bluuebunny/crossref_metadata_2025 huggingface dataset:
Instabilities in Nonlinear-Optical Systems Due to an Abrupt Change of Parameters
Authors: Ning C. Z. , Haken H.
Published: February 2023

Instabilities due to an abrupt change of parameters are considered in terms of general dynamical systems. A definition of the threshold for such instability is proposed by using the language of attractors and their basins. An analytically solvable one­dimensional model is constructed to illustrate this definition. As simple examples in optical systems, the Lorenz-Haken model with a step-type pump and the single-mode optical bistable systems with the input field changed in a form of a jump are considered. In the former example this consideration leads to a much lower pulse threshold than the well-known second threshold for the bad cavity case, whereas in the good cavity case for which there is no instability of the lasing state, pulsing motions can be observed using this method. In the latter example, we show the existence of the anomalous switching for the purely absorptive case as well, in contrast to the earlier assertions. The switchings with and without critical slowing-down are revealed and explained. Application of this study are proposed as a means to experimentally observe various pulsations including chaos in both systems whose observation is otherwise impossible or requires high pump or external field values.
Dynamic Instabilities in Optically Pumped Lasers with Linearly Polarized Pump and Generated Laser Beams
Authors: Corbalán R. , Arjona M. , Laguarta F. , Pujol J. , Vilaseca R.
Published: February 2023

We analyze the influence of light polari­zation on the dynamics of coherently pumped lasers using a single-mode ring laser model which considers a homogeneously broadened four-level medium. As typical in FIR laser experiments, we consider linearly polarized pump and generated laser beams. Phase diagrams as a function of cavity detuning and amplitude of the resonant pump field have been obtained, which show domains of stationary, oscillatory and chaotic output. We show that the laser is much more stable when the polarizations of the pump and generated laser beams are parallel than when they are orthogonal. In the later case the laser exhibits Lorenz-like dynamics at a reduced instability pump threshold.
Experimental Evidence of Quasi-Periodicity Route to Chaos in a CO2 Laser with Delayed Feedback
Authors: Arecchi F. T. , Giacomelli G. , Lapucci A. , Meucci R.
Published: February 2023

In the past few years great efforts have been devoted to the understanding of dissipative systems ruled by nonlinear delayed feedbacks.
Dynamics of a Class B Bidirectional Ring Laser: Linear and Nonlinear Scattering Competition and Cavity Nonreciprocity Effect
Authors: Khandokhin P. A. , Khanin Ya. I. , Koryukin I. V.
Published: February 2023

Competition of two instability mechanisms results in chaotic pulsations and occurrence of bistability in a bidirectional ring laser. Phase non-reciprocity affects the location of bifurcation boundaries and the frequency dynamics.
Response to Modulation of Parameters in the Vibro-Rotational Model for a CO2 Laser
Authors: Gao J.Y. , Zhang H.Z.
Published: February 2023

The effect of detuning of the laser cavity from resonance with the material transition frequency on the response of a single mode laser to modulation of parameters has been investigated for the two-level rate equation model [1,2]. However, in order to satisfactorily compare the results of this type of analysis with experiments on a CO2 laser, it has been shown that a more sophisticated model [3] that incorporates the vibrational and rotation level structure of the CO2 molecule must be used.
Multistability and Steady States in a Laser with a Saturable Absorber
Authors: Grigoryeva E. V. , Kotomtseva L. A. , Samson A. M.
Published: February 2023

Multistability and instabilities in single- and multimode lasers with, a saturable absorber are considered theoretically. Regular and chaotic regimes are described. The structure of chaotic states is also analyzed.
Theoretical Analysis of the Dynamics in a Laser with Lagging Negative Feedback
Authors: Grigoryeva E. V. , Loiko N. A. , Samson A. M. , Kashchenko S. A.
Published: February 2023

This paper is devoted to the investigation of the dynamics in a laser with a nonlinear element whose loss depends on the laser intensity at a preceding instance of time determined by the length of the additional feedback loop. The phenomenon of multistability and the structure of the set of solutions are analytically described. The regions of the existence and the initial conditions at which their realization is possible have been determined. The possibility of the system’s complicated behaviour is shown and the sequence of bifurcations leading to chaos has been found.
New Asymptotic Theory for the Periodically Forced Laser
Authors: Erneux Thomas , Schwartz Ira B.
Published: February 2023

Sustained relaxation oscillations and irregular spiking have been observed in many periodically modulated lasers [2]. These observations have been substantiated numerically by recent studies of the laser rate equations [3,4]. In this paper, we propose a new asymptotic analysis of the laser equations which assumes that the laser oscillations correspond to relaxation oscillations. We identify a large parameter and construct these periodic solutions using singular perturbation techniques. We obtain the equations for the Poincare map and determine the first period doubling bifurcation.
Multimode Instability in a CO2 Laser with Saturable Absorber
Authors: Tanii Kazuhito , Tachikawa Maki , Hong Feng-Lei , Tohei Takehisa , Shimizu Tadao
Published: February 2023

Instabilities in the two-mode oscillation of a CO2 laser with a saturable absorber are studied both experimentally and theoretically. Depending on the passive Q-switching behavior in one of the modes, exclusive mode exchange and simultaneous two-mode oscillation are observed. These instabilities are reproduced with the rate-equation model in which detailed vibrational relaxation mechanism and spatial mode coupling are considered. The rate-equation analysis predicts chaotic two-mode oscillation. Structure of the strange attractor of the two-mode chaos is compared with that in the single-mode case through the return map method and the fractal dimension measurement.
Comparison Between Two-Level and Inhomogeneously Broadened FIR Three-Level Laser Dynamics
Authors: Vilaseca R. , Roldán E. , de Valcárcel G. J. , Corbalán R.
Published: February 2023

The Doppler-broadened FIR three-level laser equations and solutions are analysed and compared to those of a Lorenz-Haken laser. The influence of velocity averaging and optical pumping is found to be large, but it does not give rise to strong new features on the dynamic behavior, which remains similar to that of a Lorenz-Haken laser with effective parameters. Noticeable differences, however, are found between both classes of lasers.
Decay of the Intensity Correlation Function for Dye Lasers with White Gain Noise
Authors: Pesquera L. , Noriega J. M. , Rodríguez M. A.
Published: February 2023

We consider a single-mode dye laser model incorporating pump white noise through gain-parameter fluctuations. The relaxation function C(t) is analyzed with the use of a method based on the combination of the low and high frequency expansions of the Laplace transform of C(t). The correlation function is approximated by a superposition of two decaying exponentials. It is found that the intensity correlation function does not show two separated time scales as observed experimentally.
Spatiotemporal Instabilities in a Two-Level Medium Interacting with Counterpropagating Waves
Authors: LeBerre M. , Ressayre E. , Tallet A.
Published: February 2023

The threshold of the static and periodic instabilities of the feedback mirror experiment is shown to be well reproduced by taking into account the non zero homogeneous response time of the medium, together with the transverse structure of the field. The phase conjugation operation is discussed.
New Mechanism of Intrinsic Bistability of the Optical Media under Repetitive Pulse Excitation
Authors: Ghiner A. V. , Surdutovich G. I.
Published: February 2023

A new type of intrinsic bistability is proposed when usually "non-bistable" nonlinear medium shows bistability under action of a time-dependent input signal. A strict criterion for observation of such a bistability is deduced. It depends on the shape of the temporal response of the nonlinear medium under action of a separate rectangular input pulse.
Mirrorless Optical Bistability of Thin Layer with Resonant Two-Level Atoms in Ultrashort Light Pulse Field
Authors: Malyshev V. A. , Trifonov E. D. , Zaitsev A. I. , Benedict M. G.
Published: February 2023

We investigate the problem of resonant re flection and transmission of an ultrashort light pulse passing through a medium consisting of two-level atoms. We show that for a thin layer it is important to take into account the difference between the external macroscopic field and the field acting on the individual atoms within the medium. The local field correction leads to an inversion dependent resonant frequency. In thin layers this generates a new mechanism of nonlinear transparency induced by the dynamical frequency shift. When the excitation frequency is larger than the original resonant frequency, then the transmission of the layer exhibits bistable behavior.
Demonstration of Regenerative Oscillation Using Optoelectronic Bistable Circuits
Authors: Li C. F. , Wang R. , Zhang L. , Liu S.
Published: February 2023

Optical instability is observed in an optoelectronic bistable circuit having two feedback signals with different time constants. Steady optical square-wave pulses have been obtained. The experimental results are helpful to the understanding of dynamic process in hybrid optical bistable devices.
Optical Bistability in a Bimode Laser Due to Coherent Bleaching of a Three-Level Absorber
Authors: Kocharovskaya Olga , Koryukin I. V.
Published: February 2023

Due to the coherent bleaching of a three-level absorber the optical bi stability in a two-mode laser is possible even in the absence of the absorber saturation.
Generic Properties of Periodic Attractors in Two-Photon Processes
Authors: Mandel Paul , Pettiaux N. P. , Kaige Wang , Galatola P. , Lugiato L. A.
Published: February 2023

We show that the periodic attractors occurring in two-photon processes displaying a phase instability have common properties including a domain of hysteresis. The case of degenerate four-wave mixing includes also some nongeneric attractors which exhibit a Berry phase phenomenon.
Chaos in Intracavity Second Harmonic Generation
Authors: James Glenn E. , Harrell Evans M. , Bracikowski Christopher , Wiesenfeld Kurt , Roy Rajarshi
Published: February 2023

Diode laser pumped Nd: YAG (yttrium aluminum garnet) lasers can generate a substantial amount of green output with an intracavity nonlinear crystal such as potassium titanyl phosphate (KTP) (Fig. 1). Large irregular fluctuations of the output have very often been observed,1 which make it difficult to utilize these lasers in applications requiring stability. Oka and Kubota have shown that a quarter wave plate can be used to stabilize the output of a laser with two orthogonally polarized modes.2 We have previously analyzed the nonlinear dynamical behavior of the laser model used by Baer.1 A thorough stability analysis of this model was carried out by Mandel and WuA.4,5
Transient Evolution, Stability for Disturbances, Multistability, and Chaos of Transverse Spatial Structures of a Lightwave Propagating in a Ring System with Inertial Nonlinear Medium
Authors: Komarov K. P.
Published: February 2023

In this paper we present our theoretical researches on shaping and stability of the transverse spatial radiation distribution in nonlinear systems. The analysis is based on constructing the Lyapunov functionals. We have determined the conditions for stable self-channelling of a light wave, its unlimited spreading, complication and chaos of transverse spatial distribution of radiation. It is demonstrated that a multithreshold self-channelling arises in nonlinear systems with several different focusing nonlinearities. The multistability phenomenon is discovered in the case of combination of focusing and defocusing nonlinea­rities.
Systematic Investigation of Chaotic Regimes in a Model for the Laser with a Saturable Absorber
Authors: Zambon Bruno
Published: February 2023

A systematic analysis for chaotic behaviour in a popular LSA theoretical model has been carried out. A crucial parameter is the relative saturability of the absorber. We find that theoretical parameter values disagree with those usually believed to be attainable in real experiments. We also propose a new mechanism for the emergence of chaotic signals in this theoretical model and study the influence of spontaneous emission noise.
Degenerate Period Doubling Route to Chaos in the Casperson-Instability Simplified Model
Authors: Meziane B.
Published: February 2023

A low-dimensional model of the "Casperson Instability" showing regular self-pulsing behavior in the 4D space is presented. The projection on to the 3D subspace exhibits period doubling bifurcations to chaos with increasing the level of excitation.
Optical Chaos Due to Multiwave Propagation in an Absorptive Vapor
Authors: Crenshaw M. E. , Bowden C. M.
Published: February 2023

Numerical propagation of a nearly resonant pump laser and a weak probe laser in a model vapor of two-level atoms demonstrates an evolution to chaos with propagation distance. We show that the maximum Lyapunov exponent increases with distance of propagation into the medium.
Periodic and Chaotic Beam Scanning in Semiconductor Laser Arrays
Authors: Winful Herbert G. , Wang Shawe-Shiuan , DeFreez Richard K.
Published: February 2023

A breakdown of phase-locking in an array of coupled semiconductor lasers leads to periodic and chaotic steering of the far-field beam position.
Experimental Characterization of the Picosecond Spatiotemporal Properties of Coherent Semiconductor Laser Arrays
Authors: DeFreez R. K. , Yu N. , Bossert D. J. , Felisky M. , Wilson G. A. , Elliott R. A. , Winful H. G. , Evans G. A. , Carlson N. W. , Amantea R.
Published: February 2023

The spatio-temporal evolution of various coherent semiconductor laser arrays has been observed with streak cameras. Laser device parameters necessary for modeling have been determined.
Spontaneous Periodic and Chaotic Beam Scanning in Semiconductor Laser Arrays
Authors: Winful Herbert G. , Wang Shawe-Shiuan , DcFreez Richard K.
Published: February 2023

A breakdown of phase-locking in an array of coupled semiconductor lasers leads to periodic and chaotic steering of the far-field beam position.
Counterpropagation in Kerr Media: Combined Diffractive–Dispersive Instabilities
Authors: Firth W. J. , Penman C.
Published: February 2023

Instabilities arising from counterpropagation in Kerr Media are analysed. Diffractive (transverse) and dispersive effects are combined in a unified framework. Analogous results for polarisation effects are presented.
Supercritical and Subcritical Transverse-Mode Instabilities in a Laser
Authors: Lin H. , Abraham N. B.
Published: February 2023

Numerical evidence is reported of supercritical and subcritical bifurcations on the spatial instability boundary for transverse mode dynamics in a laser with a rectangular cavity.
Spontaneous Spatial Structures in Simple Systems and Defocusing Media
Authors: McDonald G. S. , Stephen K. , Firth W. J.
Published: February 2023

Feedback systems in which the nonlinearity is lumped into a thin slice, while the propagation is free-space and thus linear, are simple to model and analyse. We present results for static and dynamic pattern formation in single-mirror and cavity systems of this type.
Nonlinear Dynamics of Raman Lasers
Authors: Harrison R.G. , Lu Weiping
Published: February 2023

It has recently been shown that single mode Raman lasers are reducible to a simple mathematical description [1] similar to that of the detuned Haken-Lorenz model but for which operating conditions are considerably relaxed. As such they provide excellent opportunity for quantitative tests of nonlinear dynamics. In particular instabilities prevalent close to optimum conditions for lasing, are accompanied by bistable features and exhibit period doubling routes to chaos. These findings are in accord with earlier experimental findings [2].
First Experimental and Theoretical Agreement for cw Conical Emission
Authors: Grantham J. W. , Valley J. F. , Khitrova G. , Gibbs H. M. , Jiajin Xu
Published: February 2023

A detailed comparison is made with good agreement between experimental observations and numerical computations of near-field spatial profiles, far-field spatial profiles, and frequency spectra. Essential to this good agreement is the transverse and Doppler effects that were included in the theory.
Transverse Modulational Instability of Counterpropagating Light Waves
Authors: Luther G. G. , McKinstrie C. J. , Gaeta A. L.
Published: February 2023

The transverse modulational instability (TMI) of two counterpropagating light waves in finite Kerr media is modeled by a pair of coupled nonlinear Schroedinger equations. This model predicts that transverse modulations in the wave amplitudes can be either convectively or absolutely unstable, in both self-focusing and self-defocusing media. In general, both frequency- and wavenumber-shifted sideband modes can grow if the wave intensities are unequal.
New Class of Ordered Structures in a Paul Trap: Classically Stable Clusters of Positively and Negatively Charged Particles
Authors: Blümel R.
Published: February 2023

We show that in the pseudo-potential approximation stable clusters of ions of both signs of charge can exist in a Paul trap.
Photon-Counting Statistics of the Degenerate Parametric Oscillator in the Transient Regime
Authors: Vyas Reeta , DeBrito A. L.
Published: February 2023

Photon statistics of a subthreshold degenerate parametric oscillator (DPO) are studied in the transient regime and compared with the results for steady state DPO.
Effect of Intraband Gain Saturation on Semiconductor Laser Dynamics
Authors: Agrawal Govind P.
Published: February 2023

Intraband gain saturation is a nonlinear phenomenon occurring in semiconductor lasers when the intracavity intensity is high enough to significantly modify the intraband occupation probabilities of charged carriers. The nonperturbative solution of the single-mode density-matrix equations is used to obtain the intensity-dependent changes in the gain and the refractive index of the optical mode. The effect of such gain and index nonlinearities is studied by solving a set of modified rate equations that incorporate gain saturation due to both the interband and the intraband processes. The results show how the modulation response and the noise characteristics such as the laser linewidth are affected by a finite intraband relaxation time in semiconductor lasers.
Optical Bistability in Thin Silicon Thermo-optical SEEDs at Wavelengths of 1.06 um and 514 nm
Authors: Zhai Hongchen , Jäger Dieter
Published: February 2023

We present a theoretical analysis and experimental results of thermally induced optical bistability in thin thermooptical silicon SEEDs at 1.06µm and 514nm. The theoretical and experimental results reveal that bistability is due to increasing absorption and thermally induced change of the optical and electrical parameters of the material, largely enhanced by the self-electrooptic effect.
Dynamic Model for Optical Bistability in Multiple Quantum-Well Structures
Authors: Bava G. P. , Debernadri P. , Lugiato L. A. , Castelli F.
Published: February 2023

We formulate a set of dynamical equations, which govern the dynamical evolution of optically bistable systems based on Multiple Quantum Well Structures, in conditions of quasi-resonance with an excitonic line. The steady state diagrams indicate the possibility of bistability in this system.
Multiwave Mixing in Semiconductor Lasers Through Pump Modulation
Authors: McCall M. W.
Published: February 2023

Enhancements in conjugate reflectivity of two-three orders of magnitude are predicted via external pump modulation in semiconductor lasers. Pump depletion effects are also considered numerically.
The Influence of Noise and of Spatio-Temporal Nonuniformity on the Evolution of Optically Nonlinear Systems
Authors: Ißler H. , Apanasevich S. , Grohs J. , Lyakhnovich A. , Kuball M. , Steffen J. , Klingshirn C.
Published: February 2023

The investigation of noise induced switching processes in bistable systems is a field of active research [1] due to the omnipresence of noise in real systems. In this paper we extend the research on the influence of noise on the self oscillations of a hybrid ring resonator containing an optically nonlinear or even bistable element. The optically nonlinear element is a ZnSe interference filter showing thermally induced nonlinear refraction [2], The quasistatic input-output characteristics (IOC) of the filter in reflection and transmission depend on the initial detuning of the Fabry-Perot and by changing this parameter it is possible to obtain bistable as well as monostable but strongly nonlinear behaviour. This element is incorporated in reflection mode into a ring resonator with long round trip time compared to the thermal relaxation time of the nonlinearity. The resonator is a hybrid one consisting of a photodiode transforming the light intensity reflected by the filter into a voltage signal which is delayed electronically and fed back to an electro optical modulator controlling the light falling onto the sample.
Space-time representation of a delayed dynamical system
Authors: Arecchi F.T. , Giacomelli G. , Lapucci A. , Meucci R.
Published: February 2023

In nonlinear optics the transition to high dimensional chaos is realized either by letting many modes to compete in an optical resonator [1] or by introducing a delayed feedback [2], Whenever data can be organized on a two dimensional domain, some hidden features of the complex dynamics appear explicitely as suitable patterns.
Nonlinear Effects in a Ring Resonator
Authors: Dunlop A. M. , Heatley D. R. , Firth W. J.
Published: February 2023

There has been much recent interest in using a nonlinear lensing element combined with an aperture to produce a saturable absorber for laser modelocking. [1, 2] This Kerr-lens-modelocking (KLM) technique normally uses the gain medium as the nonlinear element, but lasers with separate gain and nonlinear elements have also been demonstrated,[3] allowing application of this method to lasers in which the gain medium does not provide adequate self-focusing or gain-guiding. The analysis we have carried out seems to indicate that the nonlinear element need not be self-focusing; in fact, it appears that a larger effect can be obtained by a self-defocusing element. Additionally, in the ring resonator geometry we consider, the intensity-dependent lensing leads naturally to unidirectional propagation for continuous-wave lasing.
Instability and Chaos in Laser Oscillation between Highly Excited Molecular Vibrational States
Authors: Hong Feng-Lei , Tachikawa Maki , Sugawara Toshiki , Tohei Takehisa , Shimizu Tadao
Published: February 2023

Dynamic behavior of the laser oscillation has been extensively studied as a paradigm of nonlinear dynamics. Mechanism of laser instability is strongly correlated with detailed relaxation and excitation dynamics in the laser medium. Study of laser instability may open a way to precise measurement of those elementary atomic and molecular processes.
Quasi Vertical Hopf Bifurcation for the Multimode Class B Laser
Authors: Carr Thomas , Erneux Thomas
Published: February 2023

Using the rotating wave approximation, Risken and Nummedal [1] have simplified the Maxwell-Bloch laser equations for homogeneously broadened two-level atoms and have analyzed the linear stability of the uniform steady states. They have determined bifurcation points to periodic traveling wave solutions. If I denotes the intensity of the non-zero steady state and a is the spatial wave number of the traveling wave, the first bifurcation occurs at or near (I,a) = (Im,am). See Figure 1. The nonlinear problem has been first investigated by Haken and Ohno [2].
On the eigenvalues and eigenvectors of an inhomogeneously broadened single-mode laser stability problem
Authors: Toronov V.Yu. , Melnikov L.A.
Published: February 2023

Most of works devoted to the stability of inhomogeneously broadened single-mode laser (see Ref.[1] and Refs. in it) concern only the "leading" eigenvalues of corresponding linearized equations which determine the stability of the system steady states. However, in some cases information about all eigenvalues is required, for example to examine the bifurcation of the steady state [2]. The aim of the present work is to find all eigenvalues of the inhomogeneously broadened running-wave single mode laser equations, linearized at the steady state points. Additionally we have considered laser equations in the representation of corresponding eigenvectors (normal form of laser equations [2]).
From harmonic to pulsating periodic solutions in intracavity second harmonic generation
Authors: Pettiaux Nicolas , Erneux Thomas
Published: February 2023

We consider the problem of Second Harmonic Generation (SHG) inside a resonant cavity, pumped by an external laser. The elementary process that takes place in SHG is the absorption of 2 photons of frequency ω and the emission of one photon at frequency 2ω. Drummond et al[1] have shown that this problem can be modeled by two ordinary differential equations for the (complex) amplitudes of the electrical fields: where overbar means complex conjugate.
Transient behaviour of fibre optic Brillouin ring lasers
Authors: Hereth R. , Garus D. , Schliep F.
Published: February 2023

Stimulated Brillouin scattering (SBS) is the dominant non-linearity in silica optical fibres. In high­finesse all-fibre ring resonators with fibre lengths of the order of 10 m stimulated Brillouin scattering can be observed at input power levels in the range of 10 to 100 μW [1]. Above pump threshold fibre optic ring resonators show intensive laser oscillation at the Stokes wavelength and therefore are called Brillouin ring lasers (BRL). An important application of Brillouin ring lasers is the all-fibre optic ring laser gyro [2].
Tracking unstable phenomena in chaotic laser experiments: Extending regions of stability in a multimode laser
Authors: Gills Zelda , Iwata Christina , Roy Rajarshi , Schwartz Ira B. , Triandaf Ioana
Published: February 2023

Recently, experimental systems which exhibit chaos have been controlled using techniques such as OGY [1] and the related occasional proportional feedback, OPF [2]. The methods have been able to stabilize both low dimensional experiments, such as electronic circuits [2] as well as high dimensional multimode chaotic lasers [3]. Controlling a chaotic system consists of stabilizing an unstable steady state or periodic orbit by having the system perform small amplitude fluctuations about some fixed parameter value. The OPF method is implemented by choosing the fluctuations so that the system is brought closer to the unstable orbit of interest. In the OGY method, the fluctuations are chosen so that the iterates fall on the stable manifold of the unstable orbit, thus keeping the dynamics in the neighborhood of the point of interest in phase space. Both methods are clearly related [4].
Polarization Mode Switching and Bistability in Semiconductor Lasers
Authors: Klehr A. , Bärwolff A. , Berger G. , Müller R. , Voß M.
Published: February 2023

Generally, TE-mode emission (the transverse electric field is polarized parallel to the active-layer plane) is favored in unstrained semiconductor lasers in comparison with TM-mode emission (the magnetic field is polarized parallel to the active-layer plane) due to a larger reflectivity for the TE wave at the cleaved facets forming the laser cavity. The optical gain delivered from the active medium is the same for both modes, i. e., gTE = gTM = g given by g = A (N - N0) where A is the gain coefficient, N is the carrier density, and N0 denotes the carrier density required to achieve transparency, g = 0.
Factorial Dynamic Pattern Memory in Globally Coupled Lasers
Authors: Otsuka Kenju , Chern Jyh-Long
Published: February 2023

Recently, applicability of complex dynamics to information storage (memory) has been discussed in nonlinear optical systems. Spatial chaos memory was proposed in a bistable pixelsl1 and in a coupled bistable chain.2 Dynamic memory in a delayed feedback bistable system was demonstrated experimentally.3 On the other hand, Otsuka demonstrated that m
a
= (N − 1)! (N: number of oscillating modes) coexisting dynamical spatial patterns, i. e., antiphase periodic motions, can be selectively excited by applying seed signals to the modulated multimode lasers whose modes are globally coupled through spatial hole burning.4 In this paper, we discuss the detailed bifurcation scenario, featuring clustered states and chaotic itinerancy5 among destabilized clustered states. Also, factorial dynamical pattern memory associated with antiphase and clustered states as well as the effect of spontaneous emission on memory operation are demonstrated by numerical simulations.
Bifurcation to Standing and Traveling Waves in Large Laser Arrays
Authors: Li Ruo-ding , Erneux Thomas
Published: February 2023

Arrays of semiconductor diode lasers are promising devices for applications that require high optical power from a laser source (high-speed optical recording, high-speed printing, free-space communications, pumping of solid-state lasers) [1]. Experimental and numerical studies of arrays consisting of a small number of lasers have shown that they are unstable devices and may exhibit a large variety of spatio-temporal responses [2-5]. In order to control these instabilities by various external mechanisms (injection locking, periodic modulations), systematic bifurcation studies are needed. The laser equations are however stiff and accurate solutions for a large population of lasers require long computation times. Asymptotic methods based on the limit of weak coupling [6] also fail to provide simple phase equations because the semiconductor laser is not a limit cycle oscillator. We have recently reformulated the laser equations as a weakly perturbed system of coupled conservative oscillators which eliminate part of the stifness of the problem and allow an analytical study of the first Hopf bifurcation as the coupling strength is progressively increased. If N is even, the Hopf bifurcation is simple and corresponds to a transition from a nonuniform steady state to a time periodic standing wave solution [7]. However, if N is odd, bifurcation to periodic standing and traveling wave solutions are both possible. This multiple bifurcation problem is difficult analytically but can be simplified if we consider the limit N large.
Controlling Chaos
Authors: Romeiras Filipe J. , Grebogi Celso , Ott Edward , Dayawansa W. P.
Published: February 2023

It is common for systems to evolve with time in a chaotic way. In practice, however, it is often desired that chaos be avoided and/or that the system be optimized with respect to some performance criterion. Given a system which behaves chaotically, one approach might be to make some large (and possibly costly) alteration in the system which completely changes its dynamics in such a way as to achieve the desired objectives. Here we assume that this avenue is not available. Thus we address the following question: Given a chaotic system, how can we obtain improved performance and achieve a desired attracting time-periodic motion by making only small controlling temporal perturbations in an accessible system parameter.
Control and characterization of unstable stationary states
Authors: Bielawski S. , Bouazaoui M. , Derozier D. , Glorieux P.
Published: February 2023

The Nd-doped optical fiber laser (OFL) displays spontaneous oscillations when the pump power exceeds some threshold(1). This will be called hereafter the "second Hopf bifurcation" threshold of the laser since the first Hopf bifurcation corresponds to the onset of laser action.
Cascaded stimulated Brillouin scattering in high-finesse all-fibre ring resonators
Authors: Garus Dieter , Hereth Ralf
Published: February 2023

One of the most dominant nonlinear effects in single-mode fibers is stimulated Brillouin scattering (SBS). The generation of SBS in a ring resonator can be considered as a lasing action, with the Stokes output downshifted in frequency by an amount equal to the Brillouin frequency. In the stationary case stimulated Brillouin scattering in a length of optical fiber can be described by the following partial differential equations for the slowly varying complex amplitudes of the pump wave E
p
and the backscattered first order Stokes wave E
B1
, with the wave amplitudes E
i
related to the intensities I
i
by I
i
= |E
i
|2 (i=p,B1) [1]: (1) In a ring resonator geometry as depicted in Fig. 1 the wave amplitudes at the ports of the directional coupler obey the relations [2] (2) where

V
k
2

is the coupler intensity radiation loss, K is the field coupling coefficient, and T is the field transmission coefficient.
Transverse Modes Of Microchip Solid State Lasers
Authors: Harkness G.K. , Firth W.J.
Published: February 2023

In recent years there has been much research into lasers using solid state materials such as Nd:YAG, Nd:YLF and LNP as their active media [1]. Microchip solid state lasers use a thin slab of these materials in a short cavity to ensure single longitudinal mode operation. They may be pumped by a diode laser and they produce single transverse, single longitudinal mode output over a large range of pump powers. It is useful to be able to model the spatial and temporal behaviour of these lasers with a view to design optimisation.
Static and Dynamic Optical Bistability in Fabry-Pérot and Distributed Feedback Resonators with Quantum Well structures
Authors: Castelli F. , Lugiato L.A. , Bava G.P. , Debernardi P.
Published: February 2023

Recently relevant results on optical bistability in Multiple Quantum Well (MQW) structures at room temperature have been reported [1].

In this paper a rather complete model for optical bistability in Fabry-Pérot (FP) and Distributed Feedback devices (DFB) including a MQW structure is described. It includes the optical dielectric response of the MQW structure, the static output power vs. input power and finally the dynamical behaviour.
Dynamical aspects of polarization induced switching phenomena in diffusively nonlinear Fabry-Perot resonators
Authors: Danckaert J. , Thienpont H. , Veretennicoff I.
Published: February 2023

The combination of polarization optics and nonlinear optics gives rise to interesting new physical phenomena1. In the work presented here we will focus on planar resonators with a nonlinearity of diffusive nature, such as the nonlinear Fabry-Perot resonator (NLFP). There are two ways to display the role of polarization in the bistable response of such a device. First, in a configuration where the light wave is obliquely incident on the resonator, as the interface's reflectances depend on the polarization state of the incident light. Second, in a configuration where the beam impinges normally on a resonator now filled with an anisotropic material, as a phase shift is induced between the linear Airy resonances of the two polarization eigenmodes. In this paper, two dynamic theories for planar resonators are presented for both configurations mentioned above, for an arbitrary polarization of the incident plane wave.
Opto-Thermal Bistable Cavities with Localized Absorption under Modulated Excitation
Authors: Farjas Jordi , Boixader Francesc , Orriols Gaspar , Massaneda Josep , Pi Francese
Published: February 2023

Opto-Thermal Bistability with Localized Absorption (BOITAL) deals with etalons in which the light absorption occurs in one of the reflective coatings while the thermo-optic spacer is transparent. The separation of functions within the bistable system permits an independent and, therefore, easier optimisation of both functions and also introduces the possibility of complex structures with more than one absorbing film and/or with various layers of different thermo-optic materials [1]. These kinds of structures possess composite feedback mechanisms and may be used to achieve different logic functions and to study dynamic instabilities in passive optical systems [2].
The effect of initial phase factor on the properties of an electro-optical bistable system
Authors: Zhiren Zheng , Jinyue Gao
Published: February 2023

The hybrid bistable system with a delay in the feedback loop, which was originally proposed and studied by Ikeda[1], has been widely investigated[2,3,4] as this system plays many common instability behaviours of nonlinear dynamical systems. There is an initial phase factor in the equation describing the system dynamics as there are for most other bistable systems, which is equivalent to the bias in the device. We report the important role played by this phase factor in the bistability and instability behaviours, especially when the input intensity of the system is modulated harmonically.
Symmetry Breaking and Vortices in a Sodium-filled Fabry-Pérot Resonator
Authors: Hoffer L.M. , Lippi G.L. , Nalik J. , Vorgerd Ch. , Lange W.
Published: February 2023

In the last few years it has been found, both theoretically and experimentally, that interactions among different transverse modes may produce complicated patterns, vortices and spatiotemporal chaos in active and passive optical systems [1]. In a passive nonlinear resonator with high Fresnel number but where only a few modes are selectively excited, symmetry broken patterns and vortices have been observed. We find that, in our system, the total number of vortices in any one pattern is generally small and the total topological charge is zero. Among the symmetry broken structures observed in our experiments, we find a recurrent sequence that is similar to one particular sequence observed in an experiment performed in a laser.
Optical Vortices and Dark Spatial Solitons
Authors: Weiss C. O. , Staliunas K.
Published: February 2023

Since Zacharov and Shabat integrated one-dimensional Nonlinear Schrödinger Equation (1D NLSE) and found solitons [1,2], much have been done in one-dimensional, but very little in two-dimensional soliton physics. The integrability of 2D NLSE as well as existence of solitons in it is under the question to the time.
Role of nonlinear dispersion on the dynamics of modulational instability in Kerr media
Authors: De Angelis Costantino , Nalesso Gianfranco , Santagiustina Marco
Published: February 2023

Modulational instability (MI) refers to the growth of weak modulations of a plane wave in dispersive (or diffractive) nonlinear media. The interest for MI in optics, stems from its possible applications in optical communication and signal processing systems. For example, in optical fibers, ultrafast pulse generation [1] and all-optical switching [2] have already been proposed and exploited.
Optical Bistability by Cascading χ(2) in Prism or Grating Couplers
Authors: Reinisch R. , Popov E. , Nevière M.
Published: February 2023

The features of second harmonic generation (SHG) in the depleted pump regime are known since the early works of N. Bloembergen et al.[1]. For some years, this kind of SHG has attracted a great deal of interest[2]. The reason is as follows : in the presence of depletion of the fundamental frequency field together with a small phase mismatch, this kind of interaction can lead to a nonlinear (NL) phase shift of several π[2]. There lies the interest of such a process.
Three-Dimensional Numerical Modelling of the Second-Order Cascade Effect in a Semiconductor RIB Waveguide using Parallel Processing
Authors: Masoudi H. M. , Arnold J. M.
Published: February 2023

The second-order cascade effect is a very promising means of generating large intensity-dependent self-induced phase changes in an optical field propagating in a waveguide [1,2,3]. In practice this phenomenon must be implemented in a waveguide environment with quasi-phase-matching (QPM), but most theoretical analysis has used 1-dimensional (plane-wave) approximations along with conventional phase-matching. While 1-dimensional models do exhibit the dominant physics, at least under CW excitation conditions, they are incapable of representing a variety of effects which should be considered in actually designing an optimal device, such as the effects of higher-order guided modes and radiation modes which might be excited at the second-harmonic, radiation due to scattering from the QPM grating, and many others.
Second Harmonic Generation in a Quasi-Phase Matched Structure Containing a Saturable Absorber
Authors: Mel’nikov I. V. , Kazansky P. G. , Russell P. St. J.
Published: February 2023

Quasi-phase matching has achieved wide recognition as a powerful and versatile tool for efficient second harmonic generation (SHG) [1,2]. In such media, for imperfect phase matching, the process of frequency up-conversion evolves periodically with distance because the residual pump wave is parametrically amplified is regions of high conversion efficiency. This results in frequency down-conversion. Even when perfect phase-matching is met, any noise power at the fundamental frequency will be strongly amplified in regions of high harmonic power, causing down conversion [3,4]. In practice, these effects limit the SHG efficiencies that can be achieved under stable conditions.
Linear Perspective on Self Guidence
Authors: Snyder Allan W. , Mitchell D. John , Kivshar Yuri S.
Published: February 2023

It is often difficult to understand nonlinear guided wave effects because our intuition is built upon linear phenomena. We wish here to show that nonlinear phenomena can be approached from a linear perspective. This is not a new technique for solving nonlinear equations. Rather, we show that the linear perspective (1) anticipates the possible classes of nonlinear waves and their characteristics. It thus predicts novel phenomena, such as solitons with internal dynamics, and it facilitates previously unforeseen generalizations, such as those necessary for the universal criterion for stability. By imparting physical insight, it (2) offers a powerful predictive tool, for example one which foreshadows the phase shift and the radiation free nature of soliton collisions. Further, it (3) shows how the mathematical foundation for nonlinear waves is borrowed from the literature of linear waves. Finally, it (4) allows for closed form solutions of illustrative examples to be lifted directly from the pages of linear physics. This powerful approach is demonstrated here through the vehicle of spatial guided wave optics, embracing such phenomena as guiding and manipulating light by light itself1-7.
Orthogonally-polarized soliton interactions for all-optical logic
Authors: Blair Steve , Wagner Kelvin , McLeod Robert
Published: February 2023

Spatial soliton interactions can be used for switching and logic. Logic gates must have gain, high contrast, three-terminal operation, and be logically complete. In addition, phase-insensitivity is a system requirement for an optical logic gate, therefore we will only consider the use of solitons of orthogonal polarizations, resulting in phase-insensitive attraction between the two beams. Consider the case of 1-D asymmetric spatial soliton dragging in a waveguide [1] as illustrated in Figure 1. In the absence of a weak signal, a strong pump soliton propagates the length of the gate without diffracting and passes through an output aperture. In the presence of a weak signal spatially overlapping the pump at the input to the nonlinear medium and propagating at an angle relative to the pump, the two solitons form a bound pair and propagate off to the side so that the pump no longer passes through the aperture, thus forming an inverter with gain and high contrast. If only the undragged pump soliton, in the absence of the signal, is passed on to subsequent stages, these inverter gates become true three-terminal devices, which restore signal level and position, and can be cascaded to form logically-complete NOR gates. Asymmetric spatial soliton dragging is the analog of temporal dragging in a fiber [2, 3]. Phase-dependent dragging of spatial solitons of the same polarization has been demonstrated [4], albeit without gain.
Splitting of High-Order Optical Solitons Under the Action of Two-Photon Absorption
Authors: Afanasjev Vsevolod V. , Kivshar Yuri S. , Aitchison J. Stewart
Published: February 2023

In order to reduce the power for the soliton formation and the switching threshold, one can use materials with higher nonlinearities than that of silica. However, in many cases an enhanced nonlinear Kerr coefficient is accompanied by an enhancement of the two-photon absorption (TPA) [1]. This is the case, for example, of spatial optical solitons observed in the semiconductor ZnSe which is known to be a nonlinear medium with a rather strong TPA [2,3]. Therefore, to use solitons for all-optical switching, one should analyze the effect of the TPA on the propagation of bright and dark solitons.
Dark Optical Bullets in Light Self Trapping
Authors: Chen Yijiang , Atai Javid
Published: February 2023

Propagation of a light beam in a nonlinear medium has been a subject of great interest over the last three decades. In a uniform medium, the nonlinearity has been shown to have such an effect to offset the diffraction of a beam, leading to the stationary propagation of a CW wave.1-6 In an optical fiber where a light beam is bounded by the linear guiding structure, the nonlinearity can produce a balancing effect to the dispersion of a pulsed beam to yield the stationary propagation of the pulse.7,8 In most experimental situations of light self trapping, pulsed lasers are used as sources for excitation, especially when high power operation is involved.9-11 In these circumstances, a beam of light will experience both diffraction and dispersion in addition to self-focusing (defocusing) and self phase modulation that result from nonlinearity. In a self-focusing uniform medium, it has been shown that the nonlinearity can compensate for both the diffraction and anomalous dispersion simultaneously to result in stationary propagation of the bright pulsed self-trapped beams (light bullets that evolve without change in space and time).12 In the Kerr-law medium, this stationary state of light bullets is unstable. A perturbation will lead to collapse of the light bullet.12 Nevertheless, in a saturable nonlinear medium the collapse can be bounded and the bounding may lead to the formation of stable, nondiffracting and nondispersing bright pulses.12
Collisions of Stable Spatio-Temporal Solitons
Authors: McLeod Robert , Wagner Kelvin , Blair Steve
Published: February 2023

Silberberg1 has recently shown that, in a homogeneous nonlinear Kerr material exhibiting anomalous group-velocity dispersion (AGVD), the propagation of the slowly-varying envelope of the electric-field can be described by a 3+1D nonlinear Schrodinger equation (NLSE): which is written in a group-velocity coordinate frame. The AGVD has been used to make temporal dispersion isomorphic to spatial diffraction which in turn gives rise to the possibility of simultaneous two-dimensional, radially symmetric self-focusing and temporal pulse compression resulting in a 3D soliton or “light-bullet”. This light-bullet is fully confined by nonlinear effects alone but exhibits the behavior of both temporal solitons in fibers and spatial solitons in slab waveguides.