Information,information gain,and efficiency of self-organizing systems close to instability points

Selforganizing systems are those which can acquire macroscopic spatial, temporal, or spatio-temporal structures without interference from the outside by mere changes of control parameters. The slaving principle which has been derived for such systems close to their instability points allows one to give the probability distribution of the total system a specific form.This in turn allows one to decompose information and information gain into a part which refers to the order parameters alone and a second part which is a sum over the information of the slaved modes averaged over the distribution of the order parameters. Close to instability points the information of the order parameters changes dramatically whereas the information of the slaved modes does not. Therefore close to these points it is sufficient to study the behavior of the order parameter information and information gain which is done explicitly for a large class of systems undergoing nonequilibrium phase transitions. It is shown how information and information gain as well as efficiency (in the sense defined in this paper) can be measured directly.     

哈肯激光方程自脉冲解的稳定性分析

本文详细地研究了哈肯激光方程的自脉冲不稳定性,得出了自脉冲解的解析表达式,并对其进行了稳定性分析。结果表明,无论是对于第三类激光系统还是对于第四类激光系统,哈肯激光方程的自脉冲解都是不稳定的。     

Experimental investigation of Risken–Nummedal–Graham–Haken laser instability in fiber ring lasers

It has been suggested (by Pessina et al. in 1997) that the observed spontaneous mode beating of erbium-doped-fiber ring lasers can be explained as the multimode instability described in 1968 by Risken and Nummedal and by Graham and Haken (the RNGH instability), which is based on Rabi-splitting-induced gain. If true, this would constitute the first ever example of this instability in an actual experiment. We test the hypothesis through a quantitative experimental investigation. We demonstrate that there is indeed a clear, marked onset of the instability, a fact that went unnoticed in all previous experiments because it is very close to the lasing threshold. We intentionally raise cavity loss to better separate onset of lasing and of instability. We obtain quantitative information on the instability onset. An interpretation as the predicted second threshold is reasonable provided inhomogeneous gain line broadening is taken into account. We also observe that instability above its onset exists only intermittently; this may hint at a subcritical bifurcation and noise-driven transitions. In any event, the RNGH mechanism is present, if not in a pure form. PACS 42.65.Sf; 42.60.Mi; 42.55.Wd     

Information and information gain close to nonequilibrium phase transitions. Numerical results

Using a general result on the behavior of information and information gain close to instability points of self-organizing systems we calculate explicitly the information of a single order parameter close to a nonequilibrium phase transition. We also discuss by means of the result why the relevant quantities are interpreted as information rather than as entropy.     

Secure information transfer based on computing reservoir

There is a broad area of research to ensure that information is transmitted securely. Within this scope, chaos-based cryptography takes a prominent role due to its nonlinear properties. Using these properties, we propose a secure mechanism for transmitting data that relies on chaotic networks. We use a nonlinear on–off device to cipher the message, and the transfer entropy to retrieve it. We analyze the system capability for sending messages, and we obtain expressions for the operating time. We demonstrate the system efficiency for a wide range of parameters. We find similarities between our method and the reservoir computing.     

Review: Characterizing and quantifying quantum chaos with quantum tomography

We explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The tomographic record consists of a time series of expectation values of a Hermitian operator evolving under the application of the Floquet operator of a quantum map that possesses (or lacks) time-reversal symmetry. We find that the rate of information gain, and hence the fidelity of quantum state reconstruction, depends on the symmetry class of the quantum map involved. Moreover, we find an increase in information gain and hence higher reconstruction fidelities when the Floquet maps employed increase in chaoticity. We make predictions for the information gain and show that these results are well described by random matrix theory in the fully chaotic regime. We derive analytical expressions for bounds on information gain using random matrix theory for different classes of maps and show that these bounds are realized by fully chaotic quantum systems.     

Instability of wave packets in nonlinear inhomogeneous waveguides

Conditions for modulation instability of a wave packet to occur in cubically nonlinear single- and double-mode waveguides with various distributions of dispersion parameters over the waveguide length are investigated. Analytical expressions are obtained for the integral gain increment and other characteristics governing the modulation instability dynamics. Features of the dynamics are revealed using numerical simulation.     

Soliton-like pulse timing jitter in dispersion-managed systems

In this paper, the timing jitter in dispersion-managed soliton-like systems with the Gaussian pulse is studied by using two methods. Firstly, the derivation of the dynamic equations for the evolution of soliton-like parameters and the timing jitter expressions for the dispersion-managed soliton-like systems are carried out by the perturbed variational method. By analysing and simulating these timing jitter expressions, one can find that the timing jitter is induced by the amplified spontaneous emission noise and the frequency shift, etc. Nonlinear gain can suppress the timing jitter. The chirp sign and the filters action have also effects on the total timing jitter. Secondly, the timing jitter is calculated and analysed by using the moment method. The results of the two methods prove to be consistent with each other.     

Modulation instability of wave packets in a Gires–Tournois interferometer

We study the specific features of the perturbation dynamics of a wave packet in a Gires–Tournois interferometer. We obtain a dispersion relationship that relates the perturbation parameters to the parameters of the structure and pump wave, the analytical expressions for the gain increment of a harmonic perturbation and other important characteristics that determine the dynamics of the modulation instability of the reflected wave. Based on numerical simulation, we plot the dependences of the dispersion and nonlinearity parameters and the gain increment on the spacing between the interferometer mirrors, the angle of incidence of the radiation onto the mirrors, and the radiation intensity.     

介质的增益与损耗对高功率激光小尺度自聚焦的影响

 由光束在非线性介质中传输所满足的近轴波方程，应用Bespalov Talanov（BT）理论，导出了光束在两种介质中传输时，小尺度不稳定增长所遵循的微分方程。通过对比分析介质的增益和损耗对高功率激光的小尺度自聚焦行为的不同影响，得出了截止频率、最快增长频率、纹波的积分指数增益等特性随各参量的变化,求得了最大和最小的纹波增长的距离，以及介质的增益和损耗特性对成丝距离的影响。     

Modulational instability in systems with integrating nonlinearity

A new type of modulational instability for coherent as well as partially coherent light in systems with integrating nonlinearity caused by an irreversible process is investigated both experimentally and theoretically. In such systems plane waves never reach the stationary limit and exhibit a nontrivial time dependence resulting in new features of the modulational instability. For example, the modulational frequency of the nonexponentially increasing perturbation with maximum gain decreases while the wave is propagating. The threshold for vanishing modulational instability due to a finite degree of spatial coherence depends only on system parameters and not on the light intensity.     

Modulation instability in negative refractive metamaterials with exponential saturable nonlinearity and self-steepening effects

Modulation instability (MI) in negative refractive metamaterials with exponential saturable nonlinearity and the self-steeping effect is investigated by using the standard linear stability analysis and the Drude electromagnetic model. The dispersion relation, instability condition, cut-off frequency, gain spectrum, and their corresponding dimensionless expressions are analytically deduced and then calculated. The results show that, the self-steepening effect will suppress MI by decreasing the cut-off frequency and the maximum gain. And the larger the power density ratio is, more slowly the cut-off frequency and the maximum gain decrease with increase of the self-steepening parameter. Although the sign of the self-steepening parameter does not influence MI but its absolute value must be smaller than a certain value. Depending on different self-steepening parameters, the cut-off frequency and maximum gain may decrease or increase before decrease with increase of the power density ratio. In particular, for large self-steepening parameters, the power density ratio may have a threshold value. When the power density ratio is under this threshold, MI will disappear.     

Entropy,information and quantum measurements

The conditional entropy between two states of a quantum system is shown to be nonincreasing when a complete measurement is performed on the system. The information between two quantum systems is defined and is shown to be bounded above by the logarithmic correlation. This inequality is then applied to the measurement process. The entropy changes in the observed system and the measuring apparatus are compared with the information gain in the measurement.     

Threshold analysis for a THz-wave parametric oscillator with a quasi-phase-matching scheme in lithium niobate

The analytical expressions of the parametric gain for the terahertz wave (THz-wave) and the Stokes wave of THz-wave parametric oscillator (TPO) with a quasi-phase-matching scheme in periodically poled LiNbO₃ (PPLN) are deduced. The pump threshold expression of the TPO with a quasi-phase-matching scheme in PPLN is derived based on the gain expression of the Stokes wave. The expression is theoretically analyzed to find the relationship between the pump threshold and the parameters of the resonant cavity.     

Mechanisms for suppressing the transverse mode coupling instability in a circular accelerator

The chromatic and nonlinear suppression of the transverse mode coupling instability in a circular accelerator is analyzed. Analytical estimates are compared with the results of experiments and numerical simulations. The transverse mode coupling (or fast head—tail) instability is a significant factor that limits the beam intensity in circular accelerators. This instability arises when the bunch current exceeds a threshold value determined by the broadband impedance of the vacuum chamber. Feedback systems are traditionally used to suppress the instability. The experience of working with such systems shows that their efficiency depends strongly on the operating parameters of the amplifier, particularly on the chromaticity and nonlinearity of the magnetic lattice. Thus, both chromatic and nonlinear effects should be taken into account to better understand the physical processes and to increase the feedback efficiency.     

Third-order laser-field-expansion analysis of the Lorenz–Haken equations

This paper revisits a few aspects of laser-dynamics with a strong-harmonic expansion analysis from which new analytical information, within the intrinsic pulsing regime that characterizes the non-linearly coupled differential Lorenz–Haken equations, is extracted. The analysis is expected to provide clearer insights to the physics involved in the laser-dynamics issue. Carried out to third-order in electric field amplitude, the procedure allows for the derivation of a closed form expression which describes the permanent-oscillation frequency of the unstable periodic state. Comparison between the frequency values evaluated from the literal formula and those obtained through direct numerical simulations shows a realistic fit inside the control parameters space that displays symmetric period-one pulsing solutions.     

Role of field losses on the Risken–Nummedal–Graham–Haken laser instability: application to erbium-doped fibre lasers

We analyse the effect of both distributed and localised losses in a laser cavity on the Risken–Nummedal–Graham–Haken multimode instability. For two-level lasers, distributed losses are found to have a negligible influence on the instability conditions as long as they remain below 10 dB, a value hardly ever exceeded under common experimental conditions. If one keeps raising the distributed loss above that value, finally the uniform-field-limit results are recovered: localised loss becomes less and less important, and in the limit does not enter at all. In contrast, for three-level lasers – in particular for erbium-doped fibre lasers – distributed losses are found to have a profound quantitative influence on the instability threshold.     

Multistable selection equations of pattern formation type in the case of inhomogeneous growth rates: With applications to two-dimensional assignment problems

We study the stability of solutions of a particular type of multistable selection equations proposed by Starke, Schanz and Haken in the case of an inhomogeneous spectrum of growth parameters. We determine how the stability of feasible solutions depends on the inhomogeneity of the spectrum. We show that the strength of the competitive interaction between feasible solutions can act as a control parameter that induces bifurcations reducing the degree of multistability.     

Quantum Fisher information width in quantum metrology

In scenarios of quantum metrology, the unitary parametrization process often depends on space directions. How to characterize the sensitivity of parameter estimation to space directions is a natural question. We propose the concept of the quantum Fisher information(QFI) width, which is the difference between the maximum and minimum values of the QFI, to quantitatively study the sensitivity. We find that Fock states, the bosonic coherent states, and the displaced Fock states all have zero widths, indicating that QFI is completely inert over all directions, while the width for the spin state with all spins down or up is equal to the number of particles, so this concept will enable us to choose appropriate directions to make unitary transformation to obtain larger QFI.The QFI width of the displaced quantum states is found to be independent of the magnitude of the displacement for both spin and bosonic systems. We also find some relations between the QFI width and squeezing parameters.     

External electric field induced modulation instability of an electromagnetic beam in two-photon photorefractive materials

The modulation instability of a broad electromagnetic beam in a biased two-photon photovoltaic photorefractive material, due to two-photon-photorefractive effect has been investigated. The one-dimensional modulation instability growth rate has been estimated under the linear stability framework. The behavior of the gain spectrum is different in low and high power regions. It has been predicted that, with the application of external electric field, it is possible to initiate and control growth of the instability in those media, where modulation instability was hitherto prohibited. The influence of different system parameters on the instability growth rate has been examined.