Generation of airy solitary-like wave beams by acceleration control in inhomogeneous media

Optics Express

Volumn 19, Issue 17, 2011, Pages 16448-16454

  Chávez Cerda, Sabino ^a   Ruiz, Ulises ^b   Arrizón, Victor ^a   Moya Cessa, Héctor M ^a  

^a INSTITUTO NACIONAL DE ASTROFÍSICA   (Mexico)

^b UNIVERSITY OF CALABRIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85010123862     PISSN: None     EISSN: 10944087     Source Type: Journal    
DOI: 10.1364/OE.19.016448     Document Type: Article

References (29)

1. G. A. Siviloglou and D. N. Christodoulides, “Accelerating finite energy Airy beams, ” Opt. Lett. 32(8), 979-981 (2007).
2. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams, ” Phys. Rev. Lett. 99(21), 213-901 (2007).
3. J. Durnin, J. Miceli, Jr., and J. H. Eberly, “Diffraction-free beams, ” Phys. Rev. Lett. 58(15), 1499-1501 (1987).
4. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory, ” J. Opt. Soc. Am. A 4(4), 651-654 (1987).
5. D. DeBeer, S. R. Hartmann, and R. Friedberg, “Comment on “Diffraction-free beams”, ” Phys. Rev. Lett. 59(22), 2611 (1987).
6. J. Durnin, J. J. Miceli, Jr., and J. H. Eberly, “Durnin, Miceli, and Eberly reply, ” Phys. Rev. Lett. 59(22), 2612 (1987).
7. S. Chavez-Cerda, “A new approach to Bessel beams, ” J. Mod. Opt. 46, 923-930 (1999).
8. M. V. Berry and N. L. Balazs, “Nonspreading wave-packets, ” Am. J. Phys. 47(3), 264-267 (1979).
9. M. A. Bandres, J. C. Gutierrez-Vega, and S. Chavez-Cerda, “Parabolic nondiffracting optical wave fields, ” Opt. Lett. 29(1), 44-46 (2004).
10. C. Lopez-Mariscal, M. Bandres, J. Gutierrez-Vega, and S. Chavez-Cerda, “Observation of parabolic nondiffracting optical fields, ” Opt. Express 13(7), 2364-2369 (2005).
11. D. Marcuse, “TE modes of graded index slab waveguides, ” IEEE J. Quantum Electron. 9(10), 1000-1006 (1973).
12. C.-L. Chen, Foundations of guided-wave optics (Wiley, New Jersey 2006), Ch 3.
13. D. N. Christodoulides and T. H. Coskun, “Diffraction-free planar beams in unbiased photorefractive media, ” Opt. Lett. 21(18), 1460-1462 (1996).
14. S. Jia, J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, “Diffusion-trapped Airy beams in photorefractive media, ” Phys. Rev. Lett. 104(25), 253-904 (2010).
15. T. Ellenbogen, N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, “Nonlinear generation and manipulation of Airy beams, ” Nat. Photonics 3(7), 395-398 (2009).
16. I. Dolev, T. Ellenbogen, and A. Arie, “Switching the acceleration direction of Airy beams by a nonlinear optical process, ” Opt. Lett. 35(10), 1581-1583 (2010).
17. Ye, Zhuoyi; Liu, Sheng; Lou, Cibo; Zhang, Peng; Hu, Yi; Song, Daohong; Zhao, Jianlin; Chen, Zhigang, Quantum Electronics and Laser Science Conference (QELS) 2011 paper: JTuI32, OSA Technical Digest (CD).
18. W. Liu, D. N. Neshev, I. V. Shadrivov, A. E. Miroshnichenko, and Y. S. Kivshar, “Plasmonic Airy beam manipulation in linear optical potentials, ” Opt. Lett. 36(7), 1164-1166 (2011).
19. M. Born and E. Wolf, Principles of Optics, Seventh Ed., (Cambridge University Press, Cambridge 1999), Ch. 3.
20. There exist several forms for producing a solution of this equation, for instance by using the Zassenhaus formula [19], or by simplifying the differential equation via a transformation (see for instance [20] for a quadratic term).
21. The operators to disentangle the exponential of the sum of two operators can also be given in different orderings of the exponentials involved. Of course, they are all equivalent.
22. R. M. Wilcox, “Exponential operators and parameter differentiation in quantum physics, ” J. Math. Phys. 8(4), 962-982 (1967).
23. H. Moya-Cessa and M. Fernández Guasti, “Coherent states for the time dependent harmonic oscillator: the step function, ” Phys. Lett. A 311(1), 1-5 (2003).
24. W. H. Louissel, Quantum Statistical Properties of Radiation (Wiley-Interscience, New York 1990), Ch. 3.
25. H. Moya-Cessa and F. Soto-Eguibar, Differential equations: an operational approach, (Rinton Press, New Jersey 2011), Ch. 2.
26. G. N. Watson, A treatise on the theory of Bessel functions, Ch. VI, Cambridge University Press, Cambridge 1944.
27. W. M. Strouse, “Bouncing light beams, ” Am. J. Phys. 40(6), 913-914 (1972).
28. D. Ambrosini, A. Ponticiello, G. S. Spagnolo, R. Borghi, and F. Gori, “Bouncing light beams and the Hamiltonian analogy, ” Eur. J. Phys. 18(4), 284-289 (1997).
29. SLM 512, Boulder nonlinear systems.