Abstract

A major application of optics is imaging all types of structural, physical, chemical and biological features of matter. Techniques based on most known properties of light have been developed over the years to remotely acquire information about such features. They include the spin angular momentum, encoded in the polarization, but not yet the orbital angular momentum encoded in its spiral spectrum. Here we put forward the potential of such spiral spectra. In particular, we use several canonical examples to show how the orbital angular momentum spectra of a light beam can be used to image a variety of intrinsic and extrinsic properties encoded, e.g., in phase and amplitude gradients, dislocations or delays.

© 2005 Optical Society of America

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References

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  1. L. Allen, M. J. Padgett and M. Babiker, �??The orbital angular momentum of light,�?? Progress in Optics 39, 291-372 (1999).
    [CrossRef]
  2. M. J. Padgett, J. Courtial, and L. Allen, �??Light�??s Orbital Angular Momentum,�?? Phys. Today 57, 35-40 (2004).
    [CrossRef]
  3. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics (Wiley, New York, 1989).
  4. S. M. Barnett, �??Optical angular-momentum flux,�?? J. Opt. B 4, S7-S16 (2002).
    [CrossRef]
  5. A. T. Neil, I. MacVicar, L. Allen, M. J. Padgett, �??Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,�?? Phys. Rev. Lett. 88, 053601 (2002).
    [CrossRef]
  6. L. Paterson, M. P. MacDonald, J.Arlt,W. Sibbett, P. E. Bryant, and K. Dholakia, �??Controlled rotation of optically trapped microscopic particles,�?? Science 292, 912-914 (2001).
    [CrossRef] [PubMed]
  7. N. B. Simpson, K. Dholakia, L. Allen, and M. Padgett, �??Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,�?? Opt. Lett. 22, 52-54 (1997).
    [CrossRef] [PubMed]
  8. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, �??Direct observation of transfer of angular momentum to absorbing particles from a laser beam with a phase singularity,�?? Phys. Rev. Lett. 75, 826-829 (1995).
    [CrossRef] [PubMed]
  9. N. R. Heckenberg, T. A. Nieminen, M. E. J. Friese, and H. Rubinsztein-Dunlop, �??Trapping microscopic particles with singular beams,�?? in International Conference on Singular Optics, M. S. Soskin ed., Proc. SPIE 3487, 46-53 (1998).
  10. P. Galajda and P. Ormos, �??Complex micromachines produced and driven by light,�?? Appl Phys. Lett. 78, 249-251 (2001).
    [CrossRef]
  11. G. Swartzlander, �??Peering into darkness with a vortex spatial filter,�?? Opt. Lett. 26, 497-499 (2001).
    [CrossRef]
  12. E. Santamato, A. Sasso, B. Piccirillo, and A. Vella, �??Optical angular momentum transfer to transparent isotropic particles using laser beam carrying zero average angular momentum,�?? Opt. Express 10, 871-878 (2002). <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-871">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-17-871</a>
    [PubMed]
  13. D. G. Grier, �??A revolution in optical manipulation,�?? Nature (London) 424, 810-816 (2003).
    [CrossRef]
  14. K. Dholakia, G. Spalding, and M. MacDonald, �??Optical tweezers: the next generation,�?? Physics World 15, 31 (2002).
  15. K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W Sibbett, �??Imaging in optical micromanipulation using two-photon excitation,�?? New J. Phys. 6, 136 (2004).
    [CrossRef]
  16. E. Santamato, �??Photon orbital angular momentum: problems and perspectives,�?? Fortschr. Phys. 52, 1141-1153 (2004).
    [CrossRef]
  17. 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]
  18. G. Molina-Terriza, J. P. Torres, and L. Torner, �??Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,�?? Phys. Rev. Lett. 88, 013601 (2002).
    [CrossRef] [PubMed]
  19. A. Vaziri, G. Weihs and A. Zeilinger, �??Experimental two-photon, three-dimensional entanglement for quantum communication,�?? Phys. Rev. Lett. 89, 240401 (2002).
    [CrossRef] [PubMed]
  20. M. S. Soskin and M. V. Vasnetsov, �??Singular Optics,�?? Progress in Optics 42, 219-276 (2001).
    [CrossRef]
  21. E. G. Johnson, J. Stack, and Ch. Koehler, �??Light coupling by a vortex lens into graded index fiber,�?? J. Lightwave Technol. 19, 753-758 (2001).
    [CrossRef]
  22. C. Rockstuhl, M. Salt, and H. P. Herzing, �??Theoretical and experimental investigation of phase singularities generated by optical micro- and nano-structures,�?? J. Opt. A 6, S271-S276 (2004).
    [CrossRef]
  23. R. J. Voogd, M. Singh, S. Pereira, A. van de Nes, and J. Braat, �??The use of orbital angular momentum of light beams for super-high density optical data storage,�?? OSA Annual Meeting, Rochester, NY, October 2004, paper FTuG14.
  24. M. M. Varma, D. D. Nolte, H. D. Inerowicz, and F. E. Regnier, �??Spinning-disk self-referencing interferometry of antigen-antibody recognition,�?? Opt. Lett. 29, 950-952 (2004).
    [CrossRef] [PubMed]

Appl Phys. Lett. (1)

P. Galajda and P. Ormos, �??Complex micromachines produced and driven by light,�?? Appl Phys. Lett. 78, 249-251 (2001).
[CrossRef]

Fortschr. Phys. (1)

E. Santamato, �??Photon orbital angular momentum: problems and perspectives,�?? Fortschr. Phys. 52, 1141-1153 (2004).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. A (1)

C. Rockstuhl, M. Salt, and H. P. Herzing, �??Theoretical and experimental investigation of phase singularities generated by optical micro- and nano-structures,�?? J. Opt. A 6, S271-S276 (2004).
[CrossRef]

J. Opt. B (1)

S. M. Barnett, �??Optical angular-momentum flux,�?? J. Opt. B 4, S7-S16 (2002).
[CrossRef]

Nature (London) (2)

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]

D. G. Grier, �??A revolution in optical manipulation,�?? Nature (London) 424, 810-816 (2003).
[CrossRef]

New J. Phys. (1)

K. Dholakia, H. Little, C. T. A. Brown, B. Agate, D. McGloin, L. Paterson, and W Sibbett, �??Imaging in optical micromanipulation using two-photon excitation,�?? New J. Phys. 6, 136 (2004).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

OSA Annual Meeting (1)

R. J. Voogd, M. Singh, S. Pereira, A. van de Nes, and J. Braat, �??The use of orbital angular momentum of light beams for super-high density optical data storage,�?? OSA Annual Meeting, Rochester, NY, October 2004, paper FTuG14.

Phys. Rev. Lett. (4)

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

A. T. Neil, I. MacVicar, L. Allen, M. J. Padgett, �??Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,�?? Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef]

G. Molina-Terriza, J. P. Torres, and L. Torner, �??Management of the angular momentum of light: preparation of photons in multidimensional vector states of angular momentum,�?? Phys. Rev. Lett. 88, 013601 (2002).
[CrossRef] [PubMed]

A. Vaziri, G. Weihs and A. Zeilinger, �??Experimental two-photon, three-dimensional entanglement for quantum communication,�?? Phys. Rev. Lett. 89, 240401 (2002).
[CrossRef] [PubMed]

Phys. Today (1)

M. J. Padgett, J. Courtial, and L. Allen, �??Light�??s Orbital Angular Momentum,�?? Phys. Today 57, 35-40 (2004).
[CrossRef]

Physics World (1)

K. Dholakia, G. Spalding, and M. MacDonald, �??Optical tweezers: the next generation,�?? Physics World 15, 31 (2002).

Proc. SPIE (1)

N. R. Heckenberg, T. A. Nieminen, M. E. J. Friese, and H. Rubinsztein-Dunlop, �??Trapping microscopic particles with singular beams,�?? in International Conference on Singular Optics, M. S. Soskin ed., Proc. SPIE 3487, 46-53 (1998).

Progress in Optics (2)

L. Allen, M. J. Padgett and M. Babiker, �??The orbital angular momentum of light,�?? Progress in Optics 39, 291-372 (1999).
[CrossRef]

M. S. Soskin and M. V. Vasnetsov, �??Singular Optics,�?? Progress in Optics 42, 219-276 (2001).
[CrossRef]

Science (1)

L. Paterson, M. P. MacDonald, J.Arlt,W. Sibbett, P. E. Bryant, and K. Dholakia, �??Controlled rotation of optically trapped microscopic particles,�?? Science 292, 912-914 (2001).
[CrossRef] [PubMed]

Other (1)

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics (Wiley, New York, 1989).

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Figures (8)

Fig. 1.
Fig. 1.

Intensity distribution of two different LG modes: (a) LG 00 (m=0, p=0), and (b) LG 20 (m=2, p=0).

Fig. 2.
Fig. 2.

Spiral spectra of the output field reflected/refracted from a target imprinting a π phase dislocation across in the center of the illuminating beam. The transfer function of such a target has the form: R(x,y)=1 for x<0, and R(x,y)=-1 otherwise. The input field is a Gaussian beam (pure LG 00 mode).

Fig. 3.
Fig. 3.

(a) Spiral spectra of the output field reflected/refracted from a target imprinting a ϕ phase dislocation across in the center of the illuminating beam for four selected values of the phase dislocation. (b) Weight of the central (n=0), P 0 and the first adjacent (n=±1) sidelobes, P 1+P (-1) versus the normalized phase dislocation ϕ/π. The transfer function of the target has the form: R(x,y)=1 for x<0, and R(x,y)=e otherwise. The input field is a Gaussian beam.

Fig. 4.
Fig. 4.

Weight of the central (n=0), P 0 and the first adjacent (n=±1) sidelobes, P 1+P (-1) for a Gaussian beam of beam waist η=1 illuminating an off-axis π phase dislocation placed at a distance D from the center of the beam.

Fig. 5.
Fig. 5.

Output intensity distributions (left column), and spiral spectra (right column) for a Gaussian beam of beam waist η=1 illuminating a target imprinting a comb of π phase dislocations. Each row displays a different value D of the separation between the edges. Top row, D=1; middle row, D=0.5; bottom row, D=0.25.

Fig. 6.
Fig. 6.

Spiral spectra of the output field for a Gaussian beam of beam waist η=1 illuminating a target featuring an antisymmetric phase gradient across the input beam for different selected strengths α of the phase gradient. The transfer function of the target has the form R(x,y)=eiαπx/η .

Fig. 7.
Fig. 7.

Same as in Fig. 6, for a symmetric phase gradient target of the form R(x,y)=eiαπ|x|/η .

Fig. 8.
Fig. 8.

Intensity distributions (left column), and spiral spectra (right column) of the output field reflected from a perfect mirror with a blocking strip of different widths D placed in the center of the illuminating beam. The transfer function of such a target has the form R(x, y)=1 for |x|>D/2, and R(x,y)=0 otherwise. The input beam is a pure LG mode with m=2, and a beam waist η=1.

Equations (3)

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L G m , p ( ρ , φ ) = ( 2 p ! π ( m + p ) ! ) 1 2 1 η ( 2 ρ η ) m L p m ( 2 ρ 2 η 2 ) exp ( ρ 2 η 2 ) exp ( i m φ ) ,
u ( ρ , φ ; z ) = 1 2 π n = n = a n ( ρ , z ) exp ( i n φ ) ,
P n = C n q = C q

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