Vol. 49
Latest Volume
All Volumes
PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2016-07-13
Novel Finite Airy Array Beams Generated from Gaussian Array Beams Illuminating an Optical Airy Transform System
By
Progress In Electromagnetics Research M, Vol. 49, 41-50, 2016
Abstract
In this work, a novel family of Finite Airy array beams have been produced by an optical Airy transform system illuminated by Gaussian Array beams. Based on the generalized Huygens- Fresnel integral, an analytical expression is developed to describe the pattern properties of the beam generated at the output plan of the optical system. The well-known Finite Airy beam generated from the fundamental Gaussian beam using an optical Airy transform system is deduced, here, as a particular case of the main result of the actual study. Numerical calculations are performed to show the possibility to create a multitude of Finite Airy array beams with controllable parameters depending on the number of beamlets, the distance between the adjacent modules and the positions and orientations of the beamlets.
Citation
Lahcen EZ-ZARIY Zoubir Hricha Abdelmajid Belafhal , "Novel Finite Airy Array Beams Generated from Gaussian Array Beams Illuminating an Optical Airy Transform System," Progress In Electromagnetics Research M, Vol. 49, 41-50, 2016.
doi:10.2528/PIERM16041909
http://www.jpier.org/PIERM/pier.php?paper=16041909
References

1. Berry, M. V. and N. L. Balazs, "Non-spreading wave packet," Am. J. Phys., Vol. 47, 264-267, 1979.
doi:10.1119/1.11855

2. Broky, J., G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, "Self-healing properties of optical Airy beams," Optics Express, Vol. 16, No. 20, 12880-12891, 2008.
doi:10.1364/OE.16.012880

3. Siviloglou, G. A., J. Broky, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beams," Physical Review Letters, Vol. 99, 213901(1-4), 2007.

4. Siviloglou, G. A., J. Broky, A. Dogariu, and D. N. Christodoulides, "Ballistic dynamics of Airy beams," Optics Letters, Vol. 33, No. 3, 207-209, 2008.
doi:10.1364/OL.33.000207

5. Siviloglou, G. A. and D. N. Christodoulides, "Accelerating finite energy Airy beams," Optics Letters, Vol. 32, 979-981, 2007.
doi:10.1364/OL.32.000979

6. Baumgartl, J., M. Mazilu, and K. Dholakia, "Optically mediated particle clearing using Airy wavepackets," Nature Photonics, Vol. 2, No. 13, 675-678, 2008.
doi:10.1038/nphoton.2008.201

7. Polynkin, P., M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, "Curved plasma channel generation using ultraintense Airy beams," Science, Vol. 324, No. 5924, 229-232, 2009.
doi:10.1126/science.1169544

8. Polynkin, P., M. Kolesik, and J. Moloney, "Filamentation of femtosecond laser Airy beams in water," Physical Review Letters, Vol. 103, No. 14, 123902, 2009.
doi:10.1103/PhysRevLett.103.123902

9. Chong, A., W. H. Renninger, D. N. Christodoulides, and F. W. Wise, "Airy-Bessel wave packets as versatile linear light bullets," Nature Photonics, Vol. 4, No. 2, 103-106, 2010.
doi:10.1038/nphoton.2009.264

10. Li, J. X., W. P. Zang, and J. G. Tian, "Vacuum laser-driven acceleration by Airy beams," Optics Express, Vol. 18, No. 7, 7300-7306, 2010.
doi:10.1364/OE.18.007300

11. Zheng, Z., B. Zhang, H. Chen, J. Ding, and H. Wang, "Optical trapping with focused Airy beams," Applied Optics, Vol. 50, No. 1, 43-49, 2011.
doi:10.1364/AO.50.000043

12. Zhang, P., J. Prakash, Z. Zhang, M. S. Mills, N. K. Efremidis, D. N. Christodoulides, and Z. Chen, "Trapping and guiding microparticles with morphing autofocusing Airy beams," Optics Letters, Vol. 36, No. 18, 2883-2885, 2011.
doi:10.1364/OL.36.002883

13. Dai, H. T., X. W. Sun, D. Luo, and Y. J. Liu, "Airy beams generated by binary phase element made of polymer dispersed liquid crystals," Optics Express, Vol. 17, 19365-19370, 2009.
doi:10.1364/OE.17.019365

14. Hu, Y., P. Zhang, C. Lou, S. Huang, J. Xu, and Z. Chen, "Optimal control of the ballistic motion of Airy beams," Optics Letters, Vol. 35, No. 15, 2260-2262, 2010.
doi:10.1364/OL.35.002260

15. Polynkin, P., M. Kolesik, J. Moloney, G. Siviloglou, and D. N. Christodoulides, "Extreme nonlinear optics with ultra-intense self-bending Airy beams," Optics and Photonics News, Vol. 21, No. 11, 38-43, 2010.
doi:10.1364/OPN.21.9.000038

16. Cottrell, D. M., J. A. Davis, and T. M. Hazard, "Direct generation of accelerating Airy beams using a 3/2 phase-only pattern," Optics Letters, Vol. 34, No. 20, 2634-2636, 2009.
doi:10.1364/OL.34.002634

17. Ellenbogen, T., N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, "Nonlinear generation and manipulation of Airy beams," Nature Photonics, Vol. 3, No. 7, 395-398, 2009.
doi:10.1038/nphoton.2009.95

18. Dolev, I., T. Ellenbogen, N. Voloch-Bloch, and A. Arie, "Control of free space propagation of Airy beams generated by quadratic nonlinear photonic crystals," Applied Physics Letters, Vol. 95, No. 20, 201112-201112, 2009.
doi:10.1063/1.3266066

19. Widder, D. V., "Airy transform," Am. Math. Mon., Vol. 86, 271-277, 1979.
doi:10.2307/2320744

20. Valée, O. and M. Soares, Airy Functions and Their Applications to Physics, Imperial College Press, 2004.
doi:10.1142/p345

21. Torre, A., "A note on the Airy beams in the light of the symmetry algebra based approach," Journal of Optics A: Pure and Applied Optics, Vol. 11, No. 14, 125701, 2009.
doi:10.1088/1464-4258/11/12/125701

22. Jiang, Y., K. Huang, and X. Lu, "The optical Airy transform and its application in generating and controlling the Airy beam," Opt. Commun., Vol. 285, 4840-4843, 2012.
doi:10.1016/j.optcom.2012.08.003

23. Jiang, Y., K. Huang, and X. Lu, "Airy related beam generated from flat-topped Gaussian beams," J. Opt. Soc. Am. A, Vol. 29, No. 7, 1412-1416, 2012.
doi:10.1364/JOSAA.29.001412

24. Navidpour, S. M., M. Uysa, and M. Kavehard, "BER performance of free-space optical transmission with spatial diversity," IEEE Trans. Wirel. Commun., Vol. 6, 2813-2819, 2007.
doi:10.1109/TWC.2007.06109

25. Lü, B. and H. Ma, "Beam propagation properties of radial laser arrays," J. Opt. Soc. Am. A, Vol. 17, 2005-2009, 2000.
doi:10.1364/JOSAA.17.002005

26. Zhou, P., X.Wang, Y. Ma, H. Ma, H. Xu, and Z. Liu, "Propagation of Gaussian beam array through an optical system in turbulent atmosphere," Applied Physics B, Vol. 103, No. 4, 1009-1012, 2011.
doi:10.1007/s00340-010-4364-4

27. Ji, X. L. and Z. C. Pu, "Effective Rayleigh range of Gaussian array beams propagating through atmospheric turbulence," Opt. Commun., Vol. 283, 3884-3890, 2010.
doi:10.1016/j.optcom.2010.06.025

28. Tang, M. and D. Zhao, "Regions of spreading of Gaussian array beams propagating through oceanic turbulence," Appl. Opt., Vol. 54, 3407-3411, 2015.
doi:10.1364/AO.54.003407

29. Ji, X. and X. Li, "Directionality of Gaussian array beams propagating in atmospheric turbulence," JOSA A, Vol. 26, No. 2, 236-243, 2009.
doi:10.1364/JOSAA.26.000236

30. Lu, L., X.-L. Ji, J.-P. Deng, and X.-Q. Li, "A further study on the spreading and directionality of Gaussian array beams in non-Kolmogorov turbulence," Chinese Physics B, Vol. 23, No. 6, 064209, 2014.
doi:10.1088/1674-1056/23/6/064209

31. Zhi, D., Y. Chen, R. Tao, Y. Ma, P. Zhou, and L. Si, "Average spreading and beam quality evolution of Gaussian array beams propagating through oceanic turbulence," Laser Physics Letters, Vol. 12, No. 13, 116001, 2015.
doi:10.1088/1612-2011/12/11/116001

32. Lu, L., P. Zhang, C. Fan, and C. Qiao, "Influence of oceanic turbulence on propagation of a radial Gaussian beam array," Optics Express, Vol. 23, No. 3, 2827-2836, 2015.
doi:10.1364/OE.23.002827

33. Collins, S. A., "Lens-system diffraction integral written in terms of matrix optics," J. Opt. Soc. Am., Vol. 60, 1168-1177, 1970.
doi:10.1364/JOSA.60.001168

34. Gradshteyn, I. S. and I. M. Ryzhik, Tables of Integrals Series and Products, 5th Ed., Academic Press, New York, 1994.