Abstract
Nonlinear dynamics of an optical pulse or a beam continue to be one of the active areas of research in the field of optical solitons. Especially, in multi-mode fibers or fiber arrays and photorefractive materials, the vector solitons display rich nonlinear phenomena. Due to their fascinating and intriguing novel properties, the theory of optical vector solitons has been developed considerably both from theoretical and experimental points of view leading to soliton-based promising potential applications. Mathematically, the dynamics of vector solitons can be understood from the framework of the coupled nonlinear Schrödinger (CNLS) family of equations. In the recent past, many types of vector solitons have been identified both in the integrable and non-integrable CNLS framework. In this article, we review some of the recent progress in understanding the dynamics of the so called nondegenerate vector bright solitons in nonlinear optics, where the fundamental soliton can have more than one propagation constant. We address this theme by considering the integrable two coupled nonlinear Schrödinger family of equations, namely the Manakov system, mixed 2-CNLS system (or focusing-defocusing CNLS system), coherently coupled nonlinear Schrödinger (CCNLS) system, generalized coupled nonlinear Schrödinger (GCNLS) system and two-component long-wave short-wave resonance interaction (LSRI) system. In these models, we discuss the existence of nondegenerate vector solitons and their associated novel multi-hump geometrical profile nature by deriving their analytical forms through the Hirota bilinear method. Then we reveal the novel collision properties of the nondegenerate solitons in the Manakov system as an example. The asymptotic analysis shows that the nondegenerate solitons, in general, undergo three types of elastic collisions without any energy redistribution among the modes. Furthermore, we show that the energy sharing collision exhibiting vector solitons arises as a special case of the newly reported nondegenerate vector solitons. Finally, we point out the possible further developments in this subject and potential applications.
Highlights
Solitons are stable localized nonlinear wave packets which can propagate without distortion over long distances
We have shown that such an inclusion of additional distinct propagation constants brings out a general form of vector bright soliton solution to the several integrable coupled nonlinear Schrödinger (CNLS) systems [76,77], namely the Manakov system or 2-CNLS system, mixed 2-CNLS system, two-component coherently coupled nonlinear Schrödinger (NLS) system, generalized CNLS system, and two-component long-wave short-wave resonance interaction system [77]
In order to differentiate the above class of vector bright solitons from more general fundamental solitons, we classify them as degenerate and nondegenerate solitons based on the absence or presence of more than one wave number in the multi-component soliton solution
Summary
Solitons are stable localized nonlinear wave packets which can propagate without distortion over long distances. Like in the scalar NLS equation, the optical vector solitons are formed due to an exact balance between the dispersion/diffraction and the self-phase modulation and cross-phase modulation This interesting class of optical solitons was first predicted by Manakov in 1974, where he derived the one-soliton solution and made an asymptotic analysis for the two-soliton solution through the IST method, by introducing a set of two CNLS equations for the nonlinear interaction of the two orthogonally polarized optical waves in birefringent fibers [33]. We have shown that such an inclusion of additional distinct propagation constants brings out a general form of vector bright soliton solution to the several integrable CNLS systems [76,77], namely the Manakov system or 2-CNLS system, mixed 2-CNLS system (with one mode in the anomalous dispersion regime and the other mode in the normal dispersion regime), two-component coherently coupled NLS system, generalized CNLS system, and two-component long-wave short-wave resonance interaction system [77].
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