volume | PIER Journals

Abstract

An analytical expression of an Airy-Gauss beam passing through a fractional Fourier transform (FRFT) system is derived. The normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter of the Airy-Gauss beam are demonstrated in FRFT plane, respectively. The influence of the fractional order p on the normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter of the Airy-Gauss beam are examined in FRFT plane. The fractional order p controls the normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter. The period of the normalized intensity, phase, and centre of gravity versus the fractional order p is 4. The period of effective beam size, linear momentum, and kurtosis parameter versus the fractional order p is 2. The periodic behaviors of the normalized intensity distribution, phase distribution, centre of gravity, effective beam size, linear momentum, and kurtosis parameter can bring novel applications such as optical switch, optical micromanipulation, and optical image processing.

1. Berry, M. V. and N. L. Balazs, "Nonspreading wave packets," Am. J. Phys., Vol. 47, 264-267, 1979.
doi:10.1119/1.11855 Google Scholar

2. Chen, R. P., H. P. Zheng, and C. Q. Dai, "Wigner distribution function of an Airy beam," J. Opt. Soc. Am. A, Vol. 28, 1307-1311, 2011.
doi:10.1364/JOSAA.28.001307 Google Scholar

3. Kaganovsky, Y. and E. Heyman, "Wave analysis of Airy beams," Opt. Express, Vol. 18, 8440-8452, 2010.
doi:10.1364/OE.18.008440 Google Scholar

4. Brokly, J., G. A. Siviloglou, A. Dogariu, and D. N. Christodoulides, "Self-healing properties of optical Airy beams," Opt. Express, Vol. 16, 12880-12891, 2008.
doi:10.1364/OE.16.012880 Google Scholar

5. Sztul, H. I. and R. R. Alfano, "The Poynting vector and angular momentum of Airy beams," Opt. Express, Vol. 16, 9411-9416, 2008.
doi:10.1364/OE.16.009411 Google Scholar

6. Siviloglou, G. A., J. Brokly, A. Dogariu, and D. N. Christodoulides, "Ballistic dynamics of Airy beams," Opt. Lett., Vol. 33, 207-209, 2008.
doi:10.1364/OL.33.000207 Google Scholar

7. Chen, R. P. and C. F. Ying, "Beam propagation factor of an Airy beam," J. Opt., Vol. 13, 085704, 2011.
doi:10.1088/2040-8978/13/8/085704 Google Scholar

8. Zhou, G. Q., R. P. Chen, and X. X. Chu, "Fractional Fourier transform of Airy beams," Appl. Phys. B, Vol. 109, 549-556, 2012.
doi:10.1007/s00340-012-5117-3 Google Scholar

9. Xu, Y. Q. and G. Q. Zhou, "The far-field divergent properties of an Airy beam," Opt. & Laser Tech., Vol. 44, 1318-1323, 2012.
doi:10.1016/j.optlastec.2011.12.037 Google Scholar

10. Siviloglou, G. A., J. Brokly, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beam," Phys. Rev. Lett., Vol. 99, 213901, 2007.
doi:10.1103/PhysRevLett.99.213901 Google Scholar

11. Siviloglou, G. A. and D. N. Christodoulides, "Accelerating finite energy Airy beams," Opt. Lett., Vol. 32, 979-981, 2007.
doi:10.1364/OL.32.000979 Google Scholar

12. Polynkin, P., M. Kolesik, and J. Moloney, "Filamentation of femtosecond laser Airy beams in water," Phys. Rev. Lett., Vol. 103, 123902, 2009.
doi:10.1103/PhysRevLett.103.123902 Google Scholar

13. Chen, R. P., C. F. Yin, X. X. Chu, and H. Wang, "Effect of Kerr nonlinearity on an Airy beam," Phys. Rev. A, Vol. 82, 043832, 2010.
doi:10.1103/PhysRevA.82.043832 Google Scholar

14. Chu, X. X., "Evolution of an Airy beam in turbulence," Opt. Lett., Vol. 36, 2701-2703, 2011.
doi:10.1364/OL.36.002701 Google Scholar

15. Jia, S., J. Lee, J. W. Fleischer, G. A. Siviloglou, and D. N. Christodoulides, "Diffusion-trapped Airy beams in photorefractive media," Phys. Rev. Lett., Vol. 104, 253904, 2010.
doi:10.1103/PhysRevLett.104.253904 Google Scholar

16. Zhou, G. Q., R. P. Chen, and X. X. Chu, "Propagation of Airy beams in uniaxial crystals orthogonal to the optical axis," Opt. Express, Vol. 20, 2196-2205, 2012.
doi:10.1364/OE.20.002196 Google Scholar

17. Zhou, G. Q., R. P. Chen, and G. Y. Ru, "Propagation of an Airy beam in a strongly nonlocal nonlinear media," Laser Phys. Lett., Vol. 11, 105001, 2014.
doi:10.1088/1612-2011/11/10/105001 Google Scholar

18. Wen, W., X. Y. Lu, C. L. Zhao, and Y. J. Cai, "Propagation of Airy beam passing through the misaligned optical system with hard aperture," Opt. Commun., Vol. 313, 350-355, 2014.
doi:10.1016/j.optcom.2013.10.056 Google Scholar

19. Chu, X. X., Z. J. Liu, and P. Zhou, "Generation of a high-power Airy beam by coherent combining technology," Laser Phys. Lett., Vol. 10, 125102, 2013.
doi:10.1088/1612-2011/10/12/125102 Google Scholar

20. Baumgartl, J., M. Mazilu, and K. Dholakia, "Optically mediated particle clearing using Airy wavepackets," Nature Photon., Vol. 2, 675-678, 2008.
doi:10.1038/nphoton.2008.201 Google Scholar

21. Ellenbogen, T., N. Voloch-Bloch, A. Ganany-Padowicz, and A. Arie, "Nonlinear generation and manipulation of Airy beams," Nature Photon., Vol. 3, 395-398, 2009.
doi:10.1038/nphoton.2009.95 Google Scholar

22. Lu, W., J. Chen, Z. Lin, and S. Liu, "Driving a dielectric cylindrical particle with a one dimensional airy beam: A rigorous full wave solution," Progress In Electromagnetics Research, Vol. 115, 409-422, 2011.
doi:10.2528/PIER11031704 Google Scholar

23. Piksarv, P., A. Valdmann, H. Valtna-Lukner, and P. Saari, "Ultrabroadband Airy light bullets," Laser. Phys., Vol. 24, 085301, 2014.
doi:10.1088/1054-660X/24/8/085301 Google Scholar

24. Bandres, M. A. and J. C. Gutiérrez-Vega, "Airy-Gauss beams and their transformation by paraxial optical systems," Opt. Express, Vol. 15, 16719-16728, 2007.
doi:10.1364/OE.15.016719 Google Scholar

25. Deng, D. M. and H. Li, "Propagation properties of Airy-Gaussian beam," Appl. Phys. B, Vol. 106, 677-681, 2012.
doi:10.1007/s00340-011-4799-2 Google Scholar

26. Deng, X. B., D. M. Deng, C. Chen, and C. Y. Liu, "Analytical vectorial structure of Airy-Gaussian beam," Acta Phys. Sin., Vol. 62, 174201, 2013. Google Scholar

27. Lohmann, A. W., "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Am. A, Vol. 10, 2181-2186, 1993.
doi:10.1364/JOSAA.10.002181 Google Scholar

28. Namias, V., "The fractional order Fourier transform and its application to quantum mechanics," J. Inst. Math. Appl., Vol. 25, 241-265, 1980.
doi:10.1093/imamat/25.3.241 Google Scholar

29. Cai, Y. J. and Q. Lin, "Transformation and spectrum properties of partially coherent beams in the fractional Fourier transform plane," J. Opt. Soc. Am. A, Vol. 20, 1528-1536, 2003.
doi:10.1364/JOSAA.20.001528 Google Scholar

30. Du, X. Y. and D. M. Zhao, "Fractional Fourier transform of truncated elliptical Gaussian beams," Appl. Opt., Vol. 45, 9049-9052, 2006.
doi:10.1364/AO.45.009049 Google Scholar

31. Zhou, G. Q., "Fractional Fourier transform of Lorentz-Gauss beams," J. Opt. Soc. Am. A, Vol. 26, 350-355, 2009.
doi:10.1364/JOSAA.26.000350 Google Scholar

32. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, 1980.

33. Carter, W. H., "Spot size and divergence for Hermite Gaussian beams of any order," Appl. Opt., Vol. 19, 1027-1029, 1980.
doi:10.1364/AO.19.001027 Google Scholar

34. Yakimenko, A. I., V. M. Lashkin, and O. O. Prikhodko, "Dynamics of two-dimensional coherent structures in nonlocal nonlinear media," Phys. Rev. E, Vol. 73, 066605, 2006.
doi:10.1103/PhysRevE.73.066605 Google Scholar

35. Bock, B. D., Multivariate Statistical Method in Behavioral Research, McGraw-Hill, 1975.

36. Dai, C. Q., X. G. Wang, G. Q. Zhou, and J. L. Chen, "Optical image-hiding method with false information disclosure based on the interference principle and partial-phase-truncation in the fractional Fourier domain," Laser Phys. Lett., Vol. 11, 075603, 2014.
doi:10.1088/1612-2011/11/7/075603 Google Scholar

37. Yu, L. and Y. Zhang, "Application of the fractional fourier transform to moving train imaging," Progress In Electromagnetics Research M, Vol. 19, 13-23, 2011.
doi:10.2528/PIERM11051401 Google Scholar

Dr. Yimin Zhou

Dr. Guoquan Zhou

Dr. Guoyun Ru