## Experimental observation and analysis of all-fiber plasmonic double Airy beams |

Optics Express, Vol. 22, Issue 15, pp. 18365-18371 (2014)

http://dx.doi.org/10.1364/OE.22.018365

Acrobat PDF (4129 KB)

### Abstract

The propagation dynamics of all-fiber plasmonic double parallel and orthogonal Airy beams are experimentally demonstrated. Two slits and groove arrays were fabricated by focused ion beam (FIB) milling on the gold coated end facet of an optical fiber to generate two Airy beams simultaneously. Sub-wavelength self-focusing of double parallel Airy beams in free space is experimentally verified. Effects of geometrical parameters on the intensity profiles of the focal spot are analyzed in detail. The characteristics at the junction of the two main lobes can be adjusted by controlling the initial phase difference of the two Airy beams. The propagation of two orthogonal Airy beams is also experimentally investigated. Multi-Airy beams are of importance to realize all-fiber optical trapping, fiber integrated devices, and laser shaping.

© 2014 Optical Society of America

## 1. Introduction

1. K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics **5**(6), 335–342 (2011). [CrossRef]

4. A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. **101**(7), 071110 (2012). [CrossRef]

5. I. Epstein and A. Arie, “Arbitrary Bending plasmonic light waves,” Phys. Rev. Lett. **112**(2), 023903 (2014). [CrossRef] [PubMed]

6. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics **2**(11), 675–678 (2008). [CrossRef]

7. I. M. Besieris and A. M. Shaarawi, “A note on an accelerating finite energy Airy beam,” Opt. Lett. **32**(16), 2447–2449 (2007). [CrossRef] [PubMed]

8. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. **99**(21), 213901 (2007). [CrossRef] [PubMed]

8. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. **99**(21), 213901 (2007). [CrossRef] [PubMed]

9. P. Zhang, 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,” Opt. Lett. **36**(15), 2883–2885 (2011). [CrossRef] [PubMed]

10. D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. **36**(10), 1842–1844 (2011). [CrossRef] [PubMed]

11. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science **324**(5924), 229–232 (2009). [CrossRef] [PubMed]

8. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. **99**(21), 213901 (2007). [CrossRef] [PubMed]

9. P. Zhang, 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,” Opt. Lett. **36**(15), 2883–2885 (2011). [CrossRef] [PubMed]

12. G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. **33**(3), 207–209 (2008). [CrossRef] [PubMed]

13. Y. Fan, J. Wei, J. Ma, Y. Wang, and Y. Wu, “Tunable twin Airy beams induced by binary phase patterns,” Opt. Lett. **38**(8), 1286–1288 (2013). [CrossRef] [PubMed]

14. A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science **308**(5722), 670–672 (2005). [CrossRef] [PubMed]

15. A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. **107**(11), 116802 (2011). [CrossRef] [PubMed]

16. L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam generated by in-plane diffraction,” Phys. Rev. Lett. **107**(12), 126804 (2011). [CrossRef] [PubMed]

17. I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. **109**(20), 203903 (2012). [CrossRef] [PubMed]

18. C. Y. Guan, M. Ding, J. H. Shi, P. F. Wang, P. Hua, L. B. Yuan, and G. Brambilla, “Compact all-fiber plasmonic Airy-like beam generator,” Opt. Lett. **39**(5), 1113–1116 (2014). [CrossRef] [PubMed]

## 2. Double parallel Airy beams

### 2.1 Symmetrical double Airy beams

*d*between the two slits is 2.89μm. SPPs are excited in the two air slits, propagate along the metal surface and are decoupled into free space by the graded metal grating arrays [17

17. I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. **109**(20), 203903 (2012). [CrossRef] [PubMed]

18. C. Y. Guan, M. Ding, J. H. Shi, P. F. Wang, P. Hua, L. B. Yuan, and G. Brambilla, “Compact all-fiber plasmonic Airy-like beam generator,” Opt. Lett. **39**(5), 1113–1116 (2014). [CrossRef] [PubMed]

19. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. **94**(5), 053901 (2005). [CrossRef] [PubMed]

6. J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics **2**(11), 675–678 (2008). [CrossRef]

*s*=

*x*/

*x*

_{0},

*ξ*=

*z*/(

*kx*

_{0}

^{2}),

*a*is the exponential truncation factor. A density plot |

*E*(

*x*,

*z*)|

^{2}of two symmetrical Airy beams (

*x*

_{0}= 1.0μm and

*a*= 0.001) with the separated distance

*d*= 2.9 μm is shown in Fig. 2(c). Two pure Airy beams focus at 20.5μm and then interfere after the focal point. The full-width-at-half-maximum (FWHM) of the focal point is 0.86μm. The phases of two Airy beams at x = 0 are equal, so the junction of the main lobes of two beams is always a bright spot.

*h*= 75nm) is depicted in Fig. 2(d), showing good agreement between the numerical simulation and measured field maps. The calculated far-field along the x-axis is shown in Fig. 2(e). The far-field intensity is very weak, attributed to the propagation characteristics of finite-energy single Airy beam, which only propagates over a finite distance. Five distinct interference fringes occur between the far-field divergence angles of −25° and 25°. The central fringe is bright, caused by the interference of the two Airy beams after the focal point, which can be seen at z>25μm in Fig. 2(d). The longitudinal position of the focal point is a little longer than that of the experiment due to the limitations associated to measurement precision. The normalized intensity profiles of the focal spot, both experimental and calculated, are shown in Fig. 2(f) and agree well with each other. The experimental and theoretical FWHMs of the focal point are

*x*

_{0}takes a smaller value, the main lobe of the Airy beam will become narrower, and then the FWHM of the focal spot will be further reduced. For example, for

*x*

_{0}= 0.6μm FWHM = 0.46μm.

*h*= 45nm is shown in Fig. 3(b), accompanied by obvious side lobes near the focal spot.

*d*= 2.1μm and 2.5μm are also presented in Fig. 4. The field maps for

*d*= 2.1μm and

*d*= 2.89μm are very similar because of the periodicity of plasmon assisted two-slit transmission [19

19. H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. **94**(5), 053901 (2005). [CrossRef] [PubMed]

*d*= 2.9μm is slightly further than that for

*d*= 2.1μm while the position of the dark fringes of the main lobe depends on the distance between the two slits that affects the plasmon interference. In contrast, when

*d*= 2.5μm, the nodes of the standing-wave pattern along the interface between the fiber core and gold film coincide with the slits and the SPP transmission is minimum. So, although the phase of two light beams at x = 0 is the same, the output intensity is very weak due to the lower efficiency of generating the Airy beam. In order to measure the interference field, the incident light power for

*d*= 2.5μm is increased nearly fourfold compared to the other two cases.

### 2.2 Asymmetrical double Airy beams

## 3. Double orthogonal Airy beams

11. P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science **324**(5924), 229–232 (2009). [CrossRef] [PubMed]

## 4. Conclusion

## Acknowledgment

## References and links

1. | K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics |

2. | W. M. Lee, X.-C. Yuan, and W. C. Cheong, “Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation,” Opt. Lett. |

3. | D. G. Grier, “A revolution in optical manipulation,” Nature |

4. | A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett. |

5. | I. Epstein and A. Arie, “Arbitrary Bending plasmonic light waves,” Phys. Rev. Lett. |

6. | J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics |

7. | I. M. Besieris and A. M. Shaarawi, “A note on an accelerating finite energy Airy beam,” Opt. Lett. |

8. | G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. |

9. | P. Zhang, 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,” Opt. Lett. |

10. | D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett. |

11. | P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science |

12. | G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett. |

13. | Y. Fan, J. Wei, J. Ma, Y. Wang, and Y. Wu, “Tunable twin Airy beams induced by binary phase patterns,” Opt. Lett. |

14. | A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science |

15. | A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett. |

16. | L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam generated by in-plane diffraction,” Phys. Rev. Lett. |

17. | I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett. |

18. | C. Y. Guan, M. Ding, J. H. Shi, P. F. Wang, P. Hua, L. B. Yuan, and G. Brambilla, “Compact all-fiber plasmonic Airy-like beam generator,” Opt. Lett. |

19. | H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. |

**OCIS Codes**

(060.2340) Fiber optics and optical communications : Fiber optics components

(140.3300) Lasers and laser optics : Laser beam shaping

(230.3120) Optical devices : Integrated optics devices

(240.6680) Optics at surfaces : Surface plasmons

(050.6624) Diffraction and gratings : Subwavelength structures

**ToC Category:**

Plasmonics

**History**

Original Manuscript: June 11, 2014

Revised Manuscript: July 9, 2014

Manuscript Accepted: July 10, 2014

Published: July 22, 2014

**Citation**

Chunying Guan, Ming Ding, Jinhui Shi, Ping Hua, Pengfei Wang, Libo Yuan, and Gilberto Brambilla, "Experimental observation and analysis of all-fiber plasmonic double Airy beams," Opt. Express **22**, 18365-18371 (2014)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-15-18365

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### References

- K. Dholakia and T. Čižmár, “Shaping the future of manipulation,” Nat. Photonics5(6), 335–342 (2011). [CrossRef]
- W. M. Lee, X.-C. Yuan, and W. C. Cheong, “Optical vortex beam shaping by use of highly efficient irregular spiral phase plates for optical micromanipulation,” Opt. Lett.29(15), 1796–1798 (2004). [CrossRef] [PubMed]
- D. G. Grier, “A revolution in optical manipulation,” Nature424(6950), 810–816 (2003). [CrossRef] [PubMed]
- A. Mathis, F. Courvoisier, L. Froehly, L. Furfaro, M. Jacquot, P. A. Lacourt, and J. M. Dudley, “Micromachining along a curve: Femtosecond laser micromachining of curved profiles in diamond and silicon using accelerating beams,” Appl. Phys. Lett.101(7), 071110 (2012). [CrossRef]
- I. Epstein and A. Arie, “Arbitrary Bending plasmonic light waves,” Phys. Rev. Lett.112(2), 023903 (2014). [CrossRef] [PubMed]
- J. Baumgartl, M. Mazilu, and K. Dholakia, “Optically mediated particle clearing using Airy wavepackets,” Nat. Photonics2(11), 675–678 (2008). [CrossRef]
- I. M. Besieris and A. M. Shaarawi, “A note on an accelerating finite energy Airy beam,” Opt. Lett.32(16), 2447–2449 (2007). [CrossRef] [PubMed]
- G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett.99(21), 213901 (2007). [CrossRef] [PubMed]
- P. Zhang, 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,” Opt. Lett.36(15), 2883–2885 (2011). [CrossRef] [PubMed]
- D. G. Papazoglou, N. K. Efremidis, D. N. Christodoulides, and S. Tzortzakis, “Observation of abruptly autofocusing waves,” Opt. Lett.36(10), 1842–1844 (2011). [CrossRef] [PubMed]
- P. Polynkin, M. Kolesik, J. V. Moloney, G. A. Siviloglou, and D. N. Christodoulides, “Curved plasma channel generation using ultraintense airy beams,” Science324(5924), 229–232 (2009). [CrossRef] [PubMed]
- G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Ballistic dynamics of Airy beams,” Opt. Lett.33(3), 207–209 (2008). [CrossRef] [PubMed]
- Y. Fan, J. Wei, J. Ma, Y. Wang, and Y. Wu, “Tunable twin Airy beams induced by binary phase patterns,” Opt. Lett.38(8), 1286–1288 (2013). [CrossRef] [PubMed]
- A. P. Hibbins, B. R. Evans, and J. R. Sambles, “Experimental verification of designer surface plasmons,” Science308(5722), 670–672 (2005). [CrossRef] [PubMed]
- A. Minovich, A. E. Klein, N. Janunts, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “Generation and near-field imaging of Airy surface plasmons,” Phys. Rev. Lett.107(11), 116802 (2011). [CrossRef] [PubMed]
- L. Li, T. Li, S. M. Wang, C. Zhang, and S. N. Zhu, “Plasmonic Airy Beam generated by in-plane diffraction,” Phys. Rev. Lett.107(12), 126804 (2011). [CrossRef] [PubMed]
- I. Dolev, I. Epstein, and A. Arie, “Surface-plasmon holographic beam shaping,” Phys. Rev. Lett.109(20), 203903 (2012). [CrossRef] [PubMed]
- C. Y. Guan, M. Ding, J. H. Shi, P. F. Wang, P. Hua, L. B. Yuan, and G. Brambilla, “Compact all-fiber plasmonic Airy-like beam generator,” Opt. Lett.39(5), 1113–1116 (2014). [CrossRef] [PubMed]
- H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett.94(5), 053901 (2005). [CrossRef] [PubMed]

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