Abstract

Subwavelength-resolution phase images of phase dislocations at the focal region of a 20×, 0.4-N.A. lens have been obtained by use of an optical fiber interferometer with a tapered probe in one arm. A phase-stepping algorithm is used to determine a quantitative value of the phase at each point in the scan, clearly showing the presence of edge dislocations between the Airy rings of the diffraction pattern near the lens focus, as well as four isolated screw-type singularties caused by astigmatism in the lens.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
    [CrossRef]
  2. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
    [CrossRef]
  3. J. J. McClelland and M. R. Scheinfein, J. Opt. Soc. Am. B 8, 1974 (1991).
    [CrossRef]
  4. M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
    [CrossRef] [PubMed]
  5. P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, and P. St. J. Russell, Appl. Phys. Lett. 76, 541 (2000).
    [CrossRef]
  6. J. Scheuer and M. Orenstein, Science 285, 230 (1999).
    [CrossRef] [PubMed]
  7. G. P. Karman, M. W. Beijersbergen, A. van Duijl, D. Bouwmeester, and J. P. Woerdman, J. Opt. Soc. Am. A 15, 884 (1998).
    [CrossRef]
  8. A. Ashkin, Proc. Natl. Acad. Sci. U.S.A. 94, 4853 (1997).
    [CrossRef]
  9. E. Betzig and J. K. Trautman, Science 257, 189 (1992).
    [CrossRef] [PubMed]
  10. Y. Li, J. Opt. Soc. Am. A 2, 1677 (1985).
    [CrossRef]
  11. L. V. Kreminskaya, M. S. Soskin, and A. I. Khizhnyak, Opt. Commun. 145, 377 (1998).
    [CrossRef]
  12. M. V. Berry, J. Mod. Opt. 45, 1845 (1998).
    [CrossRef]
  13. H. J. Erkkila and M. E. Rogers, J. Opt. Soc. Am. 71, 904 (1981).
    [CrossRef]
  14. J. J. Stamnes and B. Spjelkavik, Opt. Commun. 40, 81 (1981).
    [CrossRef]
  15. G. P. Karman and J. P. Woerdman, J. Opt. Soc. Am. A 15, 2862 (1998).
    [CrossRef]
  16. M. Mansuripur, J. Opt. Soc. A 3, 2086 (1986).
    [CrossRef]
  17. A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlinear Opt. Phys. Mater. 6, 169 (1997).
    [CrossRef]
  18. S. K. Rhodes, A. Barty, A. Roberts, and K. A. Nugent, Opt. Commun. 145, 9 (1998).
    [CrossRef]
  19. H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
    [CrossRef] [PubMed]
  20. J. N. Walford, K. A. Nugent, A. Roberts, and R. E. Scholten, Appl. Opt. 38, 3508 (1999).
    [CrossRef]
  21. J. M. Huntley, Appl. Opt. 28, 3268 (1989).
    [CrossRef] [PubMed]

2000 (2)

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, and P. St. J. Russell, Appl. Phys. Lett. 76, 541 (2000).
[CrossRef]

1999 (2)

1998 (5)

G. P. Karman, M. W. Beijersbergen, A. van Duijl, D. Bouwmeester, and J. P. Woerdman, J. Opt. Soc. Am. A 15, 884 (1998).
[CrossRef]

L. V. Kreminskaya, M. S. Soskin, and A. I. Khizhnyak, Opt. Commun. 145, 377 (1998).
[CrossRef]

M. V. Berry, J. Mod. Opt. 45, 1845 (1998).
[CrossRef]

G. P. Karman and J. P. Woerdman, J. Opt. Soc. Am. A 15, 2862 (1998).
[CrossRef]

S. K. Rhodes, A. Barty, A. Roberts, and K. A. Nugent, Opt. Commun. 145, 9 (1998).
[CrossRef]

1997 (2)

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlinear Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

A. Ashkin, Proc. Natl. Acad. Sci. U.S.A. 94, 4853 (1997).
[CrossRef]

1995 (1)

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

1992 (2)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

1991 (1)

1989 (1)

1986 (1)

M. Mansuripur, J. Opt. Soc. A 3, 2086 (1986).
[CrossRef]

1985 (1)

1981 (2)

H. J. Erkkila and M. E. Rogers, J. Opt. Soc. Am. 71, 904 (1981).
[CrossRef]

J. J. Stamnes and B. Spjelkavik, Opt. Commun. 40, 81 (1981).
[CrossRef]

1974 (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Ashkin, A.

A. Ashkin, Proc. Natl. Acad. Sci. U.S.A. 94, 4853 (1997).
[CrossRef]

Balistreri, M. L. M.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

Barty, A.

S. K. Rhodes, A. Barty, A. Roberts, and K. A. Nugent, Opt. Commun. 145, 9 (1998).
[CrossRef]

Beijersbergen, M. W.

Berry, M. V.

M. V. Berry, J. Mod. Opt. 45, 1845 (1998).
[CrossRef]

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Betzig, E.

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

Bouwmeester, D.

Erkkila, H. J.

Friese, M. E. J.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

He, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Heckenberg, N. R.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Huntley, J. M.

Ilyenkov, A. V.

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlinear Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

Kakarantzas, G.

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, and P. St. J. Russell, Appl. Phys. Lett. 76, 541 (2000).
[CrossRef]

Karman, G. P.

Khizhnyak, A. I.

L. V. Kreminskaya, M. S. Soskin, and A. I. Khizhnyak, Opt. Commun. 145, 377 (1998).
[CrossRef]

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlinear Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

Knight, J. C.

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, and P. St. J. Russell, Appl. Phys. Lett. 76, 541 (2000).
[CrossRef]

Korterik, J. P.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

Kreminskaya, L. V.

L. V. Kreminskaya, M. S. Soskin, and A. I. Khizhnyak, Opt. Commun. 145, 377 (1998).
[CrossRef]

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlinear Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

Kuipers, L.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

Li, Y.

Mansuripur, M.

M. Mansuripur, J. Opt. Soc. A 3, 2086 (1986).
[CrossRef]

McClelland, J. J.

McDuff, R.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Nugent, K. A.

J. N. Walford, K. A. Nugent, A. Roberts, and R. E. Scholten, Appl. Opt. 38, 3508 (1999).
[CrossRef]

S. K. Rhodes, A. Barty, A. Roberts, and K. A. Nugent, Opt. Commun. 145, 9 (1998).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Orenstein, M.

J. Scheuer and M. Orenstein, Science 285, 230 (1999).
[CrossRef] [PubMed]

Phillips, P. L.

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, and P. St. J. Russell, Appl. Phys. Lett. 76, 541 (2000).
[CrossRef]

Pottage, J. M.

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, and P. St. J. Russell, Appl. Phys. Lett. 76, 541 (2000).
[CrossRef]

Rhodes, S. K.

S. K. Rhodes, A. Barty, A. Roberts, and K. A. Nugent, Opt. Commun. 145, 9 (1998).
[CrossRef]

Roberts, A.

J. N. Walford, K. A. Nugent, A. Roberts, and R. E. Scholten, Appl. Opt. 38, 3508 (1999).
[CrossRef]

S. K. Rhodes, A. Barty, A. Roberts, and K. A. Nugent, Opt. Commun. 145, 9 (1998).
[CrossRef]

Rogers, M. E.

Rubinsztein-Dunlop, H.

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Russell, P. St. J.

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, and P. St. J. Russell, Appl. Phys. Lett. 76, 541 (2000).
[CrossRef]

Scheinfein, M. R.

Scheuer, J.

J. Scheuer and M. Orenstein, Science 285, 230 (1999).
[CrossRef] [PubMed]

Scholten, R. E.

Smith, C. P.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Soskin, M. S.

L. V. Kreminskaya, M. S. Soskin, and A. I. Khizhnyak, Opt. Commun. 145, 377 (1998).
[CrossRef]

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlinear Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

Spjelkavik, B.

J. J. Stamnes and B. Spjelkavik, Opt. Commun. 40, 81 (1981).
[CrossRef]

Stamnes, J. J.

J. J. Stamnes and B. Spjelkavik, Opt. Commun. 40, 81 (1981).
[CrossRef]

Trautman, J. K.

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

van Duijl, A.

van Hulst, N. F.

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

Vasnetsov, M. V.

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlinear Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

Walford, J. N.

Wegener, M. J.

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Woerdman, J. P.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

P. L. Phillips, J. C. Knight, J. M. Pottage, G. Kakarantzas, and P. St. J. Russell, Appl. Phys. Lett. 76, 541 (2000).
[CrossRef]

J. Mod. Opt. (1)

M. V. Berry, J. Mod. Opt. 45, 1845 (1998).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

A. V. Ilyenkov, A. I. Khizhnyak, L. V. Kreminskaya, M. S. Soskin, and M. V. Vasnetsov, J. Nonlinear Opt. Phys. Mater. 6, 169 (1997).
[CrossRef]

J. Opt. Soc. A (1)

M. Mansuripur, J. Opt. Soc. A 3, 2086 (1986).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (1)

Opt. Commun. (3)

S. K. Rhodes, A. Barty, A. Roberts, and K. A. Nugent, Opt. Commun. 145, 9 (1998).
[CrossRef]

L. V. Kreminskaya, M. S. Soskin, and A. I. Khizhnyak, Opt. Commun. 145, 377 (1998).
[CrossRef]

J. J. Stamnes and B. Spjelkavik, Opt. Commun. 40, 81 (1981).
[CrossRef]

Opt. Quantum Electron. (1)

N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).
[CrossRef]

Phys. Rev. Lett. (2)

M. L. M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, Phys. Rev. Lett. 85, 294 (2000).
[CrossRef] [PubMed]

H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (1)

A. Ashkin, Proc. Natl. Acad. Sci. U.S.A. 94, 4853 (1997).
[CrossRef]

Proc. R. Soc. London Ser. A (1)

J. F. Nye and M. V. Berry, Proc. R. Soc. London Ser. A 336, 165 (1974).
[CrossRef]

Science (2)

E. Betzig and J. K. Trautman, Science 257, 189 (1992).
[CrossRef] [PubMed]

J. Scheuer and M. Orenstein, Science 285, 230 (1999).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Qualitative representation showing how the vortex ring associated with the first dark Airy ring in a focal pattern is distorted by astigmatism. (a) In the absence of astigmatism, the vortex ring lies entirely in the focal plane. (b) With astigmatism, the vortex ring is deformed along the optical axis. A phase image recorded in a transverse plane will show a quadrupole of optical vortices at the points where the ring cuts the image plane. (c) Calculated cosine of the phase of the field produced in the focal plane of a lens, with N.A. of 0.4 in the presence of 0.3λ lateral astigmatism.

Fig. 2
Fig. 2

Experimental apparatus. PZT, piezoelectric transducer; PMT, photomultiplier tube. 99/1, 50/50, fiber couplers.

Fig. 3
Fig. 3

Images of the cosine of phase (left) and intensity (right) in the focal plane of a 0.4-N.A. lens. The dimensions of the images are 12 µm by 12 µm.

Fig. 4
Fig. 4

Detail of the bottom left-hand phase singularity from Fig. 3, as a gray scale of the cosine of the phase (left) and as a shaded surface of the phase (right).

Equations (2)

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

ϕdS=2nπ
n=ϕi+1,j-ϕi,jdiv π+ϕi+1,j+1-ϕi+1,jdiv π+ϕi,j+1-ϕi+1,j+1div π+ϕi,j-ϕi,j+1div π.

Metrics