Multisoliton interactions and wavelength-division multiplexing

Chakravarty, Sarbarish; Ablowitz, Mark J.; Sauer, J.R.; Jenkins, Ron

doi:10.1364/ol.20.000136

Cited by 72 publications

(31 citation statements)

References 8 publications

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“…Then the resulting propagation equation is a set of coupled nonlinear Schrödinger (CNLS) equations [4], which are nonintegrable in general. The CNLS equations are ubiquitous in the sense that they have diverse applications such as in the theory of soliton wavelength division multiplexing [5], multi-channel bit parallel-wavelength optical fiber networks [6], and so on. They even occur in the study of launching and propagation of solitons along the three spines of an alpha-helix in protein [7].…”

Section: Introductionmentioning

confidence: 99%

Shape changing collisions of optical solitons, universal logic gates and partially coherent solitons in coupled nonlinear Schrödinger equations

Lakshmanan

Kanna²

2001

Pramana - J Phys

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Coupled nonlinear Schrödinger equations (CNLS) very often represent wave propagation in optical media such as multicore fibers, photorefractive materials and so on. We consider specifically the pulse propagation in integrable CNLS equations (generalized Manakov systems). We point out that these systems possess novel exact soliton type pulses which are shape changing under collision leading to an intensity redistribution. The shape changes correspond to linear fractional transformations allowing for the possibility of construction of logic gates and Turing equivalent all optical computers in homogeneous bulk media as shown by Steiglitz recently. Special cases of such solitons correspond to the recently much discussed partially coherent stationary solitons (PCS). In this paper, we review critically the recent developments regarding the above properties with particular reference to 2-CNLS.

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Section: Introductionmentioning

confidence: 99%

Shape changing collisions of optical solitons, universal logic gates and partially coherent solitons in coupled nonlinear Schrödinger equations

Lakshmanan

Kanna²

2001

Pramana - J Phys

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“…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.…”

mentioning

confidence: 99%

“…(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.…”

mentioning

confidence: 99%

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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“…System (9) is a Manakov system, which is seen in the pulse propagation in two-mode optical fibres [22] and in the theory of soliton wavelength division multiplexing [23]. Furthermore, the bright and dark vector soliton solutions [24,25], periodic solutions [26], and effects of an initial phase difference and interactions of two solitons with different amplitudes for System (9) [27] have also been investigated.…”

Section: Reduction and New Solutions For (1)mentioning

confidence: 99%

Reductions and Solutions of Two Types of Coupled Nonlinear Evolution Equations in Optical Fibers and Fluid Dynamics

Liu

Tian

Qin

et al. 2011

Zeitschrift Für Naturforschung A

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Under investigation in this paper are the coupled nonlinear Schrödinger equations (CNLSEs) and coupled Burgers-type equations (CBEs), which are, respectively, a model for certain birefringent optical fibers Raman-scattering, Kerr and gain/loss effects, and a generalized model in fluid dynamics. Special attention should be paid to the existing claim that the solitons for the CNLSEs do not exist. Through certain dependent-variable transformations, the CNLSEs are reduced to a Manakov system and the CBEs are linearized. In that way, some new solutions of the CNLSEs and CBEs are obtained via symbolic computation. Especially the one-dark-soliton-like solutions for the CNLSEs have been found, against the existing claim.

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Multisoliton interactions and wavelength-division multiplexing

Cited by 72 publications

References 8 publications

Shape changing collisions of optical solitons, universal logic gates and partially coherent solitons in coupled nonlinear Schrödinger equations

Shape changing collisions of optical solitons, universal logic gates and partially coherent solitons in coupled nonlinear Schrödinger equations

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

Reductions and Solutions of Two Types of Coupled Nonlinear Evolution Equations in Optical Fibers and Fluid Dynamics

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