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We investigate the temporal dynamics of transverse optical patterns spontaneously formed in a photorefractive single-feedback system with a virtual feedback mirror. The linear stability analysis for the system is reviewed and extended to the region of larger propagation lengths. The stationary patterns obtained experimentally are classified as a fu...
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... Honda and Banerjee. 12 However, for larger positive values of n 0 L/l the behavior changes significantly, and the sideband angle shows a sharp increase for certain large positive values of n 0 L/l, which has not yet been confirmed experi- mentally. This behavior can be explained by the particu- lar shape of the threshold curve, which is shown in Fig. 3 for n 0 L/l 1.4. For mirror positions near or in the crys- tal, the global minimum of the threshold curve is the first, i.e., the left, local minimum of the curve. Figure 3 repre- sents the situation when the global minimum leaps from the first to the second local minimum, causing a leap of in the sideband angle. This situation ...
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... mirror positions near or in the crys- tal, the global minimum of the threshold curve is the first, i.e., the left, local minimum of the curve. Figure 3 repre- sents the situation when the global minimum leaps from the first to the second local minimum, causing a leap of in the sideband angle. This situation corresponds to the sharp increase of in Fig. 2 at n 0 L/l 1.4. ...
Citations
... It has been widely used to observe various families of optical discrete solitons [3][4][5], to study wave properties of quasicrystals [6] and graphene-like structures [7,8] as well as to evidence weak or strong transverse localisation in disordered lattices [9,10]. On the other hand, in homogeneous configuration, nonlinear patterns formation dynamics [11][12][13], scale-free optics [14], as well as quantum hydrodynamical features of light [15][16][17][18] have been investigated. ...
We show that the refractive index modification photoinduced in a biased nonlinear photorefractive crystal can be accurately measured and controlled by means of a background incoherent illumination and an external electric field. The proposed easy-to-implement method is based on the far-field measurement of the diffraction patterns of a laser beam propagating through a self-defocusing medium undergoing spatial self-phase modulation. For various experimental conditions, both saturation intensity and maximum refractive index modification have been measured. We also clearly evidence and characterise the anisotropic nonlinear response of the crystal in the stationary regime.
... It has been widely used to observe various families of optical discrete solitons [3][4][5], to study wave properties of quasicrystals [6] and graphene-like structures [7,8] as well as to evidence weak or strong transverse localisation in disordered lattices [9,10]. On the other hand, in homogeneous configuration, nonlinear patterns formation dynamics [11][12][13] as well as quantum hydrodynamical features of light [14][15][16] have been investigated. ...
We show that the refractive index modification photoinduced in a biased nonlinear photorefractive crystal can be accurately measured and controlled by means of a background incoherent illumination and an external electric field. The proposed easy-to-implement method is based on the far-field measurement of the diffraction patterns of a laser beam propagating through a self-defocusing medium undergoing spatial self-phase modulation. For various experimental conditions, both saturation intensity and maximum refractive index modification have been measured. We also clearly evidence and characterise the anisotropic nonlinear response of the crystal in the stationary regime.
... We note that a similar phenomenon was predicted in photorefractives [34,35], in spite of different mechanism of non-linearity. However, the experimental observation of the essentially complete extinction of patterns with the smallest Talbot wavevector in favour of the second Talbot wavevector was not reported before in the literature, only the excitation of the second wavenumber (see Fig. 4 of [7], quantified in Fig. 14 b) of this manuscript, for the two-level case and Fig. 7 of [34] for the photorefractive case). ...
We study a pattern forming instability in a laser driven optically thick cloud of cold two-level atoms with a planar feedback mirror. A theoretical model is developed, enabling a full analysis of transverse patterns in a medium with saturable nonlinearity, taking into account diffraction within the medium, and both the transmission and reflection gratings. Focus of the analysis is on combined treatment of nonlinear propagation in a diffractively- and optically-thick medium and the boundary condition given by feedback. We demonstrate explicitly how diffraction within the medium breaks the degeneracy of Talbot modes inherent in thin slice models. Existence of envelope curves bounding all possible pattern formation thresholds is predicted. The importance of envelope curves and their interaction with threshold curves is illustrated by experimental observation of a sudden transition between length scales as mirror displacement is varied.
... Many nonlinear optical media display modulational instability patterns in the optical field propagating through them. Examples include lasers, [1][2][3][4] Kerr media and optical parametric oscillators, [5][6][7] atomic gases, [8][9][10][11][12] photorefractive crystals, [13] and liquid crystal light valves, [14,15]. These instabilities are typically triggered by phase-conjugate wave mixing [16], and some common examples of patterns are stripes and hexagons. ...
Phase-conjugate scattering can trigger modulational instabilities in a fluid of exciton-polaritons created in a pumped semiconductor quantum-well microcavity. These instabilities can settle into density patterns, e.g. hexagons and stripes, which produce corresponding patterns in the emitted light. The density patterns can be switched by relatively weak control optical beams. This paper reviews progress in our theoretical understanding of the physical processes that regulate the competitions among various patterns and drive the optical switching. Simulation results of pattern switching using a microscopic model of polariton dynamics are shown, and the mechanisms underlying competitions and switching are analyzed using reduced models that restrict the polariton motions to a limited number of relevant modes. We also briefly indicate the effects of the spin dependence of the polariton dynamics on the patterns.
... Many nonlinear optics systems have displayed modulational instability patterns, including lasers [14][15][16][17], Kerr media and optical parametric oscillators [18][19][20], atomic gases [21][22][23][24][25], photorefractive crystals [26], and liquid crystal light valves [27,28]. In a larger context, the optical patterns are analogs of density instability patterns in nonlinear fields that include fluid dynamics, chemical, and biological systems [29][30][31][32][33]. ...
The occurrence of instability-driven polariton density patterns in semiconductor quantum-well microcavities has been predicted and demonstrated experimentally. Simulations have shown that different patterns can become dominant under variations of excitation and structural conditions. We have devised and analyzed low-dimensional models to help understand the physics underlying these patterns’ competition. This paper reviews the results of these model studies, mainly on optical switching of the patterns. We also present results on how the control beam strength required for switching and the time scale of switching vary with physical parameters.
... Coherent nonlinear optics, driven by laser-matter interactions, is among the areas where these modulational patterns have been fruitfully studied. The optical systems displaying these patterns include lasers,5678 Kerr media and optical parametric oscillators,91011 atomic gases,1213141516 photorefractive crystals, [17] liquid crystal light valves, [18, 19] and, most recently, semiconductor quantum well microcavities202122232425. In most cases, phase-conjugate wave-mixing processes drive directional instabilities in the wave field fed by a uni-directional input light beam. ...
We present a detailed study of a low-dimensional population-competition (PC) model suitable for analysis of the dynamics of certain modulational instability patterns in extended systems. The model is applied to analyze the transverse optical exciton–polariton patterns in semiconductor quantum well microcavities. It is shown that, despite its simplicity, the PC model describes quite well the competitions among various two-spot and hexagonal patterns when four physical parameters, representing density saturation, hexagon stabilization, anisotropy, and switching beam intensity, are varied. The combined effects of the last three parameters are given detailed considerations here. Although the model is developed in the context of semiconductor polariton patterns, its equations have more general applicability, and the results obtained here may benefit the investigation of other pattern-forming systems. The simplicity of the PC model allows us to organize all steady state solutions in a parameter space ‘phase diagram’. Each region in the phase diagram is characterized by the number and type of solutions. The main numerical task is to compute inter-region boundary surfaces, where some steady states either appear, disappear, or change their stability status. The singularity types of the boundary points, given by Catastrophe theory, are shown to provide a simple geometric overview of the boundary surfaces. With all stable and unstable steady states and the phase boundaries delimited and characterized, we have attained a comprehensive understanding of the structure of the four-parameter phase diagram. We analyze this rich structure in detail and show that it provides a transparent and organized interpretation of competitions among various patterns built on the hexagonal state space.
... The system's transverse translational symmetry is thus spontaneously broken, resulting in periodic or quasiperiodic modulational patterns, e.g., stripes and hexagons, in the intensity profile. These spontaneously formed optical patterns have been observed in experiments with lasers, 9,10 and such passive optical systems as atomic gases, [11][12][13][14] liquid crystal light valves, 15 photorefractive crystals, 16 and, most recently, semiconductor quantum well microcavities. 17 (For general reviews, see, e.g., Refs. ...
Transverse patterns in polariton fluids were recently studied as promising candidates for all-optical low-intensity switching. Here, we demonstrate these patterns in a specifically designed double-cavity system. We theoretically and experimentally analyse their formation and optical control. Our detailed theoretical analysis of the coupled nonlinear dynamics of the optical fields inside the double-cavity and the excitonic excitations inside the embedded semiconductor quantum wells is firmly based on a microscopic many-particle theory. Our calculations in the time domain enable us to study both the ultrafast transient dynamics of the patterns and their steady-state behavior under stationary excitation conditions. The patterns we report and analyze go beyond what can be observed and understood in a simple scalar quantum field. We find that polarization-selective excitation of the polaritons leads to a complex interplay between longitudinal-transverse splitting of the cavity modes and the spin-dependent interactions of the polaritons' excitonic component.
... Les faisceaux satellites tournaient un peu puis revenaient brutalement en arrière. Ce phénomène a été décrit sous l'expression "rocking motion" [74]. ...
In systems through which flows of energy or matter propagate, it is possible to observe self-organization phenomena. The system can leave its thermodynamical equilibrium state. Its components self-organize themselves in " dissipative structures ", also called " patterns ". In optics, we observe such patterns in the transverse dimensions of laser beams during their propagation in certain nonlinear materials.This thesis aims to study the patterns observed in a photorefractive single feedback system. The forward beam and the beam reflected by the mirror interfere in the photorefractive crystal and modify its electro-optical properties. This modification influences in return the propagation of the beams. If the incident beam is sufficiently powerful, the system reaches the " modulation instability " threshold : the observation of the backward beam reveals that the intensity has self-organized in patterns.Particularly, we deal in depth with two axes of research. Firstly, we study the influence of an orbital angular momentum of the input beam (therefore called a " vortex " beam) on the pattern formation process. This property influences the self-organization phenomenon and the dynamics of the transverse structures. Moreover the results provided by a numerical model of the wave mixing process are in a good accordance with the experimental observations. Secondly, we study the highly nonlinear regime obtained with a classical gaussian pump but very powerful. We show by a statistical analysis that the turbulent state far from the instability threshold contains some extreme events, also called " rogue waves ".
... Another approach has been used in some nonlinear optical experiments in which far field patterns of laser fields modified by nonlinear interactions have been directly observed on screens or cam-eras placed far from the nonlinear medium. [11][12][13][14][15][16]. ...
We study theoretically the accuracy of the method based on the Fourier
property of lenses that is commonly used for the far field measurement. We
consider a simple optical setup in which the far-field intensity pattern of a
light beam passing through a Kerr medium is recorded by a CCD camera located in
the back focal plane of a thin lens. Using Fresnel diffraction formula and
numerical computations, we investigate the influence of a slight longitudinal
mispositioning of the CCD camera. Considering a coherent gaussian beam, we show
that a tiny error in the position of the CCD camera can produce a narrowing of
the transverse pattern instead of the anticipated and well-understood
broadening. This phenomenon is robust enough to persist for incoherent beams
strongly modified by the presence of noise. The existence of this phenomenon
has important consequences for the design and the realization of experiments in
the field of optical wave turbulence in which equilibrium spectra reached by
incoherent waves can only be determined from a careful far-field analysis. In
particular, the unexpected narrowing of the far field may be mistaken for the
remarkable phenomenon of classical condensation of waves. Finally, we show that
the finite-size of optical components used in experiments produces diffraction
patterns having wings decaying in a way comparable to the Rayleigh-Jeans
distribution reached by incoherent wave systems at thermodynamical equilibrium.
... The experimental setup in which optical spatial rogue peaks of intensity occur is composed of a Kerr slice medium subjected to optical feedback (Fig. 1) (Louvergneaux., 2001). This system configuration allows the generating of a rich variety of transverse patterns (from rolls or hexagons to spatial solitons) and has been extensively investigated, see, for example, (D'Alessandro and Firth, 1992; Denz et al., 1998; Arecchi et al., 2000; Ackemann and Lange, 2001; Agez et al., 2006 ). Here, it essentially consists of a nematic liquid crystal (LC) layer irradiated by a strong laser beam which is reflected back onto the sample by a plane mirror M placed at a variable distance d from the LC layer (Fig. 1). ...
We study pattern formation in an optical system composed of a Kerr medium subjected to optical feedback but in a regime very far from the modulational instability threshold. In this highly nonlinear regime, the dynamics is turbulent and the associated one-dimensional patterns depict rare and intense localized optical peaks. We analyse numer-ically and experimentally the statistics and features of these intense optical peaks and show that their probability density functions (PDF) have a long tail indicating the occurrence of rogue events.
