Inelastic collision and switching of coupled bright solitons in optical fibers

Radhakrishnan, R.; Lakshmanan, M.; Hietarinta, Jarmo

doi:10.1103/physreve.56.2213

Cited by 323 publications

(315 citation statements)

References 25 publications

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“…In particular, we point out that the shape changing inelastic collision property persists for the N ≥ 3 cases also as in the N = 2 (Manakov) case reported recently [5], giving rise to many possibilities of energy exchange. Furthermore, we point out that in the context of spatial solitons the partially coherent stationary solitons(PCS) reported in the recent literature [9][10] are special cases of the above general soliton solutions which undergo shape changing collisions.…”

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confidence: 94%

“…For N = 2, the above Eq. (1) governs the integrable Manakov system [4] and recently for this case the exact two-soliton solution has been obtained and novel shape changing inelastic collision property has been brought out [5]. However, the results are scarce for N ≥ 3, even though the underlying systems are of considerable physical interest.…”

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confidence: 99%

“…The nature of the interaction of the underlying solitons can be well understood by making an asymptotic analysis of the two-soliton solution [5]. Asymptotically, the two-soliton solution(5) can be written as a combination of two one-soliton solutions and their forms in the two different regimes z → −∞ and z → ∞ are similar to those of the one-soliton solution given in Eq.…”

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confidence: 99%

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Exact Soliton Solutions, Shape Changing Collisions, and Partially Coherent Solitons in Coupled Nonlinear Schrödinger Equations

2001

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We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schrödinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general N -coupled nonlinear Schrödinger equations (N -CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among the modes. We also analyse the various possibilities and conditions for such collisions to occur. Further, we report the significant fact that the various partial coherent solitons (PCS) discussed in the literature are special cases of the higher order bright soliton solutions of the N -CNLS equations.PACS numbers: 42.81. Dp, 42.65.Tg In recent years the concept of soliton has been receiving considerable attention in optical communications since soliton is capable of propagating over long distances without change of shape and with negligible attenuation [1][2][3]. It has been found that soliton propagation through optical fiber arrays is governed by a set of equations related to the CNLS equations [1,2],where q j is the envelope in the jth core, z and t represent the normalized distance along the fiber and the retarded time, respectively. Here 2µ gives the strength of the nonlinearity. Eq. (1) reduces to the standard envelope soliton possessing integrable nonlinear Schrödinger equation for N = 1. For N = 2, the above Eq. (1) governs the integrable Manakov system [4] and recently for this case the exact two-soliton solution has been obtained and novel shape changing inelastic collision property has been brought out [5]. However, the results are scarce for N ≥ 3, even though the underlying systems are of considerable physical interest. For example, in addition to optical communication, in the context of biophysics the case N = 3 can be used to study the launching and propagation of solitons along the three spines of an alpha-helix in protein [6]. Similarly the CNLS Eq.(1) and its generalizations for N ≥3 are of physical relevance in the theory of soliton wavelength division multiplexing [7], multi-channel bit-parallel-wavelength optical fiber networks [8] and so on. In particular, for arbitrary N , Eq.(1) governs the propagation of N -self trapped mutually incoherent wavepackets in Kerr-like photorefractive media [9] in which q j is the jth component of the beam, z and t represents the normalized coordinates along the direction of propagation and the transverse coordinate, respectively, and N p=1 |q p | 2 represents the change in the refractive index profile created by all incoherent components of the light beam [9] when the medium response is slow.The parameter µ = k 2 0 n 2 /2, where n 2 is the nonlinear Kerr coefficient and k 0 is the free space wave vector.In this letter, we report the exact bright one and two soliton solutions, first for the N = 3 case and then for the arbitrary N case, where the procedure can be extended in principle to higher order soliton solutions, using the Hirota bilinearization method. In particular, ...

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confidence: 94%

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confidence: 99%

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confidence: 99%

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Exact Soliton Solutions, Shape Changing Collisions, and Partially Coherent Solitons in Coupled Nonlinear Schrödinger Equations

2001

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“…The precession is initiated through the atom transfer between the dark states in the defect region, which changes S 1 and perturbs the initial one-soliton solution. The integrability of the system is "restored" after the soliton passes the defect, but the soliton is now transformed into a breather characterized by the internal frequency (for the discussion of the two-soliton solutions of the MS see, e.g., [21]). Small modification of also strongly affects the component S 3 (t), which acquires a nearly constant value after scattering [∼1 in Fig.…”

Section: The Scattering Problemmentioning

confidence: 99%

Bose-Einstein condensates with localized spin-orbit coupling: Soliton complexes and spinor dynamics

2014

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Spin-orbit (SO) coupling can be introduced in a Bose-Einstein condensate (BEC) as a gauge potential acting only in a localized spatial domain. The effect of such a SO "defect" can be understood by transforming the system to the integrable vector model. The properties of the SO BEC change drastically if the SO defect is accompanied by the Zeeman splitting. In such a nonintegrable system, the SO defect qualitatively changes the character of soliton interactions and allows for formation of stable nearly scalar soliton complexes with almost all atoms concentrated in only one dark state. These solitons exist only if the number of particles exceeds a threshold value. We also report on the possibility of transmission and reflection of a soliton upon its scattering on the SO defect. Scattering strongly affects the pseudospin polarization and can induce pseudospin precession. The scattering can also result in almost complete atomic transfer between the dark states.

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“…These Manakov and mixed-ICNLS systems find important applications in optical communication and in artificial metamaterials. They have been intensively studied in literature [2,[8][9][10][11][12][13][14][15][16][17][18][19]. Also, the integrable multicomponent generalization of ICNLS system (1) can be written as…”

Section: Introductionmentioning

confidence: 99%