PIER M
 
Progress In Electromagnetics Research M
ISSN: 1937-8726
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 40 > pp. 143-151

PROPERTIES OF AIRY-GAUSS BEAMS IN THE FRACTIONAL FOURIER TRANSFORM PLANE

By Y. Zhou, G. Zhou, and G. Ru

Full Article PDF (873 KB)

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.

Citation:
Y. Zhou, G. Zhou, and G. Ru, "Properties of Airy-Gauss Beams in the Fractional Fourier Transform Plane," Progress In Electromagnetics Research M, Vol. 40, 143-151, 2014.
doi:10.2528/PIERM14120103

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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


© Copyright 2010 EMW Publishing. All Rights Reserved