Abstract

Laguerre–Gaussian (LG) beams of various higher-order radial modes are generated by using a reflective phase-only liquid crystal on silicon (LCOS) spatial light modulator (SLM). Because of the LCOS SLM’s phase-modulation characteristic of a wide spatial bandwidth, a phase modulation scheme effectively generates higher-order LG beams of up to the fifth-order radial mode. We also perform correlation analyses between the observed and the theoretical two-dimensional mode profiles to universally obtain correlation coefficients of more than 0.946, which suggest mode generations of high quality.

© 2007 Optical Society of America

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  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
    [CrossRef] [PubMed]
  2. L. Allen, J. Opt. B 4, S1 (2002).
    [CrossRef]
  3. D. G. Grier, Nature 424, 810 (2003).
    [CrossRef] [PubMed]
  4. D. G. Grier and Y. Roichman, Appl. Opt. 45, 880 (2006).
    [CrossRef] [PubMed]
  5. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
    [CrossRef]
  6. M. Padgett, J. Arlt, N. Simpson, and L. Allen, Am. J. Phys. 64, 77 (1996).
    [CrossRef]
  7. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
    [CrossRef]
  8. M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
    [CrossRef]
  9. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
    [CrossRef]
  10. S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
    [CrossRef]
  11. J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
    [CrossRef]
  12. T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, Proc. SPIE 6487, 64870Y (2007).
    [CrossRef]
  13. M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
    [CrossRef]

2007 (1)

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

2006 (1)

2003 (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

2002 (2)

L. Allen, J. Opt. B 4, S1 (2002).
[CrossRef]

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

2000 (1)

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

1998 (2)

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

1997 (1)

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

1996 (2)

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

M. Padgett, J. Arlt, N. Simpson, and L. Allen, Am. J. Phys. 64, 77 (1996).
[CrossRef]

1993 (1)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

1992 (1)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Abraham, E. R. I.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Allen, L.

L. Allen, J. Opt. B 4, S1 (2002).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

M. Padgett, J. Arlt, N. Simpson, and L. Allen, Am. J. Phys. 64, 77 (1996).
[CrossRef]

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Arlt, J.

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

M. Padgett, J. Arlt, N. Simpson, and L. Allen, Am. J. Phys. 64, 77 (1996).
[CrossRef]

Beijersbergen, M. W.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Clifford, M. A.

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
[CrossRef]

Courtial, J.

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Dholakia, K.

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
[CrossRef]

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Fukuchi, N.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Golub, M. A.

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

Grier, D. G.

Hara, T.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Hitomi, T.

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

Igasaki, Y.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, 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, Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Kaganov, E. L.

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

Kennedy, S. A.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Kobayashi, Y.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Kondorov, A. A.

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

Matsumoto, N.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Padgett, M.

M. Padgett, J. Arlt, N. Simpson, and L. Allen, Am. J. Phys. 64, 77 (1996).
[CrossRef]

Padgett, M. J.

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Porterfield, J. Z.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Roichman, Y.

Simpson, N.

M. Padgett, J. Arlt, N. Simpson, and L. Allen, Am. J. Phys. 64, 77 (1996).
[CrossRef]

Soîfer, V. A.

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Szabo, M. J.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, 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, 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, Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Teslow, H.

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

Usplen'ev, G. V.

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (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, Opt. Commun. 96, 123 (1993).
[CrossRef]

Woerdman, J. P.

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

Yoshida, N.

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Am. J. Phys. (1)

M. Padgett, J. Arlt, N. Simpson, and L. Allen, Am. J. Phys. 64, 77 (1996).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

J. Arlt, T. Hitomi, and K. Dholakia, Appl. Phys. B 71, 549 (2000).
[CrossRef]

J. Mod. Opt. (1)

J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, J. Mod. Opt. 45, 1231 (1998).
[CrossRef]

J. Opt. B (1)

L. Allen, J. Opt. B 4, S1 (2002).
[CrossRef]

Nature (1)

D. G. Grier, Nature 424, 810 (2003).
[CrossRef] [PubMed]

Opt. Commun. (2)

M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).
[CrossRef]

M. A. Clifford, J. Arlt, J. Courtial, and K. Dholakia, Opt. Commun. 156, 300 (1998).
[CrossRef]

Phys. Rev. A (3)

L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).
[CrossRef] [PubMed]

S. A. Kennedy, M. J. Szabo, H. Teslow, J. Z. Porterfield, and E. R. I. Abraham, Phys. Rev. A 66, 043801 (2002).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).
[CrossRef]

Proc. SPIE (1)

T. Inoue, H. Tanaka, N. Fukuchi, M. Takumi, N. Matsumoto, T. Hara, N. Yoshida, Y. Igasaki, and Y. Kobayashi, Proc. SPIE 6487, 64870Y (2007).
[CrossRef]

Sov. J. Quantum Electron. (1)

M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev, Sov. J. Quantum Electron. 26, 184 (1996) M. A. Golub, E. L. Kaganov, A. A. Kondorov, V. A. Soîfer, and G. V. Usplen'ev,[Kvantovaya Elektron. (Moscow) 23, 188 (1996)].
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Phase patterns for generating (a) LG 3 3 and (b) LG 5 1 beams. Beams assigned with positive radial indices possess counterclockwise helical wavefronts when observed against propagating beams. (c) Schematic diagram of experimental setup. BS, beam splitter; SLM, phase-only reflective LCOS SLM; L, convex lens whose focal length is f = 400 mm .

Fig. 2
Fig. 2

Observed mode patterns of multiringed LG beams whose mode indices are up to three. Patterns are aligned so that each column consists of mode patterns of the same azimuthal index l while each row consists of those of the same radial index p.

Fig. 3
Fig. 3

Cross sections of observed mode patterns (dots) with corresponding theoretical curves (solid curves). A correlation coefficient between observed and fitted profiles ( R ) and theoretical mode purity ( η ) are also shown for each mode. Results are arranged to correspond to Fig. 2.

Fig. 4
Fig. 4

Interference patterns of generated beams and plane reference waves for (a) LG 2 2 and (b) LG 3 3 .

Fig. 5
Fig. 5

(a) Observed mode pattern and (b) cross-sectional profiles of observed (dots) and fitted (solid curve) mode pattern for LG 5 1 beam.

Equations (5)

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

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 ) ]
c q k = 1 π R 0 0 2 π d ϕ 0 R 0 r d r u q k ( r , ϕ , 0 ) * exp ( i l ϕ ) × { 2 θ [ L p l ( 2 r 2 w 0 2 ) ] 1 } ,
c q l = [ p ! ( p + l ) ! ] 1 2 ( 1 ) p 2 a 0 2 a 2 d ζ ζ l 2 e ζ 2 L q l ( ζ ) × { 2 θ [ L p l ( ζ ) ] 1 } ,
I p l ( x , y ) = A 0 [ r 0 2 ( x , y ) ] l exp [ r 0 2 ( x , y ) ] × [ L p l ( r 0 2 ( x , y ) ) ] 2 + B 0 ,

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