Abstract

We propose a new (to our knowledge) method for performing beam shaping. Calculations show that beam patterns including diamond, rhombus, and hollow beam with diamond-shaped dark core can be generated in the focal plane of a square Fresnel zone plate by choosing appropriate parameters of an incident elliptic vortex beam. Numerical simulations have demonstrated the validity and effectiveness of this method.

© 2011 Optical Society of America

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References

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  1. Y. Li, “Light beams with flat-topped profiles,” Opt. Lett. 27, 1007–1009 (2002).
    [CrossRef]
  2. F. Wang and Y. Cai, “Experimental generation of a partially coherent flat-topped beam,” Opt. Lett. 33, 1795–1797 (2008).
    [CrossRef] [PubMed]
  3. S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: The Super-Gaussian Approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
    [CrossRef]
  4. F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
    [CrossRef]
  5. Y. Li, “Flat-topped light beams with non-circular cross-sections,” J. Mod. Opt. 50, 1957–1966 (2003).
    [CrossRef]
  6. F. K. Fatemi and M. Bashkansky, “Generation of hollow beams by using a binary spatial light modulator,” Opt. Lett. 31, 864–866 (2006).
    [CrossRef] [PubMed]
  7. Z. Liu, H. Zhao, J. Liu, J. Lin, M. A. Ahmad, and S. Liu, “Generation of hollow Gaussian beams by spatial filtering,” Opt. Lett. 32, 2076–2078 (2007).
    [CrossRef] [PubMed]
  8. Y. Song, D. Milam, and W. T. Hill III, “Long, narrow all-light atom guide,” Opt. Lett. 24, 1805–1807 (1999).
    [CrossRef]
  9. 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, 1796–1798(2004).
    [CrossRef] [PubMed]
  10. Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10, 324–331 (2002).
    [PubMed]
  11. B. Hao, J. Burch, and J. Leger, “Smallest flattop focus by polarization engineering,” Appl. Opt. 47, 2931–2940 (2008).
    [CrossRef] [PubMed]
  12. B. Zhang and D. Zhao, “Square Fresnel zone plate with spiral phase for generating zero axial irradiance,” Opt. Lett. 35, 1488–1490 (2010).
    [CrossRef] [PubMed]
  13. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
    [CrossRef] [PubMed]
  14. C. Guo, L. Lu, and H. Wang, “Characterizing topological charge of optical vortices by using an annular aperture,” Opt. Lett. 34, 3686–3688 (2009).
    [CrossRef] [PubMed]
  15. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Optical vortices generated by multi-level achromatic spiral phase plates for broadband beams,” Opt. Lett. 17, 221–223(1992).
    [CrossRef] [PubMed]
  16. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiansen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327(1994).
    [CrossRef]
  17. V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and Jari Turunen, “Elliptic Laguerre–Gaussian beams,” J. Opt. Soc. Am. A 23, 43–56 (2006).
    [CrossRef]
  18. S. A. Collins, “Lens-system diffraction integral written in terms of matrix optics,” J. Opt. Soc. Am. 60, 1168–1177 (1970).
    [CrossRef]
  19. L. J. Janicijevic, “Diffraction characteristics of square zone plates,” J. Opt. 13, 199–205 (1982).
    [CrossRef]
  20. J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, “Diffractive performance of square Fresnel zone plate,” Opt. Commun. 282, 3402–3407 (2009).
    [CrossRef]

2010

2009

C. Guo, L. Lu, and H. Wang, “Characterizing topological charge of optical vortices by using an annular aperture,” Opt. Lett. 34, 3686–3688 (2009).
[CrossRef] [PubMed]

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, “Diffractive performance of square Fresnel zone plate,” Opt. Commun. 282, 3402–3407 (2009).
[CrossRef]

2008

2007

2006

2004

2003

Y. Li, “Flat-topped light beams with non-circular cross-sections,” J. Mod. Opt. 50, 1957–1966 (2003).
[CrossRef]

2002

1999

1994

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiansen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327(1994).
[CrossRef]

1992

N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Optical vortices generated by multi-level achromatic spiral phase plates for broadband beams,” Opt. Lett. 17, 221–223(1992).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

1988

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: The Super-Gaussian Approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

1982

L. J. Janicijevic, “Diffraction characteristics of square zone plates,” J. Opt. 13, 199–205 (1982).
[CrossRef]

1970

Ahmad, M. A.

Alda, J.

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, “Diffractive performance of square Fresnel zone plate,” Opt. Commun. 282, 3402–3407 (2009).
[CrossRef]

Allen, L.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Almazov, A. A.

Bashkansky, M.

Beijersbergen, M. W.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiansen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327(1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Burch, J.

Cai, Y.

Cheong, W. C.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiansen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327(1994).
[CrossRef]

Collins, S. A.

De Silvestri, S.

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: The Super-Gaussian Approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

Fatemi, F. K.

Gori, F.

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

Guo, C.

Hao, B.

Heckenberg, N. R.

Hill, W. T.

Janicijevic, L. J.

L. J. Janicijevic, “Diffraction characteristics of square zone plates,” J. Opt. 13, 199–205 (1982).
[CrossRef]

Jefimovs, K.

Khonina, S. N.

Kotlyar, V. V.

Kristiansen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiansen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327(1994).
[CrossRef]

Laporta, P.

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: The Super-Gaussian Approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

Lee, W. M.

Leger, J.

Leger, J. R.

Li, Y.

Y. Li, “Flat-topped light beams with non-circular cross-sections,” J. Mod. Opt. 50, 1957–1966 (2003).
[CrossRef]

Y. Li, “Light beams with flat-topped profiles,” Opt. Lett. 27, 1007–1009 (2002).
[CrossRef]

Lin, J.

Liu, J.

Liu, S.

Liu, Z.

Lu, L.

Magni, V.

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: The Super-Gaussian Approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

McDuff, R.

Milam, D.

Rico-Garcia, J. M.

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, “Diffractive performance of square Fresnel zone plate,” Opt. Commun. 282, 3402–3407 (2009).
[CrossRef]

Salgado-Remacha, F. J.

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, “Diffractive performance of square Fresnel zone plate,” Opt. Commun. 282, 3402–3407 (2009).
[CrossRef]

Sanchez-Brea, L. M.

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, “Diffractive performance of square Fresnel zone plate,” Opt. Commun. 282, 3402–3407 (2009).
[CrossRef]

Smith, C. P.

Soifer, V. A.

Song, Y.

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Svelto, O.

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: The Super-Gaussian Approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

Turunen, Jari

Wang, F.

Wang, H.

White, A. G.

Woerdman, J. P.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiansen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327(1994).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

Yuan, X. C.

Zhan, Q.

Zhang, B.

Zhao, D.

Zhao, H.

Appl. Opt.

IEEE J. Quantum Electron.

S. De Silvestri, P. Laporta, V. Magni, and O. Svelto, “Solid-state laser unstable resonators with tapered reflectivity mirrors: The Super-Gaussian Approach,” IEEE J. Quantum Electron. 24, 1172–1177 (1988).
[CrossRef]

J. Mod. Opt.

Y. Li, “Flat-topped light beams with non-circular cross-sections,” J. Mod. Opt. 50, 1957–1966 (2003).
[CrossRef]

J. Opt.

L. J. Janicijevic, “Diffraction characteristics of square zone plates,” J. Opt. 13, 199–205 (1982).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristiansen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327(1994).
[CrossRef]

J. Alda, J. M. Rico-Garcia, F. J. Salgado-Remacha, and L. M. Sanchez-Brea, “Diffractive performance of square Fresnel zone plate,” Opt. Commun. 282, 3402–3407 (2009).
[CrossRef]

F. Gori, “Flattened Gaussian beams,” Opt. Commun. 107, 335–341 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes,” Phys. Rev. A 45, 8185–8189 (1992).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

(a) Illustration of the structure of a square FZP, (b) the profile of a Gaussian beam (dash curve). The solid lines from the center denote the positions of the tenth, twentieth, thirtieth, and fortieth square zones, respectively. The size of the Gaussian beam is chosen as w = 3 mm , and the side length of the first zone a = 1.5 mm .

Fig. 2
Fig. 2

Intensity distributions in the principal focal plane ( z = f = 0.89 m ): (a)  m = 0 , (b)  m = 1 , (c)  m = 2 , (d)  m = 3 . (e) The profile of intensity on the x axis of (a)–(d). The elliptic coefficient is set as α = 1 , i.e., the incident beam is a circular vortex beam. The other parameters are the same as in Fig. 1.

Fig. 3
Fig. 3

Effect of the elliptic coefficient of the incident beam on beam patterns in the principal focal plane. The topological charge for (a), (c), and (e) is m = 0 ; for (b), (d), and (f) it is m = 1 . The elliptic coefficient in (a) and (b) is α = 0.6 ; in (c) and (d) it is α = 1.2 ; in (e) and (f) it is α = 1.5 . (g)–(l) The intensity profiles on the x axis and y axis of (a)–(f), respectively. The other parameters are the same as in Fig. 1.

Fig. 4
Fig. 4

Propagation of elliptic vortex beams diffracted by a square FZP. (a)  m = 0 , α = 1 , z = 0.92 m ; (b)  m = 0 , α = 1 , z = 0.95 m ; (c)  m = 1 , α = 1 , z = 0.92 m ; (d)  m = 1 , α = 1 , z = 0.95 m ; (e)  m = 1 , α = 1.2 , z = 0.92 m ; (f)  m = 1 , α = 1.2 , z = 0.95 m . The other parameters are the same as in Fig. 1.

Fig. 5
Fig. 5

Phase in the square FZP under the illumination of a circular vortex beam with the topological charge m = 1 . The color bar indicates the magnitude of the phase.

Equations (2)

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E ( 0 ) ( x , y ) = ( x 2 + α 2 y 2 w 2 ) m / 2 exp ( x 2 + α 2 y 2 w 2 ) exp [ i m tan 1 ( α y x ) ] ,
E ( x , y , z ) = ( i k 2 π z ) exp ( i k z ) S E ( 0 ) ( x , y ) { i k 2 z [ ( x 2 + y 2 ) 2 ( x x + y y ) + ( x 2 + y 2 ) ] } d x d y ,

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