Propagation dynamics of finite-energy Airy beams in nonlocal nonlinear media

Abstract

We investigate periodic inversion and phase transition of normal and displaced finite-energy Airy beams propagating in nonlocal nonlinear media with the split-step Fourier method. Numerical simulation results show that parameters such as the degree of nonlocality and amplitude have profound effects on the intensity distribution of the period of an Airy beam. Nonlocal nonlinear media will reduce into a harmonic potential if the nonlocality is strong enough, which results in the beam fluctuating in an approximately cosine mode. The beam profile changes from an Airy profile to a Gaussian one at a critical point, and during propagation the process repeats to form an unusual oscillation. We also briefly discus the two-dimensional case, being equivalent to a product of two one-dimensional cases.

Keywords

Airy beam / nonlocal nonlinear / phase transition / intensity distribution

References

[1] M. V. Berry and N. L. Balazs, Nonspreading wave packets, Am. J. Phys. 47(3), 264 (1979)

[2] G. A. Siviloglou and D. N. Christodoulides, Accelerating finite energy Airy beams, Opt. Lett. 32(8), 979 (2007)

[3] G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, Observation of accelerating Airy beams, Phys. Rev. Lett. 99(21), 213901 (2007)

[4] J. Broky, G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, Self-healing properties of optical Airy beams, Opt. Express 16(17), 12880 (2008)

[5] T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, Nonlinear generation and manipulation of Airy beams, Nat. Photonics 3(7), 395 (2009)

[6] A. Chong, W. H. Renninger, D. N. Christodoulides, and F. W. Wise, Airy-Bessel wave packets as versatile linear light bullets, Nat. Photonics 4(2), 103 (2010)

[7] P. Zhang, J. Prakash, Z. Zhang, M. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. G. Chen, Trapping and guiding microparticles with morphing autofocusing Airy beams, Opt. Lett. 36(15), 2883 (2011)

[8] P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, Curved plasma channel generation using ultraintense Airy beams, Science 324(5924), 229 (2009)

[9] J. Amako, D. Sawaki, and E. Fujii, Microstructuring transparent materials by use of nondiffracting ultrashort pulse beams generated by diffractive optics, J. Opt. Soc. Am. B 20(12), 2562 (2003)

[10] C. Lee, J. Huang, H. Deng, H. Dai, and J. Xu, Nonlinear quantum interferometry with Bose condensed atoms, Front. Phys. 12, 053010 (2010)

[11] D. Abdollahpour, S. Suntsov, D. Papazoglou, and S. Tzortzakis, Spatiotemporal Airy light bullets in the linear and nonlinear regimes, Phys. Rev. Lett. 105(25), 253901 (2010)

[12] Y. Q. Zhang, M. R. BelićZ. K. Wu, H. B. Zheng, K. Q. Lu, Y. Y. Li, and Y. P. Zhang, Soliton pair generation in the interactions of Airy and nonlinear accelerating beams, Opt. Lett. 38(22), 4585 (2013)

[13] Y. Q. Zhang, M. R. BelićH. B. Zheng, H. X. Chen, C. B. Li, Y. Y. Li, and Y. P. Zhang, Interactions of Airy beams, nonlinear accelerating beams, and induced solitons in Kerr and saturable nonlinear media, Opt. Express 22(6), 7160 (2014)

[14] Q. Kong, Q. Wang, O. Bang, and W. Krolikowski, Analytical theory for the dark-soliton interaction in nonlocal nonlinear materials with an arbitrary degree of nonlocality, Phys. Rev. A 82, 013826 (2010)

[15] W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals, Appl. Phys. Lett. 89, 071111 (2006)

[16] R. Bekenstein and M. Segev, Self-accelerating optical beams in highly nonlocal nonlinear media, Opt. Express 19(24), 23706 (2011)

[17] G. Q. Zhou, R. P. Chen, and G. Y. Ru, Propagation of an Airy beam in a strongly nonlocal nonlinear media, Laser. Phys. Lett. 11, 105001 (2014)

[18] R. Bekenstein, R. Schley, M. Mutzafi, C. Rotschild, and M. Segev, Optical simulations of gravitational effects in the Newton-Schrodinger system, Nat. Phys. 11, 872 (2015)

[19] M. Shen, J. S. Gao, and L. J. Ge, Solitons shedding from Airy beams and bound states of breathing Airy solitons in nonlocal nonlinear media, Sci. Rep. 5, 9814 (2015)

[20] M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, Routing of anisotropic spatial solitons and modulational instability in liquid crystals, Nature 432(7018), 733 (2004)

[21] C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, Longrange interactions between optical solitons, Nat. Phys. 2(11), 769 (2006)

[22] J. K. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems, SIAM, 2010

[23] Y. Q. Zhang, M. R. BelićL. Zhang, W. P. Zhong, D. Y. Zhu, R. M. Wang, and Y. P. Zhang, Periodic inversion and phase transition of finite energy Airy beams in a medium with parabolic potential, Opt. Express 23(8), 10467 (2015)

[24] F. Xiao, B. Li, M. Wang, W. Zhu, P. Zhang, S. Liu, M. Premaratne, and J. Zhao, Optical Bloch oscillations of an Airy beam in a photonic lattice with a linear transverse index gradient, Opt. Express 22(19), 22763 (2014)

[25] Y. Q. Zhang, X. Liu, M. R. BelićW. P. Zhong, M. S. Petrović and Y. P. Zhang, Automatic Fourier transform and self-Fourier beams due to parabolic potential, Ann. Phys. 363, 305 (2015)

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