obtained in the case of weak modulation. The solution corresponding to harmonic modulation is compared to the solutions obtained earlier and described in the literature. The problem of beam transformation corresponding to the bunching regime in high-power klystrons is also considered (including overtaking). A discrete analytic solution to the problem is obtained in the ??frozen beam approximation.?? This solution is tested for the problem of spilling of a monovelocity bunch and for the problem of the efficiency of a two-cavity klystron with infinitely narrow gaps. In both cases, physically correct results are obtained.     

Self-focusing in the complex Ginzburg-Landau limit of the critical nonlinear Schrödinger equation

We analyze self-focusing and singularity formation in the complex Ginzburg-Landau equation (CGL) in the regime where it is close to the critical nonlinear Schrödinger equation. Using modulation theory [Fibich and Papanicolaou, Phys. Lett. A 239 (1998) 167], we derive a reduced system of ordinary differential equations that describes self-focusing in CGL. Analysis of the reduced system shows that in the physical regime of the parameters there is no blowup in CGL. Rather, the solution focuses once and then defocuses. The validity of the analysis is verified by comparison of numerical solutions of CGL with those of the reduced system.     

高斯变迹布拉格光纤光栅中的调制不稳定性

利用激光脉冲在光纤光栅中传播时所遵守的相干耦合非线性薛定谔方程,研究了激光脉冲在高斯变迹布拉格光纤光栅中传输时，在反常色散区和正常色散区所产生的调制不稳定性.结果表明在反常色散区和正常色散区都能产生调制不稳定性；在反常色散区，当输入功率达到一定数值时，产生明显的有规律的增益谱；在正常色散区，在产生调制不稳定性功率区域，调制不稳定性存在并从给定值一直持续到无穷；并且，在反常色散区和在正常色散区，增益谱都受到高斯变迹函数的制约. 关键词： 高斯变迹 布拉格光栅 调制不稳定性 增益     

局部高斯变迹布拉格光纤光栅中的调制不稳定性

利用激光脉冲在光纤光栅中传播时所遵守的相干耦合非线性薛定谔方程,研究了激光脉冲在局部高斯变迹布拉格光纤光栅中传输时,在反常色散区和正常色散区所产生的调制不稳定性。结果表明在反常色散区和正常色散区都能产生调制不稳定性;在反常色散区,当输入功率达到一定数值、传输距离一定时,当f=-1禁带之上能带底时,调制不稳定性增益的强度最强、宽度最窄;当远离能带底时强度减弱、宽度变宽;在正常色散区,在产生调制不稳定性功率区域,调制不稳定性存在并从给定值一直持续到无穷;并且,在反常色散区和在正常色散区,增益谱都受到局部高斯变迹函数的制约。     

Large Signal Modulation Characteristics in the Transition Regime for Two-State Lasing Quantum Dot Lasers

Large-signal modulation capability,as an important performance indicator,is directly related to the high-speed optical communication technology involved.We experimentally and theoretically investigate the large-signal modulation characteristics of the simultaneous ground-state(GS) and the excited-state(ES) lasing in InAs/GaAs quantum dot laser diodes.The large-signal modulation capability of total light intensity in the transition regime from GS lasing to two-state lasing is unchanged as the bias-current increases.However,GS and ES large-signal eye diagrams show obvious variations during the transition.Relaxation oscillations and large-signal eye diagrams for GS,ES,and total light intensities are numerically simulated and analyzed in detail by using a rate-equation model.The findings show that a complementary relationship between the light intensities for GS and ES lasing exists in both the transition regime and the two-state lasing regime,leading to a much smaller overshooting power and a shorter settling time for the total light intensity.Therefore,the eye diagrams of GS or ES lasing are diffuse whereas those of total light intensity are constant as the bias-current increases in the transition regime.     

The time-dependence of exchange-induced relaxation during modulated radio frequency pulses

The problem of the relaxation of identical spins 1/2 induced by chemical exchange between spins with different chemical shifts in the presence of time-dependent RF irradiation (in the first rotating frame) is considered for the fast exchange regime. The solution for the time evolution under the chemical exchange Hamiltonian in the tilted doubly rotating frame (TDRF) is presented. Detailed derivation is specified to the case of a two-site chemical exchange system with complete randomization between jumps of the exchanging spins. The derived theory can be applied to describe the modulation of the chemical exchange relaxation rate constants when using a train of adiabatic pulses, such as the hyperbolic secant pulse. Theory presented is valid for quantification of the exchange-induced time-dependent rotating frame longitudinal T1rho,ex and transverse T2rho,ex relaxations in the fast chemical exchange regime.     

Dark solitons in optical fiber with inhomogeneous effects

We study the nonlinear wave propagation in an inhomogeneous optical fiber core in the normal dispersive regime. In order to include the inhomogeneous physical effects, the nonlinear Schrödinger equation (NLSE), which governs the solitary pulse propagation in optical fiber, is modified by adding terms for phase modulation and power gain or loss. The modified NLSEs are bilinearized and exact dark soliton solutions are obtained. The results are discussed.     

Probing the excitation spectrum of a fermi gas in the BCS-BEC crossover regime

We measure excitation spectra of an ultracold gas of fermionic (40)K atoms in the BCS-Bose-Einstein-condensation (BEC) crossover regime. The measurements are performed with a novel spectroscopy that employs a small modulation of the B field close to a Feshbach resonance to give rise to a modulation of the interaction strength. With this method we observe both a collective excitation as well as the dissociation of fermionic atom pairs in the strongly interacting regime. The excitation spectra reveal the binding energy or excitation gap for pairs in the crossover region.     

Kinetic description of the field-gas interaction in intense optical lattices

In this paper the effects of coupling a non-resonant optical lattice to a gas are studied. When the lattice induces a periodic modulation of the gas density, strong Bragg diffraction of light can occur limiting the achievable intensities inside the lattice reducing the ability to manipulate the gas with the lattice. We calculate the evolution of the light fields by finding solutions to the wave equation with a periodic refractive index induced by the lattice. The local gas density perturbation induced by the lattice is determined by solving the Boltzmann kinetic equation in the collisional regime.     

Mixed synchronization in chaotic oscillators using scalar coupling

We report experimental evidence of mixed synchronization in two unidirectionally coupled chaotic oscillators using a scalar coupling. In this synchronization regime, some of the state variables may be in complete synchronization while others may be in anti-synchronization state. We extended the theory by using an adaptive controller with an updating law based on Lyapunov function stability to include parameter fluctuation. Using the scheme, we implemented a cryptographic encoding for digital signal through parameter modulation.     

Acousto-optic mode-locker for Nd:Lasers using paratellurite

The design of an acousto-optic modulator using paratellurite requiring only low driving power is described. Because of the high figure of merit a high modulation index can be achieved. To avoid an intermediate transmission peak the modulator should not be operated in the Bragg-regime but rather in the transition regime. The time dependent transmission for this regime is calculated as a function of the material parameters. Experimentally, modulation indices up to 10 are obtained. Using such a TeO₂ mode-locker a pulsed Nd:Cr:GSGG laser delivered pulses down to 70 ps.     

非线性双折射色散光纤中极化调制不稳定性分析

利用光脉冲在光纤中传播时所遵守的相干非线性薛定谔耦合方程,研究了线偏振光在光纤中的传输特性.结果表明:由于线性双折射、非线性效应和色散的相互作用,导致光的偏振状态发生变化,产生交叉相位调制(XPM),从而导致调制不稳定性.这一调制不稳性不仅在反常色散区产生,在正常色散区也能产生,并且线性双折射发生变化时,增益谱也随之发生变化.     

Formulation of Zeeman modulation as a signal filter

The Bloch equation containing a Zeeman modulation field is solved analytically by treating the Zeeman modulation frequency as a perturbation. The absorption and dispersion signals at both 0 degrees and 90 degrees modulation phase are obtained. The solutions are valid to first order in the modulation frequency, but are otherwise valid for any value of modulation amplitude or microwave amplitude. A first order treatment of modulation frequency is shown to be a valid approximation over a wide range of typical experimental EPR conditions. The solutions derived from the Bloch equation suggest that the effect of over-modulation on first and second harmonic EPR spectra can be formulated as a mathematical filter that smoothes and broadens the under-modulated signal. The only adjustable filter parameter is a width that is equivalent to the applied peak-to-peak modulation amplitude. The true spin-spin and spin-lattice relaxation rates are completely determined from the under-modulated spectrum. The filters derived from the analytic solutions of the Bloch equation in the linear limit of modulation frequency are tested against numerical solutions of the Bloch equation that are valid for any modulation frequency to show their applicability. The filters are further tested using experimental EPR spectra. Experimental under-modulated spectra are mathematically filtered and compared with the experimental over-modulated spectra. The application of modulation filters to STEPR spectra is explored and limitations are discussed.     

Inhibition of light tunneling in chirped and longitudinally modulated semi-infinite waveguide arrays

The inhibition of light tunneling in chirped and longitudinally modulated semi-infinite waveguide arrays where the refractive index is linearly modulated in the transverse direction and harmonically modulated along the light propagation direction is considered. We report on the effect of the refractive index transverse amplitude modulation rate, longitudinal modulation frequency and depth on tunneling inhibition in both linear and nonlinear regimes. We show that in the linear regime an optimal value for the transverse amplitude modulation rate of refractive index exists and can determine the optimal longitudinal modulation frequency or depth leading to a maximum of distance-averaged power fraction. In the nonlinear regime the tunneling inhibition dynamics is affected dramatically by the transverse amplitude modulation rate and the associated electric field amplitude of the input beam.     

Saturation effects at backward-stimulated scattering in the single-mode regime of interaction

The effects of amplitude modulation of interacting waves at stimulated Mandelstam-Brillouin scattering (SMBS) in a monomode fibre caused by the noise origin of the initial Stokes wave are investigated both theoretically and experimentally. Depending on the determined conditions, there can taken place either a smoothing of the noise amplitude modulation or its preservation in the Stokes radiation in the deep saturation regime of SMBS. Amplitude modulation with period corresponding to the double time of radiation propagation through the fibre is observed along with noise-amplitude modulation of the Stokes and pump waves. The effect of this period prolongation is discussed. The influence of phase fluctuations on amplitude modulation of interacting waves is investigated. The role of phase correlations in the feedback regime of SMBS is considered. Experimental results are in good agreement with numerical calculations.     

Mode transition in dusty micro-plasma driven by pulsed radio-frequency source in C_2H_2/Ar mixture

Physical qualities of dusty plasma in the pulsed radio-frequency C_2H_2/Ar microdischarges are carefully investigated by a one-dimensional hydrodynamic model and aerosol dynamics model.Since the thermophoretic force has a great effect on the nanoparticle density spatial distribution,the neutral gas energy equation is taken into accounted.The effects of pulse parameters(dust ratio,modulation frequency) on the nanoparticle formation and growth process are mainly discussed.The calculation results show that,as the duty ratio increases,the mode transition from the sheath oscillation(a regime) to the secondary electron heating(7 regime) occurred,which is quite different from the conventional pulsed discharge.Moreover,the effect of modulation frequency on the width of sheath and plasma density is analyzed.Compared with the H_2CC~-ions,the modulation frequency effect on the nanoparticles density becomes more prominent.     

Transient phenomena in phase-modulated self-induced transparency soliton behaviour

The threshold behaviour of self-induced transparency solitons in the transient regime is numerically detected as a result of regular or random phase modulation of the input pulse. Depending on the depth of modulation either random noise filtering or SIT damping occurs. An interpretation is given in terms of the inverse scattering transformation.     

非线性管理光纤光栅中的调制不稳定性研究

基于非线性耦合模方程,研究了非线性管理光纤光栅中的调制不稳定性,得到了调制不稳定性的色散关系。与常规的非线性光纤光栅相比,在非线性管理光纤光栅中,克尔非线性的变化改变了调制不稳定性增益谱的谱宽和幅度,并导致新的不稳定性区域的出现:在反常色散区,原来关于零波数对称的两个旁瓣随着克尔非线性变化的增加其增益幅度递减至零,在经历了一段无增益区域之后,又逐渐形成了在零波数附近区域的一个新的单峰;而在正常色散区,除了原来的两个增益区域之外,零波数附近出现了新的增益区,增益的幅度随克尔非线性变化的增加而递增。可见,非线性管理光纤光栅给调制不稳定性的产生提供了更多的空间。     

Synchronization of Huygens' clocks and the Poincaré method

We study two models of connected pendulum clocks synchronizing their oscillations, a phenomenon originally observed by Huygens. The oscillation angles are assumed to be small so that the pendulums are modeled by harmonic oscillators, clock escapements are modeled by the van der Pol terms. The mass ratio of the pendulum bobs to their casings is taken as a small parameter. Analytic conditions for existence and stability of synchronization regimes, and analytic expressions for their stable amplitudes and period corrections are derived using the Poincaré theorem on existence of periodic solutions in autonomous quasi-linear systems. The anti-phase regime always exists and is stable under variation of the system parameters. The in-phase regime may exist and be stable, exist and be unstable, or not exist at all depending on parameter values. As the damping in the frame connecting the clocks is increased the in-phase stable amplitude and period are decreasing until the regime first destabilizes and then disappears. The results are most complete for the traditional three degrees of freedom model, where the clock casings and the frame are consolidated into a single mass.