Stability of screening solitons in photorefractive media

Facão, Margarida; Parker, D. F.

doi:10.1103/physreve.68.016610

Cited by 28 publications

(23 citation statements)

References 17 publications

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“…However, other physical parameters, such as the gas pressure or the fiber geometry, may change the accelerating pulse profile characteristics imposing or not pulse decay during propagation. The amplitude oscillations, observed in both cases, do not have a constant period but their average period does increase with β 8/3 /η 2 as may be obtained by a simple analysis of the spectral stability problem [8], namely, the oscillation period should be close to the value of the edge of the continuous spectrum and that edge is, in this problem, varying with β 8/3 /η 2 . Returning to the dynamics of the decaying pulses, let us note that since the peak amplitude decreases, the corresponding stationary profile is also varying.…”

Section: Pulse Profilesmentioning

confidence: 96%

Dynamics of blueshifted floating pulses in gas-filled hollow-core photonic crystal fibers

Facão

Carvalho

2013

Appl. Phys. B

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Frequency blueshifting was recently observed in light pulses propagating on gas filled hollow-core photonic crystal fibers where a plasma has been produced due to photoionization of the gas. One of the propagation models that is adequate to describe the actual experimental observations is here investigated. It is a nonlinear Schrödinger equation with an extra term, to which we applied a self-similar change of variables and found its accelerating solitons. As in other NLS related models possessing accelerating solitons, there exist asymmetrical pulses that decay as they propagate in some parameter region that was here well defined.

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Section: Pulse Profilesmentioning

confidence: 96%

Dynamics of blueshifted floating pulses in gas-filled hollow-core photonic crystal fibers

Facão

Carvalho

2013

Appl. Phys. B

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“…The profile of dark soliton is described by an odd (antisymmetric) function which is easy to show by analysis of the structure of Eq. (27). For a coordinate ξ in the vicinity of ξ = 0, where y(0) = 0, for black solitons, the inequality y ∞ 2 ≫ y 2 holds, so Eq.…”

Section: Solution For the Dark Solitonmentioning

confidence: 98%

“…(7) is not used. Commonly, the assumption is made [1][2][3][4][5][6][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] that similar to diffusion terms, the second term in (6) can be also omitted. Thus, Eq.…”

Section: The Kukhtarev-vinetskii Model and Light-induced Space-chargementioning

confidence: 99%

On conformity of solutions for one-dimensional photorefractive screening solitons with the Kukhtarev–Vinetskii model

Wichtowski

2015

Appl. Phys. B

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(PR) crystals are photoconductive, specific doped electrooptics materials. When an optical beam propagates in a PR crystal, charge carriers are excited from photosensitive impurities into the conduction band where they move due to drift and diffusion and eventually are trapped in darker regions of the light intensity pattern. The resulting space-charge redistribution produces the spatially nonuniform internal electric field which in turn modulates the material refractive index through the linear electro-optic effect. Under an appropriate polarity of an external voltage, a local variation in the index of refraction leads to self-focusing or self-defocusing effect of an optical beam. This allows forming bright or dark soliton states when the nonlinearity compensates exactly the diffraction spreading of a light beam. As a result, the beam propagates in a PR medium without changing its transverse profile. For one-dimensional bright spatial solitons, a polarized optical beam in the form of a narrow stripe is launched at the entrance of a crystal together with orthogonally polarized background illumination. In the case of dark soliton, a black notch is superimposed on an otherwise uniform background illumination. Both types of solitons can be generated in the same crystal by reversing the bias voltage direction.Due to a possibility of soliton creation at very low laser power levels, and their potential applications in all optical switching devices, PR screening solitons have been subjected to intensive theoretical and experimental works for the last two decades. So far, the formation of (1 + 1)D solitary waves has been demonstrated experimentally in various PR materials such as ferroelectrics (SBN) [3][4][5], (LiNbO 3 ) [11,12], sillenities (BTO) [6,7], (BSO) [13] centrosymmetric paraelectrics (KLTN) [8], semiconductors (InP:Fe) [9,14], and (CdZnTe) [15] both in geometry with bulk PR crystals and in planar waveguides [10,16]. AbstractIn the present paper, the problem of one-dimensional screening photorefractive solitons is reconsidered in the context of the accordance of soliton solutions with the Kukhtarev-Vinetskii model. In all theoretical and experimental works dealing with the analysis of such type solitons, one assumes that under the slowly varying approximation for the optical field amplitude the reduced form of photorefractive rate equations can be employed. In this work, we point out that the crucial and commonly accepted approximation within this scheme has a limited range of applicability as regards dark solitons. This author proposes a relatively simple modification of the standard saturable photorefractive response formula to obtain the plausible self-consistent solutions. The improved solutions for screening black solitons have been derived and discussed by comparison with standard solutions.

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“…We will solve (1.4.7) in order to investigate the stability of travelling wave solutions. The Evans function has been computed analytically (see for example [FaP03,PW92,SE90,Ter90,HZ06]) and for complicated problems it has been computed numerically (see [MN08,AB01,BDG02,Bri01,HZ06]). …”

Section: Stability Of Travelling Wavesmentioning

confidence: 99%

A Reaction Diffusion Model for Inter-Species Competition and Intra-Species Cooperation

Rasheed

Billingham

2013

Math. Model. Nat. Phenom.

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This thesis deals with a two component reaction-diffusion system (RDS) for competing and cooperating species. We have analyse in detail the stability and bifurcation structure of equilibrium solutions of this system, a natural extension of the Lotka-Volterra system. We find seven topologically different regions separated by bifurcation boundaries depending on the number and stability of equilibrium solutions, with four regions in which the solutions are similar to those in the Lotka-Volterra system. We study RDS in the small parameter of the range 0 < λ 1 (fast diffusion and slow reaction), and in a few cases we assume λ = O(1). We consider three types of initial conditions, and we find three types of travelling wave solutions using numerical and asymptotic methods. However, neither numerical nor asymptotic methods were able to find a particular travelling wave solution which connects a coexistence state say, (u 0 , w 0 ) to an extinction state (0, 0) when 0 < λ 1. This type can be found when the reaction-diffusion system satisfy the symmetry property and λ = 1.From asymptotic methods, we find that RDS is a singular perturbation problem (one inner and two outer regions) when one of the equilibrium solutions associated with the travelling wave has u = 0, whereas, when u = 0 we get a regular perturbation problem.We find the numerical and asymptotic solutions for RDS. We have published the aboveWe study the stability of travelling wave solutions for RDS in two dimensions using numerical and asymptotic methods. We also used the Evans function as a tool for computing the stability of the three types of wave. We find that all the types of travelling wave solutions are stable for all values of the parameters.ii

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Stability of screening solitons in photorefractive media

Cited by 28 publications

References 17 publications

Dynamics of blueshifted floating pulses in gas-filled hollow-core photonic crystal fibers

Dynamics of blueshifted floating pulses in gas-filled hollow-core photonic crystal fibers

On conformity of solutions for one-dimensional photorefractive screening solitons with the Kukhtarev–Vinetskii model

A Reaction Diffusion Model for Inter-Species Competition and Intra-Species Cooperation

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