Solution of coupled nonlinear Schrödinger equations in focusing-defocusing medium by modified perturbation theory

IF 0.5 Q4 OPTICS

Photonics Letters of Poland Pub Date : 2021-06-30 DOI:10.4302/plp.v13i2.1106

J. Jasiński, M. Karpierz

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Abstract

The interaction of bright solitons of different orders and two different wavelengths propagating in the medium focusing for one wavelength and defocusing for the other is considered. The system of nonlinear Schrödinger equations is solved by means of perturbation theory. Application of an additional postulate to adjust both widths of the solitons and to modify the amplitude by a factor determined by the overlap integral greatly improves the accuracy of the description. The good accuracy of description is confirmed by numerical calculations. Full Text: PDF ReferencesY. Kivshar, G. P. Agrawal, Optical Solitons. From Fibers to Photonic Crystals, (Amsterdam, Academic Press 2003). CrossRef F. Abdullaev, S. Darmanyan, P. Khabibullaev, Optical Solitons, (Springer-Verlag, Berlin, 1993) CrossRef G.I.A Stegema, D.N. Christodoulides, M. Segev, IEEE J. Selected Topics Quantum Electron. 6, (2000), 1419 CrossRef J. Yang, "Nonlinear Waves in Integrable and Nonintegrable Systems", (SIAM, Philadelphia 2010). CrossRef Y. Kivshar, B. Malomed, "Dynamics of solitons in nearly integrable systems", Rev. Mod. Phys. 61, 763 (1989). CrossRef P.G. Kevrekidis, D.J. Frantzeskakis, "Solitons in coupled nonlinear Schrödinger models: A survey of recent developments", Reviews in Physics 1 (2016), 140 CrossRef R. de la Fuente, A. Barthelemy, "Spatial soliton-induced guiding by cross-phase modulation", IEEE J. Quantum Electron. 28, 547 (1992). CrossRef H. T. Tran, R. A. Sammut, "Families of multiwavelength spatial solitons in nonlinear Kerr media", Phys. Rev. A 52, 3170 (1995). CrossRef S. Leble, B. Reichel, "Coupled nonlinear Schrödinger equations in optic fibers theory", Eur. Phys. J. Special Topics 173, 5 (2009). CrossRef M. Vijayajayanthi, T.Kanna, M. Lakshmanan, "Multisoliton solutions and energy sharing collisions in coupled nonlinear Schrödinger equations with focusing, defocusing and mixed type nonlinearities", Eur. Phys. J. Special Topics 173, 57 (2009). CrossRef S. V. Manakov, "On the theory of two-dimensional stationary self-focusing of electromagnetic waves ", Sov. Phys. JETP 38 (1973), 248 DirectLink J. Yang, Phys. Rev. E 65, 036606 (2002). CrossRef T.Kanna, M. Lakshmanan, "Exact Soliton Solutions, Shape Changing Collisions, and Partially Coherent Solitons in Coupled Nonlinear Schrödinger Equations", Phys. Rev. Lett. 86, 5043 (2001). CrossRef M. Jakubowski, K. Steiglitz, R. Squier, "State transformations of colliding optical solitons and possible application to computation in bulk media", Phys. Rev. E 58, 6752 (1998). CrossRef P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, and M. A. Karpierz, "Supermode spatial optical solitons in liquid crystals with competing nonlinearities", Phys. Rev. A 95 (2017). CrossRef P. S. Jung, M. A. Karpierz, M. Trippenbach, D. N. Christodoulides, and W. Krolikowski, "Supermode spatial solitons via competing nonlocal nonlinearities", Photonics Lett. Pol. 10 (2018). CrossRef A. Ramaniuk, M. Trippenbach, P.S. Jung, D.N. Christodoulides, W.Krolikowski, G. Assanto, "Scalar and vector supermode solitons owing to competing nonlocal nonlinearities", Opt. Express 29, 8015 (2021) CrossRef

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用修正微扰理论求解聚焦-散焦介质中耦合非线性Schrödinger方程

考虑了两种不同波长、不同阶数的亮孤子在介质中传播时的相互作用，其中一种波长聚焦，另一种波长散焦。用摄动理论求解了非线性Schrödinger方程组。应用一个额外的假设来调整孤子的宽度，并通过由重叠积分决定的因子来修改振幅，大大提高了描述的准确性。数值计算证实了描述的良好准确性。全文:PDF参考。G. P. Agrawal，光学孤子。从光纤到光子晶体，(阿姆斯特丹，学术出版社2003)。CrossRef F. Abdullaev, S. Darmanyan, P. Khabibullaev，光学孤子，(Springer-Verlag，柏林，1993)CrossRef G.I.A Stegema, D.N. Christodoulides, M. Segev, IEEE .量子电子选辑，6，(2000)，1419 CrossRef J. Yang，“可积和不可积系统中的非线性波”，(SIAM，费城，2010)。CrossRef . Kivshar . B. Malomed .“近可积系统的孤子动力学”，物理学报，61,763(1989)。CrossRef P.G. Kevrekidis, D.J. Frantzeskakis，“耦合非线性Schrödinger模型中的孤子:近期发展综述”，物理评论1 (2016)，140 CrossRef R. de la Fuente, A. Barthelemy，“交叉相位调制的空间孤子诱导引导”，IEEE J.量子电子，28,547(1992)。陈洪涛，“非线性Kerr介质中的多波长空间孤子族”，物理学报。修订版52,3170(1995)。CrossRef S. Leble, B. Reichel，“光纤理论中的耦合非线性Schrödinger方程”，欧洲。理论物理。[j] .科学通报，2009(5)。引用本文:M. Vijayajayanthi, T.Kanna, M. Lakshmanan，“具有聚焦、散焦和混合非线性的耦合非线性Schrödinger方程的多孤子解和能量共享碰撞”，ei。理论物理。[j] .中国科学:自然科学，2009(5)。CrossRef S. V. Manakov，“电磁波二维稳态自聚焦理论的研究”，中华人民大学学报(自然科学版)。理论物理。[j]杨建军。Rev. 65, 036606(2002)。交叉参考T.Kanna, M. Lakshmanan，“精确孤子解、形状变化碰撞和耦合非线性Schrödinger方程中的部分相干孤子”，物理学报。Rev. Lett. 86, 5043(2001)。CrossRef M. Jakubowski, K. Steiglitz, R. Squier，“碰撞光孤子的状态变换及其在体介质计算中的可能应用”，物理学报。Rev. 58,6752(1998)。CrossRef P. S. Jung, W. Krolikowski, U. A. Laudyn, M. Trippenbach, M. A. Karpierz，“竞争非线性液晶中的超模空间光孤子”，物理学报。Rev. A 95(2017)。引用本文:P. S. Jung, M. A. Karpierz, M. Trippenbach, D. N. Christodoulides, W. Krolikowski，“竞争非局部非线性的超模空间孤子”，光子学杂志。波尔10(2018)。A. Ramaniuk, M. Trippenbach, P.S. Jung, D.N. Christodoulides, W.Krolikowski, G. Assanto，“竞争非局部非线性的标量和矢量超模孤子”，光学学报，29 (21

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Photonics Letters of Poland OPTICS-

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1.40

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