Vector multipole and vortex solitons in two-dimensional Kerr media

We investigate a (2+1)-dimensional coupled nonlinear Schrödinger equation with spatially modulated nonlinearity and transverse modulation, and derive analytical vector multipole and vortex soliton solution. When the modulation depth q is chosen as 0 and 1, vector multipole and vortex solitons are constructed, respectively. The number of azimuthal lobes (“petals”) for the multipole solitons is determined by the value of 2m with the topological charge m, and the number of layers in the multipole solitons is determined by the value of the soliton order number n.

[1]  Y. Kivshar,et al.  Observation of discrete vortex solitons in optically induced photonic lattices. , 2004, Physical review letters.

[2]  Edmund Taylor Whittaker,et al.  A Course of Modern Analysis , 2021 .

[3]  Humberto Michinel,et al.  Stable azimuthal stationary state in quintic nonlinear optical media , 1997 .

[4]  Chao-Qing Dai,et al.  Vector spatiotemporal localized structures in (3 $$+$$+ 1)-dimensional strongly nonlocal nonlinear media , 2016 .

[5]  Yuri S. Kivshar,et al.  Optical Solitons: From Fibers to Photonic Crystals , 2003 .

[6]  C. Dai,et al.  Dynamics of light bullets in inhomogeneous cubic-quintic-septimal nonlinear media with $${\varvec{{\mathcal {PT}}}}$$PT-symmetric potentials , 2017 .

[7]  M. Belić,et al.  Spatiotemporal soliton clusters in strongly nonlocal media with variable potential coefficients , 2017 .

[8]  Juan Belmonte-Beitia,et al.  Localized nonlinear waves in systems with time- and space-modulated nonlinearities. , 2008, Physical review letters.

[9]  W. M. Liu,et al.  Exact solutions of the Gross-Pitaevskii equation for stable vortex modes in two-dimensional Bose-Einstein condensates , 2010 .

[10]  M. Eslami,et al.  Optical solitons with Biswas–Milovic equation by extended trial equation method , 2016 .

[11]  Lei Wu,et al.  Vortex solitons in defocusing media with spatially inhomogeneous nonlinearity. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Boris A. Malomed,et al.  Stable (2+1)-dimensional solitons in a layered medium with sign-alternating Kerr nonlinearity , 2002 .

[13]  S. V. Manakov.  On the theory of two-dimensional stationary self-focusing of electromagnetic waves , 1973 .

[14]  C. Dai,et al.  Two-dimensional localized Peregrine solution and breather excited in a variable-coefficient nonlinear Schrödinger equation with partial nonlocality , 2017 .

[15]  Peiguang Yan,et al.  70-fs mode-locked erbium-doped fiber laser with topological insulator , 2016, Scientific Reports.

[16]  Chao-Qing Dai,et al.  Discussions on localized structures based on equivalent solution with different forms of breaking soliton model , 2017 .

[17]  R. Gómez-Alcalá,et al.  Vector soliton switching by using the cascade connection of saturable absorbers. , 2006, Optics letters.

[18]  Ying Liu,et al.  Bound vector solitons and soliton complexes for the coupled nonlinear Schrödinger equations. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Qin Zhou,et al.  Analytical study of solitons in non-Kerr nonlinear negative-index materials , 2016 .

[20]  Boris A. Malomed,et al.  Self-trapping of scalar and vector dipole solitary waves in Kerr media , 2011 .

[21]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[22]  W. M. Liu,et al.  Exact soliton solutions and their stability control in the nonlinear Schrödinger equation with spatiotemporally modulated nonlinearity. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  M. Belić,et al.  Two-dimensional accessible solitons in PT-symmetric potentials , 2012 .

[24]  Yan Wang,et al.  Exact spatial soliton solution for nonlinear Schrödinger equation with a type of transverse nonperiodic modulation , 2009 .

[25]  Qin Zhou.  Optical solitons for Biswas–Milovic model with Kerr law and parabolic law nonlinearities , 2016 .

[26]  Stegeman,et al.  Optical Spatial Solitons and Their Interactions: Universality and Diversity. , 1999, Science.

[27]  Qiuping Zhu,et al.  Optical solitons in media with time-modulated nonlinearities and spatiotemporal dispersion , 2015 .

[28]  K Aravinthan,et al.  A dark-bright optical soliton solution to the coupled nonlinear Schrödinger equation , 2007 .