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Self-reconstruction properties of the Mathieu beam are studied theoretically and experimentally. By means of the Mathieu-Hankel wave's theory, the self-reconstruction mechanism of Mathieu beam is analyzed. Based on the Fresnel diffraction theory, an analytical expression for the optical field of a Mathieu beam partially blocked by a circular opaque obstacle is derived, and the self-reconstruction process of Mathieu beam is simulated based on the analytical expression. Using a cylindrical lens and an axicon system to generate Mathieu beam, the self-reconstruction properties of the Mathieu beam partially blocked by a circular opaque obstacle on axis and off axis are verified. Experimental results agree well with the theoretical analysis.
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Keywords:
- non-diffracting Mathieu beam /
- Mathieu Hankel wave' /
- s theory
[1] Durnin J 1987 J. Opt. Soc. Am.A 4 651
[2] Grier D G 2003 Nat. 424 810
[3] Wang Z L, Yin J P 2008 Chin. Phys. B 17 2466
[4] Planchon T A, Gao L, Milkie D E, Davidson M W, Galbraith J A, Galbraith C G, Betzig E 2011 Nat. Meth. 8 417
[5] Ok G, Choi S W, Park K H, Chun H S 2013 IEEE Sens. J. 13 71
[6] Gutiérrez-Vega J C, Bandres M A 2005 J. Opt. Soc. Am.A 22 289
[7] Garcés-Chávez V, McGloin D, Melville H, Sibbett W, Dholakia K 2002 Nat. 419 145
[8] Chu X 2012 Eur. Phys. J. D 66 259
[9] Chu X, Zhou G, Chen R 2012 Phys.Rev. A 85 013815
[10] Fan D D, Zhang Q A, Cheng Z M, Zheng W T, Wu F T 2012 Acta Phys. Sin. 61 164103 (in Chinese) [范丹丹, 张前安, 程治明, 郑维涛, 吴逢铁 2012 61 164103]
[11] Zhang Q A, Wu F T, Zheng W T, Pu J X 2011 Sci. Sin.G: Phys. Mech. Astron. 41 1131 (in Chinese) [张前安, 吴逢铁, 郑维涛, 蒲继雄 2011 中国科学G辑:41 1131]
[12] Fan D D, Wu F T, Cheng Z M, Zhu J Q 2013 Acta Phys. Sin. 62 104219 (in Chinese) [范丹丹吴, 程治明, 朱健强 2013 62 104219]
[13] Chafiq A, Hricha Z, Belafhal A 2006 Opt. Commun. 265 594
[14] Wen J J, Breazeale M A 1988 J. Acoust. Soc. Am. 83 1752
[15] Li D, Wu F T, Xie X X 2014 Acta Phys. Sin. 63 152401 (in Chinese) [李冬, 吴逢铁, 谢晓霞 2014 63 152401]
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[1] Durnin J 1987 J. Opt. Soc. Am.A 4 651
[2] Grier D G 2003 Nat. 424 810
[3] Wang Z L, Yin J P 2008 Chin. Phys. B 17 2466
[4] Planchon T A, Gao L, Milkie D E, Davidson M W, Galbraith J A, Galbraith C G, Betzig E 2011 Nat. Meth. 8 417
[5] Ok G, Choi S W, Park K H, Chun H S 2013 IEEE Sens. J. 13 71
[6] Gutiérrez-Vega J C, Bandres M A 2005 J. Opt. Soc. Am.A 22 289
[7] Garcés-Chávez V, McGloin D, Melville H, Sibbett W, Dholakia K 2002 Nat. 419 145
[8] Chu X 2012 Eur. Phys. J. D 66 259
[9] Chu X, Zhou G, Chen R 2012 Phys.Rev. A 85 013815
[10] Fan D D, Zhang Q A, Cheng Z M, Zheng W T, Wu F T 2012 Acta Phys. Sin. 61 164103 (in Chinese) [范丹丹, 张前安, 程治明, 郑维涛, 吴逢铁 2012 61 164103]
[11] Zhang Q A, Wu F T, Zheng W T, Pu J X 2011 Sci. Sin.G: Phys. Mech. Astron. 41 1131 (in Chinese) [张前安, 吴逢铁, 郑维涛, 蒲继雄 2011 中国科学G辑:41 1131]
[12] Fan D D, Wu F T, Cheng Z M, Zhu J Q 2013 Acta Phys. Sin. 62 104219 (in Chinese) [范丹丹吴, 程治明, 朱健强 2013 62 104219]
[13] Chafiq A, Hricha Z, Belafhal A 2006 Opt. Commun. 265 594
[14] Wen J J, Breazeale M A 1988 J. Acoust. Soc. Am. 83 1752
[15] Li D, Wu F T, Xie X X 2014 Acta Phys. Sin. 63 152401 (in Chinese) [李冬, 吴逢铁, 谢晓霞 2014 63 152401]
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