Abstract

We report on the high-quality holographic generation of higher-order Laguerre–Gaussian (LG) beams using a liquid-crystal-on-silicon spatial light modulator. The effects of the input beam pattern on the output LG beam quality are investigated in detail through theoretical discussions and experiments. Correlation analyses between observed beam patterns and theoretical mode profiles reveal that higher beam quality is achieved for output LG beams generated from a top-hat input beam than from a Gaussian input beam.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  28. M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, “High-order Laguerre-Gaussian laser modes for studies of cold atoms,” Opt. Commun. 156, 300-306 (1998).
    [CrossRef]

2007 (3)

2006 (5)

2005 (2)

2004 (2)

X. Xun and R. W. Cohn, “Phase calibration of spatially nonuniform spatial light modulators,” Appl. Opt. 43, 6400-6406 (2004).
[CrossRef] [PubMed]

J. Harriman, A. Linneberger, and S. A. Serati, “Improving spatial light modulator performance through phase compensation,” Proc. SPIE 5553, 58-67 (2004).
[CrossRef]

2003 (2)

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP Publishing, 2003).
[CrossRef]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

2002 (4)

L. Allen, “Introduction to the atoms and angular momentum of light special issue,” J. Opt. B: Quantum Semiclassical Opt. 4, S1-S6 (2002).
[CrossRef]

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209, 265-271 (2002).
[CrossRef]

2001 (1)

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Pääkkönen, 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).
[CrossRef]

2000 (1)

J. Arlt, T. Hitomi, and K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

1998 (2)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, “High-order Laguerre-Gaussian laser modes for studies of cold atoms,” Opt. Commun. 156, 300-306 (1998).
[CrossRef]

1997 (1)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56, 4193-4196 (1997).
[CrossRef]

1996 (2)

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,” Sov. J. Quantum Electron. 26, 184-186 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,”[Kvantovaya Elektron. (Moscow) 23, 188-190 (1996)].
[CrossRef]

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64, 77-82 (1996).
[CrossRef]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123-132 (1993).
[CrossRef]

1992 (1)

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]

1966 (1)

H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312-1329 (1966).
[CrossRef]

Abraham, E. R. I.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Agarwal, R.

Allen, L.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP Publishing, 2003).
[CrossRef]

L. Allen, “Introduction to the atoms and angular momentum of light special issue,” J. Opt. B: Quantum Semiclassical Opt. 4, S1-S6 (2002).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56, 4193-4196 (1997).
[CrossRef]

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64, 77-82 (1996).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123-132 (1993).
[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]

Almazov, A. A.

Anderson, J. E.

Ando, T.

Arlt, J.

A. Lafong, W. J. Hossack, J. Arlt, T. J. Nowakowski, and N. D. Read, “Time-multiplexed Laguerre-Gaussian holographic optical tweezers for biological applications,” Opt. Express 14, 3065-3072 (2006).
[CrossRef] [PubMed]

J. Arlt, T. Hitomi, and K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, “High-order Laguerre-Gaussian laser modes for studies of cold atoms,” Opt. Commun. 156, 300-306 (1998).
[CrossRef]

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64, 77-82 (1996).
[CrossRef]

Banet, S.

Barnett, S. M.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP Publishing, 2003).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123-132 (1993).
[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]

Bernet, S.

Blit, S.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209, 265-271 (2002).
[CrossRef]

Bos, P. J.

Clifford, M. A.

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, “High-order Laguerre-Gaussian laser modes for studies of cold atoms,” Opt. Commun. 156, 300-306 (1998).
[CrossRef]

Cohn, R. W.

Courtial, J.

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, “High-order Laguerre-Gaussian laser modes for studies of cold atoms,” Opt. Commun. 156, 300-306 (1998).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56, 4193-4196 (1997).
[CrossRef]

Curtis, J. E.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Davidson, N.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209, 265-271 (2002).
[CrossRef]

Dholakia, K.

J. Arlt, T. Hitomi, and K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, “High-order Laguerre-Gaussian laser modes for studies of cold atoms,” Opt. Commun. 156, 300-306 (1998).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56, 4193-4196 (1997).
[CrossRef]

Duncan, B. D.

Friesem, A. A.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209, 265-271 (2002).
[CrossRef]

Fukuchi, N.

Y. Ohtake, T. Ando, N. Fukuchi, N. Matsumoto, H. Ito, and T. Hara, “Universal generation of higher-order multiringed Laguerre-Gaussian beams by using a spatial light modulator,” Opt. Lett. 32, 1411-1413 (2007).
[CrossRef] [PubMed]

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Fürhapter, S.

Goda, M. E.

Golub, M. A.

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,” Sov. J. Quantum Electron. 26, 184-186 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,”[Kvantovaya Elektron. (Moscow) 23, 188-190 (1996)].
[CrossRef]

Grier, D. G.

Hara, T.

Y. Ohtake, T. Ando, N. Fukuchi, N. Matsumoto, H. Ito, and T. Hara, “Universal generation of higher-order multiringed Laguerre-Gaussian beams by using a spatial light modulator,” Opt. Lett. 32, 1411-1413 (2007).
[CrossRef] [PubMed]

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Harriman, J.

J. Harriman, A. Linneberger, and S. A. Serati, “Improving spatial light modulator performance through phase compensation,” Proc. SPIE 5553, 58-67 (2004).
[CrossRef]

Hasman, E.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209, 265-271 (2002).
[CrossRef]

Hitomi, T.

J. Arlt, T. Hitomi, and K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

Hossack, W. J.

Igasaki, Y.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Inoue, T.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Ishaaya, A. A.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209, 265-271 (2002).
[CrossRef]

Ito, H.

Jefimovs, K.

Jesacher, A.

Kaganov, E. L.

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,” Sov. J. Quantum Electron. 26, 184-186 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,”[Kvantovaya Elektron. (Moscow) 23, 188-190 (1996)].
[CrossRef]

Kennedy, S. A.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Khonina, S. N.

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43-56 (2006).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Pääkkönen, 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).
[CrossRef]

Kobayashi, Y.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Kogelnik, H.

H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312-1329 (1966).
[CrossRef]

Kondorov, A. A.

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,” Sov. J. Quantum Electron. 26, 184-186 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,”[Kvantovaya Elektron. (Moscow) 23, 188-190 (1996)].
[CrossRef]

Koss, B. A.

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

Kotlyar, V. V.

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43-56 (2006).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Pääkkönen, 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).
[CrossRef]

Ladavac, K.

Lafong, A.

Li, T.

H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312-1329 (1966).
[CrossRef]

Liever, C. M.

Linneberger, A.

J. Harriman, A. Linneberger, and S. A. Serati, “Improving spatial light modulator performance through phase compensation,” Proc. SPIE 5553, 58-67 (2004).
[CrossRef]

Machavariani, G.

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209, 265-271 (2002).
[CrossRef]

Matsumoto, N.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Y. Ohtake, T. Ando, N. Fukuchi, N. Matsumoto, H. Ito, and T. Hara, “Universal generation of higher-order multiringed Laguerre-Gaussian beams by using a spatial light modulator,” Opt. Lett. 32, 1411-1413 (2007).
[CrossRef] [PubMed]

Maurer, C.

Miranda, F. A.

Nowakowski, T. J.

Ohtake, Y.

Pääkkönen, P.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Pääkkönen, 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).
[CrossRef]

Padgett, M.

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64, 77-82 (1996).
[CrossRef]

Padgett, M. J.

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP Publishing, 2003).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56, 4193-4196 (1997).
[CrossRef]

Porterfield, J. Z.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Pouch, J. J.

Read, N. D.

Ritsch-Marte, M.

Roichman, Y.

Schmidt, J. D.

Schwaighofer, A.

Serati, S. A.

J. Harriman, A. Linneberger, and S. A. Serati, “Improving spatial light modulator performance through phase compensation,” Proc. SPIE 5553, 58-67 (2004).
[CrossRef]

Simonen, J.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Pääkkönen, 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).
[CrossRef]

Simpson, N.

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64, 77-82 (1996).
[CrossRef]

Soifer, V. A.

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43-56 (2006).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Pääkkönen, 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).
[CrossRef]

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,” Sov. J. Quantum Electron. 26, 184-186 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,”[Kvantovaya Elektron. (Moscow) 23, 188-190 (1996)].
[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]

Szabo, M. J.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Takumi, M.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Tanaka, H.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Teslow, H.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Turunen, J.

V. V. Kotlyar, S. N. Khonina, A. A. Almazov, V. A. Soifer, K. Jefimovs, and J. Turunen, “Elliptic Laguerre-Gaussian beams,” J. Opt. Soc. Am. A 23, 43-56 (2006).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Pääkkönen, 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).
[CrossRef]

Usplen'ev, G. V.

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,” Sov. J. Quantum Electron. 26, 184-186 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,”[Kvantovaya Elektron. (Moscow) 23, 188-190 (1996)].
[CrossRef]

van der Veen, H. E. L. O.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123-132 (1993).
[CrossRef]

Wang, B.

Wang, X.

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123-132 (1993).
[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]

Xun, X.

Yoshida, N.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Yu, G.

Am. J. Phys. (1)

M. Padgett, J. Arlt, N. Simpson, and L. Allen, “An experiment to observe the intensity and phase structure of Laguerre-Gaussian laser modes,” Am. J. Phys. 64, 77-82 (1996).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. B (1)

J. Arlt, T. Hitomi, and K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549-554 (2000).
[CrossRef]

J. Mod. Opt. (2)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, “The production of multiringed Laguerre-Gaussian modes by computer-generated holograms,” J. Mod. Opt. 45, 1231-1237 (1998).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Pääkkönen, 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).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt. (1)

L. Allen, “Introduction to the atoms and angular momentum of light special issue,” J. Opt. B: Quantum Semiclassical Opt. 4, S1-S6 (2002).
[CrossRef]

J. Opt. Soc. Am. A (2)

Nature (1)

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810-816 (2003).
[CrossRef] [PubMed]

Opt. Commun. (4)

J. E. Curtis, B. A. Koss, and D. G. Grier, “Dynamic holographic optical tweezers,” Opt. Commun. 207, 169-175 (2002).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123-132 (1993).
[CrossRef]

G. Machavariani, N. Davidson, E. Hasman, S. Blit, A. A. Ishaaya, and A. A. Friesem, “Efficient conversion of a Gaussian beam to a high purity helical beam,” Opt. Commun. 209, 265-271 (2002).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, “High-order Laguerre-Gaussian laser modes for studies of cold atoms,” Opt. Commun. 156, 300-306 (1998).
[CrossRef]

Opt. Express (4)

Opt. Lett. (1)

Phys. Rev. A (3)

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, “Creation of Laguerre-Gaussian laser modes using diffractive optics,” Phys. Rev. A 66, 043801 (2002).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, “Second-harmonic generation and the conservation of orbital angular momentum with high-order Laguerre-Gaussian modes,” Phys. Rev. A 56, 4193-4196 (1997).
[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]

Proc. IEEE (1)

H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312-1329 (1966).
[CrossRef]

Proc. SPIE (2)

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, “LCOS spatial light modulator controlled by 12-bit signals for optical phase-only modulation,” Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

J. Harriman, A. Linneberger, and S. A. Serati, “Improving spatial light modulator performance through phase compensation,” Proc. SPIE 5553, 58-67 (2004).
[CrossRef]

Sov. J. Quantum Electron. (1)

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,” Sov. J. Quantum Electron. 26, 184-186 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soĭfer, and G. V. Usplen'ev, “Experimental investigation of a multibeam holographic optical element matched to Gauss-Laguerre modes,”[Kvantovaya Elektron. (Moscow) 23, 188-190 (1996)].
[CrossRef]

Other (1)

L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (IOP Publishing, 2003).
[CrossRef]

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Figures (19)

Fig. 1
Fig. 1

Structure of the LCOS-SLM device, cross-sectional picture.

Fig. 2
Fig. 2

Focal patterns of the top-hat incident beam reflected on the LCOS-SLM device (a) without and (b) with the phase compensation.

Fig. 3
Fig. 3

Schematic of experimental setups. (a) Setup for a Gaussian input beam and (b) setup for a top-hat input beam. BS, SF, and CL indicate beam splitter, spatial filter, and collimation lens, respectively.

Fig. 4
Fig. 4

Observed mode patterns of the LG 2 1 beam. (a) Without any compensations, (b) with a compensation only for phase distortion of the LCOS-SLM, and (c) with careful adjustment of the tilt of the lens.

Fig. 5
Fig. 5

Examples of phase pattern for generating (a) LG 3 3 and (b) LG 5 5 beams.

Fig. 6
Fig. 6

Phase patterns obtained by adding blazed phase grating patterns to those shown in Fig. 5 for (a) LG 3 3 and (b) LG 5 5 .

Fig. 7
Fig. 7

Theoretical output mode purities as functions of a for Gaussian-beam input under the condition of R 0 = 1.46 w i . (a) In the case of fixed l ( l = 1 ) , dotted, dashed, and solid curves are mode purities for p = 1 , 3, and 5, respectively. (b) In the case of fixed p ( p = 1 ) , dotted, dashed, and solid curves are mode purities for l = 1 , 3, and 5, respectively.

Fig. 8
Fig. 8

Theoretical output mode purities as functions of a for top-hat beam input. (a) In the case of fixed l ( l = 1 ) , dotted, dashed, and solid curves are mode purities for p = 1 , 3, and 5, respectively. (b) In the case of fixed p ( p = 1 ) , dotted, dashed, and solid curves are mode purities for l = 1 , 3, and 5, respectively.

Fig. 9
Fig. 9

Interference patterns of generated beams and the plane reference waves for (a) LG 4 4 and (b) LG 5 5 generated from a top-hat input beam.

Fig. 10
Fig. 10

Observed beam patterns of LG p l ( p , l = 1 , 2 , 3 ) beams generated from Gaussian input beams.

Fig. 11
Fig. 11

Cross sections of observed mode patterns (closed circles) with corresponding fitted profiles (solid curves) for LG p l modes of p , l = 1 , 2 , 3 . Results are aligned corresponding to Fig. 10.

Fig. 12
Fig. 12

Observed beam patterns of higher-order LG beams generated from a Gaussian input beam.

Fig. 13
Fig. 13

Cross sections of observed beam patterns (closed circles) with the corresponding fitted profiles (solid curves) for further higher-order LG beams. Results are aligned corresponding to Fig. 12.

Fig. 14
Fig. 14

Observed mode patterns of LG p l ( p , l = 1 , 2 , 3 ) beams generated from a top-hat input beam.

Fig. 15
Fig. 15

Cross sections of observed mode patterns (closed circles) with the corresponding fitted profiles (solid curves) for LG p l modes of p , l = 1 , 2 , 3 . Results are aligned corresponding to Fig. 14.

Fig. 16
Fig. 16

Observed mode patterns of higher-order LG beams generated from a top-hat input beam.

Fig. 17
Fig. 17

Cross sections of observed mode patterns (closed circles) with the corresponding fitted profiles (solid curves) for further higher-order LG beams. Results are aligned corresponding to Fig. 16.

Fig. 18
Fig. 18

Correlation coefficient R and mode purity η of holographically generated LG p l beams from (a) Gaussian and (b) top-hat input beams.

Fig. 19
Fig. 19

Plot of correlation coefficient R as a function of theoretical mode purity η. Closed circles indicate values derived from the results of top-hat input while open squares indicate those from the results of Gaussian input.

Tables (2)

Tables Icon

Table 1 Mode Contents of the First Ten Components of the Holographically Generated LG p = 0 l = 1 Beam

Tables Icon

Table 2 First 30 Mode Contents of the Holographically Generated LG p = 3 l = 1 from a Top-Hat Input Beam

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

ϕ x , y ( V ) = Δ ϕ x , y ( V ) + ϕ x , y ( 0 ) = n ( V ) d x , y + ϕ x , y fix ,
u p l ( r , ϕ , z ) = ( 1 ) p [ 2 π p ! ( p + l ) ! ] 1 2 ( 2 ξ ) l w z exp ( ξ 2 ) × L p l ( 2 ξ 2 ) exp ( i l ϕ ) exp ( i ξ 2 z z R ) × exp [ i ( 2 p + l + 1 ) tan 1 ( z z R ) ] ,
φ ( r , ϕ ) = l ϕ + π θ ( L p l ( 2 r 2 w 0 2 ) )
I p l ( r , ϕ , z ) = u p l ( r , ϕ , z ) 2 = 2 π w z 2 p ! ( p + l ) ! ( 2 r 2 w z 2 ) l × exp ( 2 r 2 w z 2 ) [ L p l ( 2 r 2 w z 2 ) ] 2 .
I p l ( x , y ; B 0 , C 0 , w z ) = B 0 + C 0 2 π w z 2 p ! ( p + l ) ! ( 2 x 2 + y 2 w z 2 ) l × exp ( 2 x 2 + y 2 w z 2 ) [ L p l ( 2 x 2 + y 2 w z 2 ) ] 2 ,
A ( r ) = { θ ( R 0 r ) top - hat exp ( r 2 w i 2 ) θ ( R 0 r ) Gaussian ) ,
Ψ p l ( r , ϕ ) = exp [ i φ ( r , ϕ ) ] = exp ( i l ϕ ) [ 2 θ ( L p l ( 2 r 2 w 0 2 ) ) 1 ] ,
c q k = A 0 0 2 π d ϕ 0 r d r A ( r ) Ψ p l ( r , ϕ ) u q k ( r , ϕ , 0 ) * ,
A 0 = [ 0 2 π d ϕ 0 r d r A ( r ) 2 ] 1 2 = { 1 π R 0 top - hat 1 π w i [ 2 1 exp ( 2 R 0 2 w i 2 ) ] 1 2 Gaussian ] .
c q l ( a ) = [ q ! ( q + l ) ! ] 1 2 ( 1 ) q R 0 A 0 π 2 3 2 a × 0 2 a 2 d ζ ζ l 2 L q l ( ζ ) [ 2 θ ( L p l ( ζ ) ) 1 ] × { exp ( ζ 2 ) top - hat exp [ ( 1 + R 0 2 w i 2 1 a 2 ) ζ 2 ] Gaussian ) ,

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