Abstract

Phase-only elements are generally more desirable than complex-amplitude-modulated elements not only because of the higher diffraction efficiency but the readier implementation and fabrication. A novel iterative algorithm is proposed for generating multiple helical modes by a single phase-only element. A superposition of four helical modes is demonstrated experimentally by using a spatial light modulator.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2005

2004

A. Jesacher, S. Furhapter, S. Bernet, and M. Ritsch-Marte, "Size selective trapping with optical 'cogwheel' tweezers," Opt. Express 12, 4129-4135 (2004).
[CrossRef] [PubMed]

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, "Free-space information transfer using light beams carrying orbital angular momentum," Opt. Express 12, 5448-5456 (2004).
[CrossRef] [PubMed]

Z. Bouchal and R. Celechovsky, "Mixed vortex states of light as information carriers," New J. Phys. 6, 131 (2004).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, and J. Turunen, "Generation and selection of laser beams represented by a superposition of two angular harmonics," J. Mod. Opt. 51, 761-773 (2004).

2003

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

D. W. Zhang and X.-C. Yuan, "Entangled double-helix phase," Opt. Lett. 28, 1864-1866 (2003).
[CrossRef] [PubMed]

2002

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

2001

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, and J. Turunen, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001).

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature (London) 412, 313-316 (2001).
[CrossRef]

1997

T. Kuga, Y. Torii, N. Shiokawa, and T. Hirano, "Novel optical trap of atoms with a doughnut beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

B. Picinbono, "On instantaneous amplitude and phase of signals," IEEE Trans. Signal Process. 45, 552-560 (1997).
[CrossRef]

D. Rozas, C. T. Law, and G. A. Swartzlander, "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3065 (1997).
[CrossRef]

1996

1995

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

1992

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]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

1986

1985

1982

1971

R. W. Gerchberg and W. O. Saxton, "Phase determination for image and diffraction plane pictures in the electron microscope," Optik (Stuttgart) 34, 275-284 (1971).

Allen, L.

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[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]

Almazov, A. A.

April, G.

Arlt, J.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Arsenault, H. H.

Barnett, S. M.

Beijersbergen, M. W.

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]

Bernet, S.

Bouchal, Z.

Z. Bouchal, O. Haderka, and R. Celechovsky, "Selective excitation of vortex fiber modes using a spatial light modulator," New J. Phys. 7, 125 (2005).
[CrossRef]

Z. Bouchal and R. Celechovsky, "Mixed vortex states of light as information carriers," New J. Phys. 6, 131 (2004).
[CrossRef]

Burge, R. E.

Celechovsky, R.

Z. Bouchal, O. Haderka, and R. Celechovsky, "Selective excitation of vortex fiber modes using a spatial light modulator," New J. Phys. 7, 125 (2005).
[CrossRef]

Z. Bouchal and R. Celechovsky, "Mixed vortex states of light as information carriers," New J. Phys. 6, 131 (2004).
[CrossRef]

Courtial, J.

Curtis, J. E.

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

Dholakia, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Doskolovich, L.

V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Elfstrom, H.

Franke-Arnold, S.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Furhapter, S.

Gahagan, K. T.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, "Phase determination for image and diffraction plane pictures in the electron microscope," Optik (Stuttgart) 34, 275-284 (1971).

Gibson, G.

Grier, D. G.

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

Haderka, O.

Z. Bouchal, O. Haderka, and R. Celechovsky, "Selective excitation of vortex fiber modes using a spatial light modulator," New J. Phys. 7, 125 (2005).
[CrossRef]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Hirano, T.

T. Kuga, Y. Torii, N. Shiokawa, and T. Hirano, "Novel optical trap of atoms with a doughnut beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Hsu, Y.

Jefimovs, K.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, and J. Turunen, "Generation and selection of laser beams represented by a superposition of two angular harmonics," J. Mod. Opt. 51, 761-773 (2004).

Jesacher, A.

Khonina, S. N.

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, "Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plane," J. Opt. Soc. Am. A 22, 849-861 (2005).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, and J. Turunen, "Generation and selection of laser beams represented by a superposition of two angular harmonics," J. Mod. Opt. 51, 761-773 (2004).

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, and J. Turunen, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001).

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

Kotlyar, V.

V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Kotlyar, V. V.

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, "Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plane," J. Opt. Soc. Am. A 22, 849-861 (2005).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, and J. Turunen, "Generation and selection of laser beams represented by a superposition of two angular harmonics," J. Mod. Opt. 51, 761-773 (2004).

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, and J. Turunen, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001).

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

Kuga, T.

T. Kuga, Y. Torii, N. Shiokawa, and T. Hirano, "Novel optical trap of atoms with a doughnut beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Law, C. T.

Lin, J.

MacDonald, M. P.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

MacVicar, I.

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Mair, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature (London) 412, 313-316 (2001).
[CrossRef]

Niu, H. B.

O'Neil, A. T.

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Paakkonen, P.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, and J. Turunen, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001).

Padgett, M. J.

G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas'ko, S. M. Barnett, and S. Franke-Arnold, "Free-space information transfer using light beams carrying orbital angular momentum," Opt. Express 12, 5448-5456 (2004).
[CrossRef] [PubMed]

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Pas'ko, V.

Paterson, L.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Peng, X.

Picinbono, B.

B. Picinbono, "On instantaneous amplitude and phase of signals," IEEE Trans. Signal Process. 45, 552-560 (1997).
[CrossRef]

Ritsch-Marte, M.

Rozas, D.

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, "Phase determination for image and diffraction plane pictures in the electron microscope," Optik (Stuttgart) 34, 275-284 (1971).

Schils, G. F.

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

Shiokawa, N.

T. Kuga, Y. Torii, N. Shiokawa, and T. Hirano, "Novel optical trap of atoms with a doughnut beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Sibbett, W.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Simonen, J.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, and J. Turunen, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001).

Soifer, V.

V. Soifer, V. Kotlyar, and L. Doskolovich, Iterative Methods for Diffractive Optical Elements Computation (Taylor & Francis, 1997).

Soifer, V. A.

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, "Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plane," J. Opt. Soc. Am. A 22, 849-861 (2005).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, and J. Turunen, "Generation and selection of laser beams represented by a superposition of two angular harmonics," J. Mod. Opt. 51, 761-773 (2004).

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, and J. Turunen, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001).

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

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]

Swartzlander, G. A.

Sweeney, D. W.

Tao, S. H.

Torii, Y.

T. Kuga, Y. Torii, N. Shiokawa, and T. Hirano, "Novel optical trap of atoms with a doughnut beam," Phys. Rev. Lett. 78, 4713-4716 (1997).
[CrossRef]

Turunen, J.

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, "Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plane," J. Opt. Soc. Am. A 22, 849-861 (2005).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, and J. Turunen, "Generation and selection of laser beams represented by a superposition of two angular harmonics," J. Mod. Opt. 51, 761-773 (2004).

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, and J. Turunen, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001).

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

Vasnetsov, M.

Vaziri, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature (London) 412, 313-316 (2001).
[CrossRef]

Volke-Sepulveda, K.

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Weihs, G.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature (London) 412, 313-316 (2001).
[CrossRef]

Woerdman, J. P.

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.

Zeilinger, A.

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature (London) 412, 313-316 (2001).
[CrossRef]

Zhang, D. W.

Appl. Opt.

IEEE Trans. Signal Process.

B. Picinbono, "On instantaneous amplitude and phase of signals," IEEE Trans. Signal Process. 45, 552-560 (1997).
[CrossRef]

J. Mod. Opt.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, K. Jefimovs, and J. Turunen, "Generation and selection of laser beams represented by a superposition of two angular harmonics," J. Mod. Opt. 51, 761-773 (2004).

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, and J. Turunen, "An analysis of the angular momentum of a light field in terms of angular harmonics," J. Mod. Opt. 48, 1543-1557 (2001).

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nature (London)

A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, "Entanglement of the orbital angular momentum states of photons," Nature (London) 412, 313-316 (2001).
[CrossRef]

New J. Phys.

Z. Bouchal and R. Celechovsky, "Mixed vortex states of light as information carriers," New J. Phys. 6, 131 (2004).
[CrossRef]

Z. Bouchal, O. Haderka, and R. Celechovsky, "Selective excitation of vortex fiber modes using a spatial light modulator," New J. Phys. 7, 125 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

Optik (Stuttgart)

R. W. Gerchberg and W. O. Saxton, "Phase determination for image and diffraction plane pictures in the electron microscope," Optik (Stuttgart) 34, 275-284 (1971).

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]

Phys. Rev. Lett.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, "Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity," Phys. Rev. Lett. 75, 826-829 (1995).
[CrossRef] [PubMed]

A. T. O'Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and extrinsic nature of the orbital angular momentum of a light beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
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[CrossRef]

Science

M. P. MacDonald, L. Paterson, K. Volke-Sepulveda, J. Arlt, W. Sibbett, and K. Dholakia, "Creation and manipulation of three-dimensional optically trapped structures," Science 296, 1101-1103 (2002).
[CrossRef] [PubMed]

Other

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Figures (3)

Fig. 1
Fig. 1

Spontaneous optimization of { B l m } .

Fig. 2
Fig. 2

Power spectra over topological charges of helical modes. (a) Required power spectrum. (b) Schils and Sweeney’s algorithm. (c) Sequential optimization. (d) Spontaneous optimization.

Fig. 3
Fig. 3

(a) Phase-only transmittance. (b) Numerical reconstruction of the multihelix beam at the distance of 0.4 m . (c) Observed intensity patterns of multihelix beam.

Tables (1)

Tables Icon

Table 1 Comparison of Three Iterative Algorithms

Equations (8)

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B exp [ i φ ( θ ) ] = m = 1 n A l m exp ( i l m θ ) ,
f ( θ ) = m = C m exp ( i m θ ) ,
m = C m 2 = 1 .
ψ ( θ ) = Re { i ln [ m = 1 n B l m exp ( i l m θ ) ] } ,
g ( θ ) = m = C m exp ( i m θ ) .
R - RMSE = m = 1 n ( C l m 2 A l m 2 ) 2 n m = 1 n C l m 2 .
B l m = B l m + β ( A l m C l m ) ,
B l m = B l m C l m × C l m ,

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