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Empirical analysis of the price fluctuations of financial markets has received extensive attention because a substantial amount of financial market data has been collected and because of advances in data-mining techniques. Price fluctuation trends can help investors to make informed trading decisions, but such decisions may also be affected by a psychological factors—the anchoring effect. This study explores the intraday price time series of Taiwan futures, and applies diffusion model and quantitative methods to analyze the relationship between the anchoring effect and price fluctuations during first passage process. Our results indicate that power-law scaling and anomalous diffusion for stock price fluctuations are related to the anchoring effect. Moreover, microscopic price fluctuations before switching point in first passage process correspond with long-term price fluctuations of Taiwan’s stock market. We find that microscopic trends could provide useful information for understanding macroscopic trends in stock markets.

Disordered cellular automata (DCA) represent an intermediate class between elementary cellular automata and the Kauffman network. Recently, Rule 126 of DCA has been explicated: the system can be accurately described by a discrete probability function. However, a means of extending to other rules has not been developed. In this investigation, a density map of the dynamical behavior of DCA is formulated based on Rule 22 and other totalistic rules. The numerical results reveal excellent agreement between the model and original automata. Furthermore, the inhomogeneous situation is also discussed.

This tutorial presents a detailed description of experiments, simulations, and characterizations of chaos synchronization phenomena in the model of a mutually coupled microchip solid-state laser array subjected to self-mixing feedback modulation. We demonstrate a transition to synchronized chaos by the method of 'phase squeezing' with increasing field overlap between the two lasers. This phenomenon is well reproduced by numerical simulation of model equations. It is also shown that low energy variation as well as high disorder are concurrently established in synchronized chaos in the present system. The deterministic random switching (i.e., chaotic itinerancy) among phase-squeezed states and synchronized chaos states is numerically demonstrated in a transition region from a phase-squeezed state to a synchronized state. We characterize observed behaviours using such methods as singular value deposition (SVD), joint time–frequency analysis (JTFA) introducing a similarity function, and coarse-grained information transfer rate (CITR) analysis of long-term experimental or numerical time series, and discuss the physical significance of observed nonlinear dynamics in conjunction with chaos synchronization in mutually coupled lasers.

We studied the antiphase self-pulsation in a globally coupled three-mode laser operating in different optical spectrum configurations. We observed locking of modal pulsation frequencies, quasiperiodicity, clustering behaviors, and chaos, resulting from the nonlinear interaction among modes. The robustness of [p:q:r] three-frequency locking states and quasiperiodic oscillations against residual noise has been examined by using joint time-frequency analysis of long-term experimental time series. Two sharply antithetical types of switching behaviors among different dynamic states were observed during temporal evolutions; noise-driven switching and self-induced switching, which manifests itself in chaotic itinerancy. The modal interplay behind observed behaviors was studied by using the statistical dynamic quantity of the information circulation. Well-organized information flows among modes, which correspond to the number of degeneracies of modal pulsation frequencies, were found to be established in accordance with the inherent antiphase dynamics. Observed locking behaviors, quasiperiodic motions, and chaotic itinerancy were reproduced by numerical simulation of the model equations.

We study chaos synchronization experimentally in a modulated globally coupled three-mode laser with different modal gains subjected to self-mixing Doppler-shifted feedback, which can apply the loss modulation to individual modes at Doppler-shift frequencies. Depending on the pump power, different forms of collective chaos synchronizations were found to appear when the laser was modulated at the highest relaxation oscillation frequency, reflecting the change in cross-saturation coefficient among modes. In the present experiment, each pair of modes exhibited phase, lag, or generalized synchronization collectively according to the inherent antiphase dynamics, where these types of synchronization have already been demonstrated in two coupled chaotic oscillators in different physical systems. Information flows among oscillating modes which are established in different forms of collective chaos synchronizations were characterized by information-circulation analysis of the experimental time series. (c) 2002 American Institute of Physics.

We observed a highly efficient self-induced "oval hollow" mode operation in a Fabry-Perot microchip solid-state laser under strongly asymmetric "sheetlike" end-pumping. This new class of microresonator lasing mode features a hollow emission near-field pattern with a dark spot inside and a narrow unidirectional line-shape far-field pattern with a uniform intensity distribution.

This paper reviews our recent research on nonlinear dynamics of microchip solid-state lasers subjected to delayed optical feedback. Instabilities in two types of physical systems including multimode lasers with feedback and lasers with frequency-shifted feedback are discussed. Applications of microchip lasers with feedback to shot-noise-limited self-mixing optical sensing and imaging are summarized.

Synchronization of mutually coupled chaotic lasers has been demonstrated in a microchip ${\mathrm{LiNdP}}_{4}{\mathrm{O}}_{12}$ laser array with self-mixing feedback modulation. An abrupt transition to synchronized chaos by way of ``phase squeezing'' was observed when coupling between the two lasers was increased. This phenomenon is well reproduced by numerical calculations using model equations. It is also shown that low energy variation as well as high disorder are concurrently established in synchronized chaos.

When a nonlinear oscillator is driven externally, it may become transparent, i.e., the output response appears without any dispersion or distortion. Such counter-intuitive feature, in fact, is a unique zero-dispersion nonlinear resonance (ZDNR). Herein, it is examined on the base of a generic input-output analysis. The conditions for ZDNR have been clarified and a power law relation has been established to feature the interplay with noise.

The noise-associated dynamical behavior of a periodically driven nonlinear diode resonator system is presented. Several counter-intuitive features, such as noise-induced order and stochastic suppression of chaos, are experimentally identified. These features are uniquely induced by the multiplicative dynamical noise rather than by the additive dynamical noise. The novel connections between multiplicative dynamical noise, noise-induced linearisation and coherence resonance are shown.

We describe a method for quickly and easily measuring the size of small particles in suspensions. This method uses a self-mixing laser Doppler measurement with a laser-diode-pumped, thin-slice LiNdP(4)O(12) laser with extremely high optical sensitivity. The average size of the particles in Brownian motion is determined by a Lorentz fitting of the measured power spectrum of the modulated self-mixing laser light resulting from the motion. The dependence of the measured power spectra on particle size and concentration was quantitatively identified from the results of a systematic investigation of small polystyrene latex particles with different diameters and concentrations. The sizes and ratios of particles with different diameters mixed in water were accurately measured. An application of this self-mixing laser method for estimation of the average size of plankton in seawater showed that it is a practical method for characterizing biological species.

Nanometer vibration analysis of a target has been demonstrated by a self-aligned optical feedback vibrometry technique that uses a laser-diode-pumped microchip solid-state laser. The laser output waveform, which was modulated through interference between a lasing field and an extremely weak (- 100-dB) frequency-modulated (FM) feedback field, was analyzed by the Hilbert transformation to yield the vibration waveform of the target. Experimental signal characteristics have been reproduced by numerical simulations. Real-time vibration measurement has also been achieved with a simple FM demodulation circuit.

We report on the experimental observations of chaos synchronizations among orthogonally polarized emissions in a dual-polarization laser. With a three-mode scheme with a single mode in one polarization and two modes in orthogonal polarizations, synchronization was achieved by the cross-saturation dynamics of population inversions when one of the dual-polarized emissions was subjected to external perturbations, i.e., self-mixing modulation or optical fiber feedback. In-phase synchronization or lag synchronization among orthogonally polarized emissions was achieved depending on the degree of cross saturation in the self-mixing modulation. Synchronization of random bursting was observed in the fiber feedback, in which two chaotic-spiking modes in one polarization with anticorrelated intensity variations synchronize the remaining mode in the orthogonal polarization cooperatively with their total intensity variation. Information sender-mediator-receiver relationships among modes, which represent the dynamical roles of individual modes for establishing the observed three types of collective synchronizations, were identified in terms of an information circulation analysis.

We observed self-formations of multiple lasing channels and two-dimensional lasing patterns consisting of composite local modes having different lasing frequencies in a laser-diode-pumped wide-aperture thin-slice solid-state laser with imperfect reflective end surfaces. Global patterns resembling higher-order Hermite-Gaussian modes or possessing N-fold rotational symmetries were experimentally shown to appear due to the standard polished surface roughness of closely spaced reflective ends and nonlinear modal interactions.

We demonstrate real-time two-channel self-mixing laser-Doppler measurement with extreme optical sensitivity using a laser-diode-pumped thin-slice LiNdP4O12 laser. Successful carrier-frequency-division-multiplexed two-channel operations are realized by using one laser, two sets of optical frequency shifters, and a two-channel frequency-modulated-wave demodulation circuit. Simultaneous independent measurements of vibrations of speakers and averaged motions of small Brownian particles in different scattering cells are demonstrated. Self-mixing photon correlation spectroscopy of particle size distributions is also discussed.

We investigated chaotic dynamics in a microchip three-mode solid-state laser subjected to frequency-shifted optical feedback. When the frequency shift was tuned to harmonic frequencies of the relaxation oscillation, a bifurcation from a periodic sustained relaxation oscillation ("soft-mode") state to a chaotic spiking ("hard-mode") state via a chaotic itinerancy was observed as the feedback intensity was increased. Dynamic characterizations of modal interplay and self-induced switching between the soft- and hard-mode chaotic states over times (i.e., chaotic itinerancy) were carried out by the information circulation analysis and joint time-frequency analysis of long-term experimental time series. Drastic changes in information transfer rates among oscillating modes and occasional frequency locking among periodicities of two chaotic states associated with switchings were identified in chaotic itinerancy. Essential dynamical behaviors were reproduced by numerical simulation.

We investigated self-induced pulsations in a globally-coupled microchip multimode solid-state laser operating on a Lambda transition. A variety of dynamic states, featuring locking of pulsation frequencies, multidimensional quasiperiodic, and chaotic pulsations, induced by nonlinear modal interactions were observed depending on the number of oscillating modes. The underlying modal interplay was characterized in terms of the dynamic statistical quantity of information circulations. Mode grouping and information sender-receiver-mediator relationships established among mode groups, i.e., "information networks," were identified. Observed dynamic states were reproduced by numerical simulation of a model equation and each dynamic state was shown to create its own information network.

We observed three types of collective chaos synchronization featuring phase, generalized and lag synchronization among pairs of modes for different pumping conditions in a three‐mode solid‐state laser subjected to self‐mixing modulations. The direction of information flow among modes formed in different collective synchronizations was characterized by information circulation analysis of the experimental time series. The combined effect of self‐mixing modulations and coherent delayed optical feedback has been investigated experimentally and random switching between stable and collective synchronization states has been demonstrated.

We observed complicated emission patterns consisting of many transverse modes and associated intensity pulsations at beat frequencies between some pairs of transverse eigenmodes in a solid‐state thin slice laser with laser‐diode asymmetric end‐pumping. The dependence of transverse patterns on pump power and crystal rotation has been demonstrated. The pump‐power dependent pulsation frequency and the resonant excitation of chaotic oscillation have been observed. The interference among non‐orthogonal transverse eigenmode fields, which are formed in a thin‐slice Fabry‐Perot cavity possessing an asymmetric gradient potential for optical waves, is shown to result in intensity modulations.

This paper demonstrates self-induced antiphase pulsations featuring three-frequency locking, quasiperiodic oscillations (i.e., motions on a 3-torus) in a three-mode microchip solid-state laser operating on a double-/spl Lambda/ transition. The origin of dynamical instabilities attributes to enhanced nonlinear stimulated absorption due to interference of lower-level atoms in a microchip laser which has a shorter photon lifetime than a fluorescence lifetime of lower-levels.

Summary form only given. Quantum interference in a three-level atomic system with two fields operating in a /spl Lambda/ or V scheme has attracted much attention as a mechanism for the mediation of interactions between light and matter. Amplification and even laser-behavior without a population inversion can be produced by such a system. Kozyreff and Pandel have recently shown analytically and numerically that atomic interference in a microchip laser with a population inversion operating on a /spl Lambda/-transition should result in antiphase pulsations in the vicinity of the Hopf bifurcation point. The phenomenon has been observed in a LiNdP/sub 4/O/sub 12/ (LNP) laser operating on a /spl Lambda/-scheme consisting of /sup 4/F/sub 3/2/(1)/spl rarr//sup 4/I/sub 11/2/(2,3) transitions in a limited pump power region. This paper outlines our demonstration of peculiar large-amplitude periodic pulsations in an intracavity frequency-doubled microchip LNP laser operating on a /spl Lambda/-transition and contains a theoretical confirmation of the mechanism for these pulsations.

We observed complicated emission patterns consisting of different transverse modes and associated intensity pulsations at beat frequencies between pairs of transverse eigenmodes in a solid-state thin-slice Fabry-Perot laser with asymmetric end-pumping. The dependence of transverse patterns and pulsation frequencies on pump power has been demonstrated. The interference among nonorthogonal transverse eigenmodes, which are formed in a deformed Fabry-Perot microcavity possessing an asymmetric, gradient refractive-index potential for optical waves, is proposed for explaining observed instabilities. Intensity modulations have been remarkably reproduced by numerical simulations of model equations.

A two-mode solid-state laser subjected to a delayed optical feedback is studied. Simultaneous random switchings between stable and chaotic antiphase spiking oscillations featuring the establishment of causal (drive response) relationships among modes have been demonstrated by a proposed information circulation analysis of an experimental time series. The observed phenomenon has been well reproduced by numerical simulations of two-mode laser equations with uncorrelated modal phase fluctuations.

A kind of chaotic oscillations featuring random switching between sustained relaxation oscillations (RO) and spiking oscillations (SO) has been demonstrated in lasers with frequency-shifted feedback. The presence of stochastic frequency locking between two periodicities of RO and SO motions and selective quantum-noise-induced ordering of chaotic spiking oscillations is demonstrated theoretically and experimentally.

We demonstrate the breakup of spatial-polarization entangled lasing patterns, which possess vector phase singularities, and the resultant dynamic instabilities featuring chaotic oscillations. The frequency splitting between a pair of Ince-Gauss (IG) lasing modes, originally forming a coherent entanglement state, and a self-excited additional nonorthogonal IG mode through a new class of transverse effect of self-injection pattern seeding, is shown to result in modal-interference-induced modulation at the beat frequency, leading to chaotic oscillations.

This study investigated the input–output characteristics of a laser-diode-end-pumped microchip Nd:GdVO4 laser under different pump-beam focusing conditions by varying the magnifications of the microscope objective lenses and pump-beam positions on a chip. Dual-polarization oscillations were generated in the entire pump region using pumping conditions associated with different temperature gradients.

The overall dynamics of Brownian particles suspended in water were captured with high time resolution by using a self-mixing thin-slice solid-state laser. The net motion of an ensemble of many particles moving in the small imaging field observed at given time intervals was found to be represented by Brownian motions of an effective medium obeying the Ornstein–Uhlenbeck process, whose physical parameters have scaling relations with those of a real turbid medium. An approach toward measuring particle diffusion constants is described.

Dual-polarization oscillations (DPO) on different transitions have been observed for the first time in a mirror-coated thin-slice Nd:GdVO(4) laser possessing a large fluorescence anisotropy with laser-diode (LD) pumping. Oscillation spectra, input-output characteristics, pump-dependent pattern formations and noise power spectra are studied experimentally. Simultaneous oscillations of orthogonally-polarized different (higher-order) transverse modes and the resultant violation of inherent antiphase dynamics in multimode lasers have been demonstrated. The experimental results have been explained in terms of the reduced three-dimensional cross-saturation of population inversions among orthogonally-polarized modes peculiar to LD-pumped wide-aperture anisotropic lasers, in which a pumped area is larger than a lasing beam diameter.

The authors propose a coupled spatially distributed local-mode laser model for understanding self-induced high-speed modulations in Nd:YAG ceramic lasers with laser-diode end pumping, which critically depend on pump positions. In addition to complicated high-speed modulations, quasiperiodic and chaotic relaxation oscillations have been demonstrated experimentally and reproduced by numerical simulation of the model of coupled local-mode lasers. Q-switching-like periodic spiking pulsations have been also observed and reproduced numerically by assuming saturable absorber type of inclusions in grain boundaries.

We found an abrupt transverse-mode transition from an irregular to a Gaussian lasing pattern or billiard-like lasing patterns with increasing the pump power in a laser-diode-pumped thin-slice Nd:GdVO4 laser with coated dielectric mirrors on both ends. A variety of irregular stationary lasing patterns were observed with a slight change in the pump position due to polished crystal surface roughness and ineffective lasing field confinement in transverse directions. A physical interpretation for observed irregular patterns was given in terms of wave formations in gradient refractive index lens with undulated reflective end surfaces. Intensity modulation of the laser, resulting from the interference of non-orthogonal transverse mode pairs embedded in the irregular lasing patterns, and associated rich chaotic pulsations were demonstrated. Observed nonlinear dynamics were well reproduced by numerical simulation.

This work reports on a beam quality and dynamic behaviors of a mirror-coated highly-doped YAG (Y(3)Al(5)O(12)) microchip ceramic laser possessing an increased number of grain boundaries. The degradation of beam quality factor in transverse patterns due to spatial inhomogeneity across the beam, multiple split-mode operations, violation of antiphase dynamics and high-speed intensity modulations due to the interference between non-orthogonal transverse modes were observed in a laser-diode end-pumping scheme.

Nanometre vibration measurement of an audio speaker and a highly sensitive sound reproduction experiment have been successfully demonstrated by a self-aligned optical feedback vibrometry technique using the self-mixing modulation effect in a laser-diode-pumped microchip solid-state laser. By applying nanometre vibrations to the speaker, which produced nearly inaudible music below 20 dB (200 µPa) sound pressure level, we could reproduce clear sound in real time by the use of a simple frequency modulated wave demodulation circuit with a -120 dB light-intensity feedback ratio.

We applied laser-diode sheetlike end pumping to a multimode Nd:YVO(4) laser and observed high-speed (400-MHz) modulation of the intensity of chaotic pulsation near 1 MHz. The frequencies of modulation were the beat frequencies for pairs of closely spaced lasing modes. Asymmetric optical confinement and the resultant modal interference are shown to lead to oval-hollow-mode operation in which modal beat notes induce high-speed modulation, the frequency range of which is 2 orders of magnitude higher than the intrinsic relaxation oscillation frequency. Good numerical reproduction of the observed chaotic pulsations and their high-speed modulation was obtained with model equations in which such effects as nonlinear gain coupling among modes and field interference between pairs of modes were included. High-speed pulsations in nonchaotic lasers were also demonstrated.

Dynamical instability, chaotic pulsations, and generalized bistability have been observed in a laser-diode-pumped microchip Nd:YAG laser operating in a double transition scheme in which lasing occurs on two transitions with overlapping gain profiles, F3/242→I11/243 and F3/241→I11/242, and simultaneously involves excited Nd atoms from different sublevels of the upper manifold. The modeling of the experimental results requires rate equations that include cross-gain coupling among oscillating modes that belong to different transitions whose population inversion densities are determined by the Boltzmann distribution.

The nonlinear dynamics of lasers with frequency-shifted delayed feedback are investigated. Resonant excitation of sustained relaxation oscillations by harmonic resonance is demonstrated. Self-induced switching between sustained relaxation oscillation and spiking oscillation is observed as the feedback coefficient is increased. Observed instabilities are well reproduced by numerical simulations of proposed model equations. A statistical analysis of this switching phenomenon is carried out numerically, and the results indicate that an inverse-power relation with the feedback coefficient determines the periods over which the system dwells in its relaxation-oscillation state.

Self-induced Q-switching-type spiking oscillations and associated instabilities have been observed in a free-running laser-diode-pumped microchip Nd:YVO4 laser operating in three-mode regimes, and dynamical characterizations of spiking pulsations have been demonstrated. Observed instabilities have been reproduced by numerical simulations of the model equations including intensity-dependent cross-gain coupling in three-mode lasers.