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| Progress In Electromagnetics Research M | ISSN: 1937-8726 |
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PROPERTIES OF AIRY-GAUSS BEAMS IN THE FRACTIONAL FOURIER TRANSFORM PLANEBy Y. Zhou, G. Zhou, and G. RuAbstract: 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.
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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. 3. Kaganovsky, Y. and E. Heyman, "Wave analysis of Airy beams," Opt. Express, Vol. 18, 8440-8452, 2010. 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. 5. Sztul, H. I. and R. R. Alfano, "The Poynting vector and angular momentum of Airy beams," Opt. Express, Vol. 16, 9411-9416, 2008. 6. Siviloglou, G. A., J. Brokly, A. Dogariu, and D. N. Christodoulides, "Ballistic dynamics of Airy beams," Opt. Lett., Vol. 33, 207-209, 2008. 7. Chen, R. P. and C. F. Ying, "Beam propagation factor of an Airy beam," J. Opt., Vol. 13, 085704, 2011. 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. 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. 10. Siviloglou, G. A., J. Brokly, A. Dogariu, and D. N. Christodoulides, "Observation of accelerating Airy beam," Phys. Rev. Lett., Vol. 99, 213901, 2007. 11. Siviloglou, G. A. and D. N. Christodoulides, "Accelerating finite energy Airy beams," Opt. Lett., Vol. 32, 979-981, 2007. 12. Polynkin, P., M. Kolesik, and J. Moloney, "Filamentation of femtosecond laser Airy beams in water," Phys. Rev. Lett., Vol. 103, 123902, 2009. 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. 14. Chu, X. X., "Evolution of an Airy beam in turbulence," Opt. Lett., Vol. 36, 2701-2703, 2011. 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. 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. 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. 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. 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. 20. Baumgartl, J., M. Mazilu, and K. Dholakia, "Optically mediated particle clearing using Airy wavepackets," Nature Photon., Vol. 2, 675-678, 2008. 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. 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. 23. Piksarv, P., A. Valdmann, H. Valtna-Lukner, and P. Saari, "Ultrabroadband Airy light bullets," Laser. Phys., Vol. 24, 085301, 2014. 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. 25. Deng, D. M. and H. Li, "Propagation properties of Airy-Gaussian beam," Appl. Phys. B, Vol. 106, 677-681, 2012. 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. 28. Namias, V., "The fractional order Fourier transform and its application to quantum mechanics," J. Inst. Math. Appl., Vol. 25, 241-265, 1980. 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. 30. Du, X. Y. and D. M. Zhao, "Fractional Fourier transform of truncated elliptical Gaussian beams," Appl. Opt., Vol. 45, 9049-9052, 2006. 31. Zhou, G. Q., "Fractional Fourier transform of Lorentz-Gauss beams," J. Opt. Soc. Am. A, Vol. 26, 350-355, 2009. 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. 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. 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. 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. |