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Periodic propagation of complex-valued hyperbolic-cosine-Gaussian solitons and breathers with complicated light field structure in strongly nonlocal nonlinear media. (English) Zbl 1477.35246

Summary: In this study, the propagation characteristics of complex-valued hyperbolic-cosine-Gaussian (CVHCG) beams were studied based on the nonlocal nonlinear Schrödinger equation in strongly nonlocal nonlinear media (SNNM). The CVHCG beams exhibited some unique propagation characteristics. By adjusting the complex-valued parameters, CVHCG beams can propagate with different forms in SNNM, including Gaussian-like, nearly flat-topped, multi-peak, and four-peak forms. CVHCG beams can form shape-invariant solitons and breathers under certain incident parameters. In addition, CVHCG beams can also form generalized shape-variant high-order spatial solitons and breathers. In general, the beam width and light intensity pattern of the CVHCG beams always change periodically. A complete theoretical model was constructed, and the expressions for the propagation, light intensity, and second-order moment beam width were obtained analytically. Some typical propagation characteristics were demonstrated via numerical simulations. The results of this study can be extended to investigate other complex-valued beams.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35Q60 PDEs in connection with optics and electromagnetic theory
78A60 Lasers, masers, optical bistability, nonlinear optics
78A40 Waves and radiation in optics and electromagnetic theory
35C08 Soliton solutions
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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[1] Kivshar, Y. S., Optical solitons: from fibers to photonic crystals (2003), Academic Press
[2] Zheng, Y.; Gao, Y.; Wang, J.; Lv, F.; Lu, D.; Hu, W.; Li, H.; Xu, S. L.; Belic, M. R.; Cheng, J. X., Three-dimensional solitons in bose-einstein condensates with spin-orbit coupling and bessel optical lattices, Phys Rev A, 98, 033827 (2018)
[3] Xu, S. L.; Zhou, Q.; Zhao, D.; Belic, M. R.; Zhao, Y., Spatiotemporal solitons in cold rydberg atomic gases with bessel optical lattices, Appl Math Lett, 104, 106230 (2020) · Zbl 1439.78015
[4] Ma, X.; Egorov, O. A.; Schumacher, S., Creation and manipulation of stable dark solitons and vortices in microcavity polariton condensates, Phys Rev Lett, 118, 157401 (2017)
[5] Dong, L. W.; Huang, C. M.; Qi, W., Nonlocal solitons in fractional dimensions, Opt Lett, 44, 4917-4920 (2019)
[6] Peng, W. Q.; Tian, S. F.; Zhang, T. T.; Fang, Y., Rational and semi-rational solutions of a nonlocal (2+1)-dimensional nonlinear schrödinger equation, Math Meth Appl Sci, 42, 6865-6877 (2019) · Zbl 1434.35192
[7] Wang, C. J.; Nie, Z. Z.; Xie, W. J.; Gao, J. Y.; Zhou, Q.; Liu, W. J., Dark soliton control based on dispersion and nonlinearity for third-order nonlinear schrödinger equation, Optik (Stuttg), 184, 370-376 (2019)
[8] Peng, W. Q.; Tian, S. F.; Zhang, T. T., Initial value problem for the pair transition coupled nonlinear schrödinger equations via the riemann-hilbert method, Complex Anal Oper Theory, 14, 38 (2020) · Zbl 1446.35186
[9] Peng, W. Q.; Tian, S. F.; Wang, X. B.; Zhang, T. T.; Fang, Y., Riemann-hilbert method and multi-soliton solutions for three-component coupled nonlinear schrödinger equations, J Geom Phys, 146, 103508 (2019) · Zbl 1427.35258
[10] Zhang, X. F.; Tian, S. F.; Yang, J. J., The riemann-hilbert approach for the focusing hirota equation with single and double poles, Anal Math Phys, 11, 86 (2021) · Zbl 1470.35249
[11] Tian, S. F., Lie symmetry analysis, conservation laws and solitary wave solutions to a fourth-order nonlinear generalized boussinesq water wave equation, Appl Math Lett, 100, 106056 (2020) · Zbl 1429.35017
[12] Yan, Y. Y.; Liu, W. J.; Zhou, Q.; Biswas, A., Dromion-like structures and periodic wave solutions for variable-coefficients complex cubic-quintic ginzburg-landau equation influenced by higher-order effects and nonlinear gain, Nonlinear Dyn, 99, 1313-1319 (2020)
[13] Liu, W. J.; Yu, W. T.; Yang, C. Y.; Liu, M. L.; Zhang, Y. J.; Lei, M., Analytic solutions for the generalized complex ginzburg-landau equation in fiber lasers, Nonlinear Dyn, 89, 2933-2939 (2017)
[14] Zheng, Y.; Gao, Y.; Wang, J.; Lv, F.; Lu, D.; Hu, W., Bright nonlocal quadratic solitons induced by boundary confinement, Phys Rev A, 95, 013808 (2017)
[15] Li, H.; Jiang, X.; Zhu, X.; Shi, Z., Nonlocal solitons in dual-periodic PT-symmetric optical lattices, Phys Rev A, 86, 023840 (2012)
[16] Wang, Q.; Yang, J.; Liang, G., Controllable soliton transition and interaction in nonlocal nonlinear media, Nonlinear Dyn, 101, 1169-1179 (2020)
[17] Chen, M.; Zeng, S.; Lu, D.; Hu, W.; Guo, Q., Optical solitons self-focusing, and wave collapse in a space-fractional schrödinger equation with a kerr-type nonlinearity, Phys Rev E, 98, 022211 (2018)
[18] Peccianti, M.; Assanto, G., Nematicons, Phys Rep, 516, 147-208 (2012)
[19] Duree, G. C.; Shultz, J. L.; Salamo, G. J.; Segev, M.; Yariv, A.; Crosignani, B.; Porto, P. D.; Sharp, E. J.; Neurgaonkar, R. R., Observation of self-trapping of an optical beam due to the photorefractive effect, Phys Rev Lett, 71, 533-536 (1993)
[20] Zhang, M.; Huo, G.; Duan, Z., Dynamic behavior of the bright incoherent spatial solitons in self-defocusing nonlinear media, Chaos, Soliton Fract, 85, 51-56 (2016) · Zbl 1366.78012
[21] Aseeva, N. V.; Gromov, E. M.; Tyutin, V. V., Interaction of short single-component vector solitons, Radiophys Quant El, 55, 184-197 (2012) · Zbl 1255.35198
[22] Baronio, F.; Degasperis, A.; Conforti, M.; Wabnitz, S., Solutions of the vector nonlinear schrödinger equations: evidence for deterministic rogue waves, Phys Rev Lett, 109, 044102 (2012)
[23] Sun, Z. Y.; Yu, X., Anomalous diffusion of discrete solitons driven by an evolving disorder, Phys Rev E, 101, 062211 (2020)
[24] Rotschild, C.; Cohen, O.; Manela, O.; Segev, M.; Carmon, T., Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons, Phys Rev Lett, 95, 213904 (2005)
[25] Pedri, P.; Santos, L., Two-dimensional bright solitons in dipolar bose-einstein condensates, Phys Rev Lett, 95, 200404 (2005)
[26] Snyder, A. W.; Mitchell, D. J., Accessible solitons, Science, 276, 1538-1541 (1997)
[27] Deng, D.; Guo, Q., Propagation of elliptic-gaussian beams in strongly nonlocal nonlinear media, Phys Rev E, 84, 046604 (2011)
[28] Buccoliero, D.; Desyatnikov, A. S.; Krolikowski, W.; Kivshar, Y. S., Spiraling multivortex solitons in nonlocal nonlinear media, Opt Lett, 33, 198 (2008)
[29] Song, L.; Yang, Z.; Li, X.; Zhang, S., Controllable gaussian-shaped soliton clusters in strongly nonlocal media, Opt Express, 26, 19182-19198 (2018)
[30] Song, L.; Yang, Z.; Zhang, S.; Li, X., Spiraling anomalous vortex beam arrays in strongly nonlocal nonlinear media, Phys Rev A, 99, 063817 (2019)
[31] Liang, G., Revolving and spinning of optical patterns by two coaxial spiraling elliptic beams in nonlocal nonlinear media, Opt Express, 27, 14667 (2019)
[32] Chen, J.; Zhang, F. S.; Bian, K.; Jiang, C. J.; Hu, W.; Lu, D. Q., Dynamics of shape-invariant rotating beams in linear media with harmonic potentials, Phys Rev A, 99, 033808 (2019)
[33] Deng, D.; Guo, Q.; Hu, W., Complex-variable-function gaussian beam in strongly nonlocal nonlinear media, Phys Rev A, 79, 023803 (2009)
[34] Siegman, A. E., Hermite-gaussian functions of complex argument as optical-beam eigenfunctions, J Opt Soc Am, 63, 1093-1094 (1973)
[35] Deng, D.; Guo, Q., Airy complex variable function gaussian beams, New J Phys, 11, 103029 (2009)
[36] Li, D.; Peng, X.; Peng, Y.; Zhang, L.; Chen, X.; Zhuang, J.; Zhao, F.; Yang, X., Deng d. (3+1)-dimensional localized self-accelerating airy elegant ince-gaussian wave packets and their radiation forces in free space, Chinese Phys B, 26, 124202 (2017)
[37] Deng, D.; Guo, Q., Elegant hermite-laguerre-gaussian beams, Opt Lett, 33, 1225-1227 (2008)
[38] Deng, D.; Guo, Q.; Hu, W., Complex-variable-function-gaussian solitons, Opt Lett, 34, 43-45 (2009)
[39] Wang, F.; Cai, Y.; Korotkova, O., Partially coherent standards and elegant laguerre-gaussian beams of all orders, Opt Express, 17, 22366-22379 (2009)
[40] Liu, Z.; Zhao, D., Radiation forces acting on a rayleigh dielectric sphere produced by highly focused elegant hermite-cosine-gaussian beams, Opt Express, 20, 2895-2904 (2012)
[41] Chabou, S.; Bencheikh, A., Elegant gaussian beams: nondiffracting nature and self-healing property, Appl Opt, 59, 9999-10006 (2020)
[42] Jana, S.; Konar, S., Tunable spectral switching in the far field with a chirped cosh-gaussian pulse, Opt Commun, 267, 24-31 (2006)
[43] Zhang, Y.; Song, Y.; Chen, Z.; Ji, J.; Shi, Z., Virtual sources for a cosh-gaussian beam, Opt Lett, 32, 292-294 (2007)
[44] Chu, X., Propagation of a cosh-gaussian beam through an optical system in a turbulent atmosphere, Opt Express, 15, 17613-17618 (2007)
[45] Zhou, G., Propagation of a higher-order cosh-gaussian beam in turbulent atmosphere, Opt Express, 19, 3945-3951 (2011)
[46] Singh, M.; Singh, R. K.; Sharma, R. P., THZ generation by cosh-gaussian lasers in rippled density plasma, EPL, 104, 35002 (2013)
[47] Vhanmore, B. D.; Takale, M. V.; Patil, S. D., Influence of light absorption in the interaction of asymmetric elegant hermite-cosh-gaussian laser beams with collisionless magnetized plasma, Phys Plasmas, 27, 063104 (2020)
[48] Guo, Q.; Luo, B.; Yi, F.; Chi, S.; Xie, Y., Large phase shift of nonlocal optical spatial solitons, Phys Rev E, 69, 016602 (2004)
[49] Agrawal, G. P., Nonlinear fiber optics (2013), Press, Oxford
[50] Krolikowski, W.; Bang, O.; Rasmussen, J. J.; Wyller, J., Modulational instability in nonlocal nonlinear kerr media, Phys Rev E, 64, 016612 (2001)
[51] Liang, G.; Hong, W.; Luo, T.; Wang, J.; Li, Y.; Guo, Q.; Hu, W., Christodoulides DN. transition between self-focusing and self-defocusing in a nonlocally nonlinear system, Phys Rev A, 99, 063808 (2019)
[52] Liang, G.; Hong, W.; Guo, Q., Spatial solitons with complicated structure in nonlocal nonlinear media, Opt Express, 24, 28784-28793 (2016)
[53] Peters, E.; Clemente, P.; Salvador-Balaguer, E.; Tajahuerce, E.; Andrěs, P.; Pěrez, D. G.; Lancis, J., Real-time acquisition of complex optical fields by binary amplitude modulation, Opt Lett, 42, 2030-2033 (2017)
[54] Chen, J.; Wan, C.; Kong, L.; Zhan, Q., Precise transverse alignment of spatial light modulator sections for complex optical field generation, Appl Opt, 56, 2614-2620 (2017)
[55] Curtis, J. E.; Koss, B. A.; Grier, D. G., Dynamic holographic optical tweezers, Opt Commun, 207, 169-175 (2002)
[56] Grier, D. G., A revolution in optical manipulation, Nature, 424, 810-816 (2003)
[57] Dou, J. P.; Ren, D. Q.; Zhu, Y. T.; Zhang, X., Focal plane wave-front sensing algorithm for high-contrast imaging, Sci China Ser-G-Phys Mech Astron, 52, 1284-1288 (2009)
[58] Eisert, J.; Plenio, M. B., Conditions for the local manipulation of gaussian states, Phys Rev Lett, 89, 097901 (2002)
[59] Zhao, C.; Cai, Y.; Lu, X.; Eyyuboǧlu, H. T., Radiation force of coherent and partially coherent flat-topped beams on a rayleigh particle, Opt Express, 17, 1753-1765 (2009)
[60] Wang, Q.; Deng, Z. Z., Controllable propagation path of imaginary value off-axis vortex soliton in nonlocal nonlinear media, Nonlinear Dyn, 100, 1589-1598 (2020)
[61] Lu, D.; Hu, W.; Zheng, Y.; Liang, Y.; Cao, L.; Lan, S.; Guo, Q., Self-induced fractional fourier transform and revivability higher-order spatial solitons in strongly nonlocal nonlinear media, Phys Rev A, 78, 043815 (2008)
[62] Bélanger, P. A., Beam propagation and the ABCD ray matrices, Opt Lett, 16, 196-198 (1991)
[63] Song, L. M.; Yang, Z. J.; Pang, Z. G.; Li, X. L.; Zhang, S. M., Interaction theory of mirror-symmetry soliton pairs in nonlocal nonlinear schrödinger equation, Appl Math Lett, 90, 42-48 (2019) · Zbl 1410.35213
[64] Liang, G.; Guo, Q.; Cheng, W.; Yin, N.; Wu, P.; Cao, H., Spiraling elliptic beam in nonlocal nonlinear media, Opt Express, 19, 24612-24625 (2015)
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