Relevant bibliographies by topics / Gap solitons

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Gap solitons'

Author: Grafiati
Published: 4 June 2021
Last updated: 20 February 2023

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Journal articles on the topic "Gap solitons"

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Abolarinwa, Abimbola. "Gap theorems for compact almost Ricci-harmonic solitons." International Journal of Mathematics 30, no. 08 (July 2019): 1950040. http://dx.doi.org/10.1142/s0129167x1950040x.

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Almost Ricci-harmonic solitons are generalization of Ricci-harmonic solitons, almost Ricci solitons and harmonic-Einstein metrics. The main focus of this paper is to establish necessary and sufficient conditions for a gradient shrinking almost Ricci-harmonic soliton on a compact domain to be almost harmonic-Einstein.
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Katti, Aavishkar, and Chittaranjan P. Katti. "Gap solitons supported by an optical lattice in biased photorefractive crystals having both the linear and quadratic electro-optic effect." Zeitschrift für Naturforschung A 75, no. 8 (September 25, 2020): 749–56. http://dx.doi.org/10.1515/zna-2020-0075.

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AbstractWe investigate the existence and stability of gap solitons supported by an optical lattice in biased photorefractive (PR) crystals having both the linear and quadratic electro-optic effect. Such PR crystals have an interesting interplay between the linear and quadratic nonlinearities. Gap solitons are predicted for the first time in such novel PR media. Taking a relevant example (PMN-0.33PT), we find that the gap solitons in the first finite bandgap are single humped, positive and symmetric solitons while those in the second finite band gap are antisymmetric and double humped. The power of the gap soliton depends upon the value of the axial propagation constant. We delineate three power regimes and study the gap soliton profiles in each region. The gap solitons in the first finite band gap are not linearly stable while those in the second finite band gap are found to be stable against small perturbations. We study their stability properties in detail throughout the finite band gaps. The interplay between the linear and quadratic electro-optic effect is studied by investigating the spatial profiles and stability of the gap solitons for different ratios of the linear and quadratic nonlinear coefficients.
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WANG, D. L., and X. H. YAN. "SOLITON ON THE SEMI-INFINITE BAND GAP OF BEC IN AN OPTICAL LATTICE." International Journal of Modern Physics B 25, no. 06 (March 10, 2011): 781–93. http://dx.doi.org/10.1142/s0217979211058250.

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By developing a multiple-scale method, we study analytically the dynamics of the soliton inside the semi-infinite band gap (SIBG) of quasi-one-dimensional Bose–Einstein condensates trapped in an optical lattice. In the linear case, a stable condition of soliton formation is obtained. For a weak nonlinearity, whether there occurs a spatially propagating or localized gap soliton is determined by the lattice depth. Meanwhile, we predict the existence of the dark (bright) gap solitons for the repulsive (attractive) interactions in the SIBG, different from that of the gap solitons in other energy gaps. And the collision of two dark (or bright) solitons is nearly elastic under a safe range of atomic numbers. An experimental protocol is further designed for observing these phenomena.
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Winful, Herbert G., and Victor Perlin. "Raman Gap Solitons." Physical Review Letters 84, no. 16 (April 17, 2000): 3586–89. http://dx.doi.org/10.1103/physrevlett.84.3586.

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Konotop, V. V. "Vector gap solitons." Physical Review A 51, no. 5 (May 1, 1995): R3422—R3425. http://dx.doi.org/10.1103/physreva.51.r3422.

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Gorbach, A. V., B. A. Malomed, and D. V. Skryabin. "Gap polariton solitons." Physics Letters A 373, no. 34 (August 2009): 3024–27. http://dx.doi.org/10.1016/j.physleta.2009.06.036.

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ALATAS, H., A. A. ISKANDAR, M. O. TJIA, and T. P. VALKERING. "DARK, ANTIDARK SOLITON-LIKE SOLUTIONS AND THEIR CONNECTION IN A FINITE DEEP NONLINEAR BRAGG GRATING WITH A MIRROR." Journal of Nonlinear Optical Physics & Materials 13, no. 02 (June 2004): 259–74. http://dx.doi.org/10.1142/s0218863504001827.

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We report the results of our study on the in-gap soliton-like solutions in a system of a uniform finite deep nonlinear Bragg grating with a mirror and continuous light source on the opposite sides of the grating. The system was shown to exhibit a new feature consisting of homoclinic and heteroclinic orbits in phase plane associated with the in-gap bright and dark/antidark solitons respectively. The multi-valued connection between the dark and antidark solitons was explicitly displayed. It was further demonstrated that a transition from dark to antidark soliton could be affected by either changing the mirror position or changing the source intensity.
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Alatas, H., A. A. Iskandar, M. O. Tjia, and T. P. Valkering. "Analytic Study of Stationary Solitons in Deep Nonlinear Bragg Grating." Journal of Nonlinear Optical Physics & Materials 12, no. 02 (June 2003): 157–73. http://dx.doi.org/10.1142/s0218863503001304.

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A study of nonlinear Bragg grating has been carried out using a modified scheme of approximation originally proposed by Iizuka and de Sterke. A complete classification of the solitonic solutions in the system was given. We further demonstrated in this work the existence of in-gap dark and antidark soliton, in addition to the out-gap solutions reported previously. We also found at the boundaries in the bifurcation diagram, the large-amplitude out-gap antidark soliton and broad in-gap dark soliton.
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Chen, W. H., Y. J. He, and H. Z. Wang. "Surface defect gap solitons." Optics Express 14, no. 23 (2006): 11271. http://dx.doi.org/10.1364/oe.14.011271.

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Peyraud, J., and J. Coste. "Dynamics of gap solitons." Physical Review B 40, no. 18 (December 15, 1989): 12201–8. http://dx.doi.org/10.1103/physrevb.40.12201.

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Dissertations / Theses on the topic "Gap solitons"

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Akter, Afroja. "Gap Solitons in a Coupled FBGs with Cubic-quintic Nonlinearity and Dispersive Reflectivity." Thesis, University of Sydney, 2020. https://hdl.handle.net/2123/23994.

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This thesis presents a comprehensive analysis of optical gap solitons in linearly coupled fibre Bragg gratings with higher-order nonlinearity, such as cubic-quintic nonlinearity and grating non-uniformity. The non-uniformity is accounted for with a dispersive reflectivity parameter. We find two disjointed families of solitons—named Type 1 and Type 2 gap solitons—in the entire bandgap. The Type 1 family shows the generalised behaviour of Kerr nonlinearity. In contrast, where quintic nonlinearity shows dominant behaviour, we find Type 2 solitons. Moreover, each family presents asymmetric and symmetric type solitons. There is no analytic solution to this model; hence, all the solutions for quiescent or moving gap solitons are found via a systematic numerical approximation, such as relaxation technique in the (η, ω) plane. The solutions have any velocity from zero to the speed of light in the medium. For a given soliton, there is a critical coupling coefficient where bifurcation has occurred and, beyond that point, only symmetric Type 1 solitons can exist. However, in the case of Type 2 solitons, there is no bifurcation. The border between Type 1 and Type 2 asymmetric solitons is found numerically. The stability of zero velocity solitons is investigated by employing numerical split-step Fourier technique and Runge-Kutta or RK4 method. The effect of dispersive reflectivity and coupling coefficient on the stability region of quiescent solitons in (η, ω) is analysed. The results indicate that the presence of dispersive reflectivity has a stabilisation effect on both Type 1 and Type 2 quiescent solitons, especially for Type 2 solitons we found that presence of the dispersive reflectivity has broadened the stable region significantly for a lower value of coupling coefficient. We find a significant region of stable Type 1 asymmetric zero velocity solitons. In the region where only symmetric Type 1 solitons can exist are highly stable. In contrast, all symmetric Type 2 solitons are highly unstable. However, after the propagation of unstable asymmetric Type 1 and symmetric Type 2 zero velocity solitons, they can generate stable moving solitons belonging to asymmetric Type 1 solitons. This study also investigates the stability of moving gap solitons, where the effect of dispersive reflectivity, coupling coefficient and the initial velocity of the moving gap solitons are considered. The results indicate that, in the case of the coupled Kerr nonlinear model, the initial velocity is insignificant in the stability of moving gap solitons. However, in this case, the initial velocity, dispersive reflectivity and coupling coefficient have a significant effect on the stable region of the moving gap solitons. Similar to their quiescent counterpart, the stable region shrinks with increasing coupling coefficient and broadens as dispersive reflectivity increases at a fixed initial velocity. This study also investigates the interaction and collision dynamics of two counterpropagating zero velocity and moving gap solitons, respectively. The presence of dispersive reflectivity brings some novel features in the case of interactions and collisions. For example, we observe some exceptional behaviour in the case of in-phase interactions and collisions of Type 2 zero and moving gap solitons, respectively, such as prevention of complete destruction of in-phase Type 2 quiescent gap solitons after their interactions for weak to moderate values of dispersive reflectivity. Another noteworthy finding is the generation of the merger to quiescent solitons from the in-phase collision of two Type 2 moving gap solitons, when higher-order dispersive reflectivity is presented. For weak to moderate values of dispersive reflectivity, the in-phase interactions of asymmetric Type 1 quiescent solitons can generate various outcomes, such as a merger, two-to-three solitons, symmetric and asymmetric separation of the solitons, and destruction of the solitons. However, for strong dispersive reflectivity interactions, the outcomes significantly alter their behaviour. As a result, we find repulsion solitons after their interactions of two in-phase Type 1 asymmetric solitons. Other typical outcomes at this condition are temporary bound state to asymmetric separation, merger and so on. On the other hand, interactions of two in-phase Type 2 asymmetric solitons can produce a temporary bound state to a single moving soliton, separation of both solitons and destruction. Initial attraction to destruction and repulsion to separation solitons are also possible from the in-phase interactions of Type 2 asymmetric solitons with strong dispersive reflectivity. Additionally, this study analyses the effect of initial separation and phase difference of two quiescent solitons on their outcomes. We also investigate the out-of-phase interactions of both Type 1 and Type 2 zero velocity solitons in the case of weak to moderate dispersive reflectivity and strong dispersive reflectivity. The asymmetric interactions of two quiescent solitons, where solitons are from two different cores, are also investigated. In the case of in-phase collisions of two Type 1 asymmetric non-zero velocity or moving gap solitons, the general outcomes are merger, two-to-three solitons, symmetric separation with reduced and increased velocity, asymmetric separation with two different velocities, destruction, and repulsion of solitons. For the in-phase collisions of two Type 2 moving solitons, we find asymmetric separation, repulsion, merger and destruction when strong dispersive reflectivity is present. Moreover, we find merger solitons in the case of π outof-phase collision of Type 2 asymmetric moving solitons. Further, in the case of collision dynamics, we investigate the effect of initial phase difference and velocity mismatch on the various outcomes of in-phase collisions. We find that the initial phase difference (velocity mismatched) can be tuned to compensate for the initial velocity mismatch (phase difference) to obtain similar results to those found for in-phase collisions. This thesis also investigates the collisions of exchange components of two Type 1 and Type 2 non-zero velocity gap solitons.
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Islam, Md Jahedul. "Gap Soliton Dynamics In Coupled Bragg Gratings With Cubic-Quintic Nonlinearity." Thesis, The University of Sydney, 2015. http://hdl.handle.net/2123/13952.

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The dynamics of gap solitons in a system of two linearly coupled Bragg gratings with cubic-quintic nonlinearity are investigated. It is found that the model supports two disjoint families of solitons, known as Type 1 and Type 2 solitons, which fill the entire bandgap. There exist symmetric and asymmetric gap solitons within each family. These gap solitons can have any velocity between zero and the speed of light in the medium. The border separating the soliton families has been identified. The stability of solitons is investigated by means of systematic numerical stability analysis. For moving solitons, the stability region is approximately independent of soliton velocities in the standard coupled Bragg gratings model. However, in the case of cubic-quintic model, the velocities of solitons have a significant effect on the stability regions. Type 1 gap solitons are adequately robust against strong perturbations; credited to quintic nonlinearity. Interactions of co-propagating quiescent gap solitons have been systematically investigated. Generally speaking, attraction is present between in-phase quiescent gap solitons interactions, while repulsion arises when the initial phase difference is at π or π/2. The interactions of in-phase Type 1 asymmetric solitons has been proven to result in a range of outcomes, namely, fusion into a single zero-velocity soliton, asymmetrical separation of solitons, symmetrical separation of solitons, formation of three solitons, and the destruction of solitons. Collisions of counter-propagating moving gap solitons are studied numerically. Collisions of in-phase Type 1 asymmetric moving gap solitons can exhibit a range of outcomes, such as the separation of solitons with identical, reduced, increased, or asymmetric velocities. The generation of a quiescent soliton, either through merger or through 2→3 transformation, is a particularly significant outcome. Compared to the merger, 2→3 transformation is deemed to be more stable.
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Mak, William Chi Keung Electrical Engineering &amp Telecommunications Faculty of Engineering UNSW. "Coupled Solitary Waves in Optical Waveguides." Awarded by:University of New South Wales. Electrical Engineering and Telecommunications, 1998. http://handle.unsw.edu.au/1959.4/17494.

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Soliton states in three coupled optical waveguide systems were studied: two linearly coupled waveguides with quadratic nonlinearity, two linearly coupled waveguides with cubic nonlinearity and Bragg gratings, and a quadratic nonlinear waveguide with resonant gratings, which enable three-wave interaction. The methods adopted to tackle the problems were both analytical and numerical. The analytical method mainly made use of the variational approximation. Since no exact analytical method is available to find solutions for the waveguide systems under study, the variational approach was proved to be very useful to find accurate approximations. Numerically, the shooting method and the relaxation method were used. The numerical results verified the results obtained analytically. New asymmetric soliton states were discovered for the coupled quadratically nonlinear waveguides, and for the coupled waveguides with both cubic nonlinearity and Bragg gratings. Stability of the soliton states was studied numerically, using the Beam Propagation Method. Asymmetric couplers with quadratic nonlinearity were also studied. The bifurcation diagrams for the asymmetric couplers were those unfolded from the corresponding diagrams of the symmetric couplers. Novel stable two-soliton bound states due to three-wave interaction were discovered for a quadratically nonlinear waveguide equipped with resonant gratings. Since the coupled optical waveguide systems are controlled by a larger number of parameters than in the corresponding single waveguide, the coupled systems can find a much broader field of applications. This study provides useful background information to support these applications.
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Hajibaratali, Babak. "Dynamics of Bragg Grating Solitons In Coupled Bragg Gratings With Dispersive Reflectivity." Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/12080.

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We study dynamics of Bragg grating solitons in a system of linearly coupled Bragg gratings with Kerr nonlinearity. The effects of dispersive reflectivity on the behaviour of solitons in the system are investigated by solving the coupled mode equations numerically. Gap solitons, are found to exist throughout the bandgap of the structure. The system supports two types of symmetric and asymmetric solitons that can have any velocities from zero to the speed of light in the medium. At given soliton parameters a critical coupling coefficient is found above which only symmetric solitons exist. Below the critical point however, both types of gap solitons may exist at the same time. Linear forms of coupled mode equations are solved analytically. The results are in excellent agreement with the gap soliton tails. Also, using the linear analysis a condition is found for the solitons to have sidelobes in their tails. Stability of solitons are investigated using systematic simulations. Generally, when dispersive reflectivity is zero, asymmetric solitons are stable for ω≥0. While with increase of dispersive reflectivity the stable region expands into the negative frequencies. Symmetric solitons on the other hand are found to be stable where they exist on their own. Interactions of quiescent gap solitons in the model are studied numerically. The outcomes generally depend on the initial separation (Δx) and phase difference. However, when the dispersive reflectivity is small, Δx-dependence is very weak. Interactions are found to result in a number of outcomes including merger into a single quiescent soliton, destruction, formation of a bound state that eventually breaks up into two separating solitons, formation of two moving and one quiescent solitons, and repulsion. The most interesting outcomes of the collisions of counter-propagating in-phase moving solitons are merger and 2→3 transformation. On the contrary, out-of-phase collisions generally result in the repulsion of the pulses.
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Gorza, Simon-Pierre. "Etude expérimentale de la propagation non linéaire dans les guides optiques plans: instabilité serpentine et soliton de Bragg." Doctoral thesis, Universite Libre de Bruxelles, 2005. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211067.

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The topic of this thesis is about experimental study of phenomena which are associated with light propagation in nonlinear dielectric media. In the first part of this work, we study experimentally the snake instability of the bright soliton stripe of the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation. The instability is observed, through spectral measurements, on spatially extended femtosecond pulses propagating in a normally dispersive self-defocusing semiconductor planar waveguide. The second part of this thesis is about light propagation in nonlinear periodic media. We experimentally observe a stationary spatial gap (or Bragg) soliton in a periodic semiconductor planar waveguide. Based on the interference pattern of the soliton beam, we measure the power parameter of the soliton which is related to the position of the spatial spectrum in the linear band gap.

Cette thèse de doctorat a pour sujet l’étude expérimentale de phénomènes associés à la propagation de la lumière dans les milieux diélectriques non linéaires. La première partie porte sur la démonstration expérimentale de l’instabilité serpentine d’une bande solitonique dans un système décrit par une équation de Schrödinger non linéaire à (2+1)-dimensions. L’instabilité est observée sur base de mesures du spectre spatial ainsi que du profil spatio-fréquentiel d’une impulsion femtoseconde après propagation dans un guide plan semi-conducteur qui présente une dispersion normale et une non-linéarité défocalisante. Le second thème abordé concerne la propagation de la lumière dans les milieux non linéaires périodiques. Les expériences réalisées ont montré l’existence du soliton de Bragg spatial stationnaire sous forme de faisceaux se propageant dans des guides plans semi-conducteurs périodiquement gravés. Sur base du profil de la distribution modale en intensité du faisceau soliton, il a été possible de mesurer le paramètre de puissance du soliton de Bragg qui détermine la position du spectre spatial dans la bande interdite linéaire.


Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished

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Anghel-Vasilescu, Petrutza. "Interactions rayonnement-matière résonantes en régime nonlinéaire : systèmes à deux niveaux et milieux quadratiques." Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2010. http://tel.archives-ouvertes.fr/tel-00664992.

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Nous avons consacré cette thèse à l'étude des différents processus non-linéaires de l'interaction rayonnement-matière et en particulier à la génération des solitons de gap dans les milieux non-linéaires à bandes interdites. Dans la première partie nous avons utilisé un modèle semi-classique de Maxwell-Bloch pour décrire l'interaction d'un milieu à deux niveaux quantiques avec charges avec un champ électromagnétique classique à travers la densité de population, qui est à l'origine même de la non-linéarité. Le couplage non-linéaire qui en résulte génère des phénomènes particulièrement intéressants (génération et diffusion des solitons de gap) à la résonance, quand la pulsation du champ appliqué est proche de la fréquence de transition du milieu à deux niveaux. La dynamique non-linéaire observée numériquement est expliquée à l'aide d'un modèle de Schrödinger non-linéaire dans un potentiel lié aux charges du milieu. La deuxième partie concerne l'étude théorique de la dynamique des solitons quadratiques dans les amplificateurs paramétriques optiques (OPA). Les équations décrivant l'interaction à trois ondes dégénérée dans un cristal biréfringent non-linéaire ont été établies en prenant en compte la diffraction transverse et le walk-off spatial. Nous avons proposé une méthode pour résoudre le problème ardu de la détermination du seuil de supratransmission non-linéaire dans les OPA et nous avons généralisé les résultats obtenus à une grande classe de systèmes non-linéaires non-intégrables à composantes multiples.
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Chevriaux, Dominique. "Supratransmission et bistabilité nonlinéaire dans les milieux à bandes interdites photoniques et électroniques." Montpellier 2, 2007. http://www.theses.fr/2007MON20039.

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Redor, Ivan. "Etude expérimentale de la turbulence intégrable en eau peu profonde." Thesis, Université Grenoble Alpes (ComUE), 2019. http://www.theses.fr/2019GREAI077.

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La turbulence d'onde est un état statistique impliquant un grand nombre d'ondes couplées par effet non linéaire. Cet état générique est potentiellement décrit, dans la limite de faible non linéarité, par la théorie de la turbulence faible. Cette théorie prédit un phénoménologie proche de celle de la turbulence hydrodynamique avec en particulier une cascade d'énergie au travers des échelles. La thèse de doctorat se concentrera sur le cas d'ondes de gravité-capillarité à la surface d'un fluide dans la limite des grandes longueurs d'onde. Ce système est potentiellement représentatif d'états de mer lorsque la houle est développée. Des expériences seront menées dans le canal à Houle 1D de 36m du LEGI. Le cas des ondes unidirectionnelles est assez particulier dans le cadre général de la théorie de la turbulence faible. En effet il est prédit que la turbulence faible est instable dans ces conditions et que l'on devrait observer plutôt l'apparence de structures cohérentes de type soliton. Au cours de cette thèse, on testera différentes conditions de forçage pour tester les prédictions théoriques concernant les cascades d'énergie et de quantité de mouvement. On sortira également du cadre strict de la théorie pour étudier des régimes de forçage fort ou de faible profondeu
In the present PhD program, we will focus on the case of 1D surface gravity waves. This situation is related to the case of the swell observed in the ocean that shows usually a quasi unidirectional propagation. Wave turbulence in 1D shows fundamental particularities that are somewhat exotic depending on whetherthe wave propagation is uni or bi directional. Energy can cascade towards small scales or in contrast to large scales;weak turbulence can become unstable and lead to formation of solitons... Wave turbulence in 1D is a potentially veryrich framework related to oceanic issues.During this PhD, the graduatestudent will have to setup experiments in the 1D wave flume of theLEGI. This flume is 36 m long and it is currently used to study the sedimentdynamics in the vicinity of the shore(see picture). The student willdevelop a new scheme to generate and control the waves and a 2Dimagingsystem to record the free surface displacementin a way that isresolved both in time and space. For control purposes, additional ultrasoniclocal measurements of the surface displacement will be performed. Itwill then be possible to study in a very fine way, the weak or strong non-linearcouplings between waves, and perform advanced comparisons betweentheory and experiments. The student will also be associated to the otherstudies of the WATU project, in particular to share the measurement and data analysis techniques and so that to compare results among various configurations
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Chevriaux, D. "Supratransmission et bistabilité nonlinéaire dansles milieux à bandes interdites photoniques et électroniques." Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2007. http://tel.archives-ouvertes.fr/tel-00180987.

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On étudie, dans cette thèse, la diffusion d'ondes dans différents milieux nonlinéaires possédant une bande interdite naturelle. On montre, en particulier, l'existence d'un comportement de bistabilité dans les milieux régis, soit par l'équation de sine-Gordon (chaîne de pendules courte, réseaux de jonctions Josephson, double couches à effet Hall quantique), soit par l'équation de Schrödinger nonlinéaire (milieu Kerr et milieu de Bragg), dans les cas discrets et continus. Ces différents milieux sont soumis à des conditions aux bords périodiques, dont la fréquence est prise dans la bande interdite et avec une amplitude déterminant l'état de stabilité du système. En effet, pour une amplitude suffisante (supratransmission), le milieu n'est plus réfléchissant et absorbe de l'énergie, faisant passer le signal de sortie d'un état d'amplitude évanescente vers un état de très grande amplitude. On donne, par ailleurs, une description analytique complète de la bistabilité qui permet de comprendre les différents états stationnaires observés dans ces milieux et de prédire le passage d'un état à un autre.
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Richter, Tobias. "Stability of Anisotropic Gap Solitons in Photorefractive Media." Phd thesis, 2008. https://tuprints.ulb.tu-darmstadt.de/1021/1/dissertation_tobias_richter.pdf.

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In modern optics, periodically modulated structures are omnipresent. Commonly known as photonic crystals, they constitute the optical analog of crystal structures in solid state physics. Consequently, photonic crystals possess a band structure, i.e., linear light propagation becomes impossible if the corresponding wave vectors lie within certain, "forbidden" intervals (photonic band gaps). In the presence of a nonlinearity however, spatially localized structures can exist inside these band gaps. The stability properties of these so-called gap solitons are the principal topic of this thesis. Considering a photorefractive nonlinearity, both elementary and more complicated gap solitons featuring phase singularities (gap vortices, vortex clusters) are investigated. It is demonstrated that the anisotropy of the photorefractive effect strongly influences the symmetry of the optically induced photonic lattices as well as the stability properties of the gap solitons. From a theoretical point of view (nonlinear Schrödinger equation, Gross-Pitaevskii equation), the system presented in this thesis is closely related to Bose-Einstein condensates in periodic potentials.
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Books on the topic "Gap solitons"

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Gesztesy, Fritz. (m)KdV solitons on the background of quasi-periodic finite-gap solutions. Providence, R.I: American Mathematical Society, 1995.

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Kavokin, Alexey V., Jeremy J. Baumberg, Guillaume Malpuech, and Fabrice P. Laussy. Quantum Fluids of Light. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198782995.003.0010.

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In this chapter, we deal with polaritons as a “quantum fluid of light”, described by variants of the Gross–Pitaevskii equation. We discuss how interactions between flowing polaritons and a defect allow to study their superfluid regime and generate topological defects. Including spin gives rise to an effective magnetic field (polariton spin-orbit coupling) that acts on the topological defects—half-solitons and half-vortices—behaving as effective magnetic monopoles. We describe various techniques to create periodic potentials, that can lead to the formation of polaritonic bands and gaps with a unique flexibility. Special focus is given to topologically nontrivial bands, leading to a polariton topological insulator, based on a polariton graphene analog.
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Ltd, ICON Group. SOLITRON DEVICES, INC.: Labor Productivity Benchmarks and International Gap Analysis (Labor Productivity Series). 2nd ed. Icon Group International, Inc., 2000.

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Ltd, ICON Group. SOLITRON DEVICES, INC.: International Competitive Benchmarks and Financial Gap Analysis (Financial Performance Series). 2nd ed. Icon Group International, Inc., 2000.

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Book chapters on the topic "Gap solitons"

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Sipe, J. E. "Gap Solitons." In Guided Wave Nonlinear Optics, 305–18. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2536-9_17.

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Trillo, S., and C. Conti. "Theory of Gap Solitons in Short Period Gratings." In Optical Solitons, 185–206. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-36141-3_9.

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Cheng, Ze, and Gershon Kurizki. "Theory of Quantum Gap Solitons." In Coherence and Quantum Optics VII, 619–20. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4757-9742-8_180.

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Winful, H. G., and V. E. Perlin. "Raman Gap Solitons in Nonlinear Photonic Crystals." In Springer Series in Photonics, 61–71. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05144-3_4.

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Kivshar, Yuri S. "Self-Supporting Gap Solitons in Nonlinear Lattices." In NATO ASI Series, 63–66. Boston, MA: Springer US, 1993. http://dx.doi.org/10.1007/978-1-4899-1609-9_10.

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Tasgal, Richard S., Roman Shnaiderman, and Yehuda B. Band. "Gap-Acoustic Solitons: Slowing and Stopping of Light." In Localized States in Physics: Solitons and Patterns, 41–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16549-8_3.

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Trillo, S., C. Conti, A. de Rossi, and G. Assanto. "Recent Developments in the Theory of Optical Gap Solitons." In Optical Solitons: Theoretical Challenges and Industrial Perspectives, 233–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/978-3-662-03807-9_13.

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Dror, Nir, and Boris A. Malomed. "Stability of Dipole Gap Solitons in Two-Dimensional Lattice Potentials." In Nonlinear Physical Systems, 111–38. Hoboken, USA: John Wiley & Sons, Inc., 2014. http://dx.doi.org/10.1002/9781118577608.ch6.

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Broderick, N. G. R. "Gap Solitons Experiments within the Bandgap of a Nonlinear Bragg Grating." In Springer Series in Photonics, 201–19. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05144-3_9.

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Salerno, Mario, F. Kh Abdullaev, and B. B. Baizakov. "Gap-Townes Solitons and Delocalizing Transitions of Multidimensional Bose–Einstein Condensates in Optical Lattices." In NATO Science for Peace and Security Series A: Chemistry and Biology, 345–57. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2590-6_16.

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Conference papers on the topic "Gap solitons"

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Jianke Yang, Cibo Lou, Xiaosheng Wang, Liqin Tang, Jingjun Xu, and Zhigang Chen. "On-axis excitation of two-dimensional gap solitons and gap soliton trains." In 2007 Quantum Electronics and Laser Science Conference. IEEE, 2007. http://dx.doi.org/10.1109/qels.2007.4431583.

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Sukhorukov, Andrey A., Dragomir N. Neshev, Alexander Dreischuh, Robert Fischer, Sangwoo Ha, Jeremy Bolger, Lam Bui, et al. "Supercontinuum spatial gap solitons." In 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference. IEEE, 2007. http://dx.doi.org/10.1109/cleoe-iqec.2007.4386096.

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de Sterke, Martijn. "Generation of gap solitons." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1991. http://dx.doi.org/10.1364/oam.1991.tubb1.

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Gap solitons can occur in nonlinear periodic stacks. They would, in general, be created using a powerful external light pulse. In doing so it is important that the external energy required be minimized. It is shown that, among other things, the refractive indices of the stack and of the surrounding media play a crucial role in determining the efficiency. Particularly important also are the parameters of the outer layers of the nonlinear stack.
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Rosberg, Christian R., Dragomir N. Neshev, Wieslaw Krolikowski, Yuri S. Kivshar, Arnan Mitchell, Rodrigo A. Vicencio, and Mario I. Molina. "Observation of surface gap solitons." In 2006 Conference on Lasers and Electro-Optics and 2006 Quantum Electronics and Laser Science Conference. IEEE, 2006. http://dx.doi.org/10.1109/cleo.2006.4627794.

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Kovalev, A. S., O. V. Usatenko, and A. V. Gorbach. "Dynamical optical near-gap solitons." In Eighth International Conference on Nonlinear Optics of Liquid and Photorefractive Crystals, edited by Gertruda V. Klimusheva and Andrey G. Iljin. SPIE, 2001. http://dx.doi.org/10.1117/12.428322.

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Alfimov, E., and V. V. Konotop. "On existence of gap solitons." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: OSA, 1999. http://dx.doi.org/10.1364/nlgw.1999.wd35.

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Pezer, Robert, Hrvoje Buljan, Jason W. Fleischer, Guy Bartal, Oren Cohen, and Mordechai Segev. "Gap random-phase lattice solitons." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: OSA, 2005. http://dx.doi.org/10.1364/nlgw.2005.wd31.

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de Sterke, C. Martijn. "Properties of dark-gap solitons." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1993. http://dx.doi.org/10.1364/oam.1993.thvv.2.

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It is well known that nonlinear periodic media support gap solitons. These solutions for the electric field, which vanish asymptotically, can exist because at high intensities the nonlinearity shifts the position of the photonic band gap. Frequencies which are inside the photonic band gap at low intensities, and thus are evanescent, may fall outside the gap at high intensities, and thus are propagating.
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Lee, Sangjae, and Seng-Tiong Ho. "Transmission of coupled-gap solitons in non-linear periodic media." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1993. http://dx.doi.org/10.1364/oam.1993.tuc.4.

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The theoretical interests in gap solitons have grown recently due to their unusual properties. For example, it was found that gap solitons can propagate in a Nonlinear Periodic Dielectric Medium (NPDM) with a group velocity much slower than the usual medium group velocity. The existence of stationary solitons in a NPDM was first investigated by Chen and Mills.1 Later, de Sterke-Sipe and Christodoulides-Joseph showed that it is possible to propagate moving solitons in a NPDM. In this paper, we study the propagation of two pulses with orthogonal linear polarizations in a nonlinear periodic structure with χ(3) nonlinearity. Specifically we derive the coupled nonlinear Schrödinger equations and find their solitary-wave solutions in a simple case. We show that two orthogonally polarized pulses can co-propagate as a coupled gap soliton through a nonlinear periodic structure while each pulse alone will be strongly reflected due to the Bragg reflection. Based on the results, we present a new all-optical switching scheme and investigate its operational characteristics.
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Peschel, Thomas, Ulf Peschel, Falk Lederer, and Boris Malomed. "Gap Solitons in Quadratically Nonlinear Waveguides." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/nlgw.1996.sac.3.

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Gap solitons are known to exist in configurations where the dispersion is created by the coupling of two waves with strongly different group velocities and the material exhibits a cubic nonlinearity [1,2]. Usually, this coupling emerges in periodically corrugated waveguides (Bragg gratings) where the forward and backward waves are coupled. Recently, it has been shown that spatial solitons may also exist due to quadratic nonlinearities [3]. In this environment temporal solitons suffer from the pulse walk-off and could not be experimentally observed until now. Hence, the question arises whether gap solitons may be supported by quadratic nonlinearities and how they are affected by the pulse walk-off. These are the subjects we are addressing in this paper.
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Reports on the topic "Gap solitons"

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Sun, Xin, Dingwei Lu, Rouli Fu, D. L. Lin, and Thomas F. George. Gap States of Charged Solitons in Polyacetylene. Fort Belvoir, VA: Defense Technical Information Center, August 1989. http://dx.doi.org/10.21236/ada212105.

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Kaup, D. J., and B. A. Malomed. Gap Solitons in Assymmetric Dual-Core Nonlinear Optical Fibers. Fort Belvoir, VA: Defense Technical Information Center, January 1997. http://dx.doi.org/10.21236/ada342070.

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