Abstract

A new setup of interferometers is proposed in which the set of specific optical markers—optical vortices—could be generated. The classical Mach–Zender two-beam interferometer has been modernized using the Wollaston prism. In this setup, the optical vortices could be obtained for a wide range of both beam parameters. The numerical analysis and experiments confirm our theoretical predictions.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. F. Nye, M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
    [CrossRef]
  2. J. Masajada, “Synthetics holograms for optical vortices generation—image evaluation,” Optik 110, 554–558 (1999).
  3. Z. S. Sacks, D. Rozas, G. A. Swartzlander, “Holographic formation of optical-vortex filaments,” J. Opt. Soc. Am. B 15, 2226–2234 (1998).
    [CrossRef]
  4. M. Vasnetsov, K. Staliunas, Optical Vortices (Nova Science, 1999).
  5. L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” Progress in Optics, Vol. XXXIX, E. Wolf, ed. (Elsevier, 1999), Chap. IV.
  6. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
    [CrossRef]
  7. S. N. Khonina, V. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
    [CrossRef]
  8. T. Ackemann, E. Kriege, W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapour,” Opt. Commun. 155, 339–346 (1995).
    [CrossRef]
  9. A. V. Mamaev, M. Saffman, A. A. Zazulya, “Propagation of dark stripe beams in nonlinear media; snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
    [CrossRef] [PubMed]
  10. W. Wang, T. Yokozei, R. Ishijma, A. Wada, Y. Myijamoto, M. Takeda, S. G. Hanson, “Optical vortex metrology for nanometric speckle displacement measurements,” Opt. Express 14, 120–127 (2006).
    [CrossRef] [PubMed]
  11. J. Masajada, B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–26 (2001).
    [CrossRef]
  12. A. Popiołek-Masajada, M. Borwińska, E. Fra¸czek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
    [CrossRef]
  13. Ch. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley-Interscience, 1998), pp. 332–333.
  14. G. P. Karman, M. W. Beijersbergen, A. van Duijl, J. P. Woerdman, “Creation and annihilation of phase singularities in a focal field,” Opt. Lett. 22, 1503–1505 (1997).
    [CrossRef]
  15. D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998).

2006

W. Wang, T. Yokozei, R. Ishijma, A. Wada, Y. Myijamoto, M. Takeda, S. G. Hanson, “Optical vortex metrology for nanometric speckle displacement measurements,” Opt. Express 14, 120–127 (2006).
[CrossRef] [PubMed]

A. Popiołek-Masajada, M. Borwińska, E. Fra¸czek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
[CrossRef]

2001

J. Masajada, B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–26 (2001).
[CrossRef]

1999

J. Masajada, “Synthetics holograms for optical vortices generation—image evaluation,” Optik 110, 554–558 (1999).

1998

1997

1996

A. V. Mamaev, M. Saffman, A. A. Zazulya, “Propagation of dark stripe beams in nonlinear media; snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef] [PubMed]

1995

T. Ackemann, E. Kriege, W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapour,” Opt. Commun. 155, 339–346 (1995).
[CrossRef]

1994

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

1992

S. N. Khonina, V. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

1974

J. F. Nye, M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Ackemann, T.

T. Ackemann, E. Kriege, W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapour,” Opt. Commun. 155, 339–346 (1995).
[CrossRef]

Allen, L.

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” Progress in Optics, Vol. XXXIX, E. Wolf, ed. (Elsevier, 1999), Chap. IV.

Babiker, M.

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” Progress in Optics, Vol. XXXIX, E. Wolf, ed. (Elsevier, 1999), Chap. IV.

Beijersbergen, M. W.

G. P. Karman, M. W. Beijersbergen, A. van Duijl, J. P. Woerdman, “Creation and annihilation of phase singularities in a focal field,” Opt. Lett. 22, 1503–1505 (1997).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Berry, M. V.

J. F. Nye, M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Borwinska, M.

A. Popiołek-Masajada, M. Borwińska, E. Fra¸czek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
[CrossRef]

Brosseau, Ch.

Ch. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley-Interscience, 1998), pp. 332–333.

Coerwinkel, R. P. C.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Dubik, B.

J. Masajada, B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–26 (2001).
[CrossRef]

Fra¸czek, E.

A. Popiołek-Masajada, M. Borwińska, E. Fra¸czek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
[CrossRef]

Hanson, S. G.

Ishijma, R.

Karman, G. P.

Khonina, S. N.

S. N. Khonina, V. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Kriege, E.

T. Ackemann, E. Kriege, W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapour,” Opt. Commun. 155, 339–346 (1995).
[CrossRef]

Kristensen, M.

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Lange, W.

T. Ackemann, E. Kriege, W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapour,” Opt. Commun. 155, 339–346 (1995).
[CrossRef]

Malacara, D.

D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998).

Malacara, Z.

D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998).

Mamaev, A. V.

A. V. Mamaev, M. Saffman, A. A. Zazulya, “Propagation of dark stripe beams in nonlinear media; snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef] [PubMed]

Masajada, J.

J. Masajada, B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–26 (2001).
[CrossRef]

J. Masajada, “Synthetics holograms for optical vortices generation—image evaluation,” Optik 110, 554–558 (1999).

Myijamoto, Y.

Nye, J. F.

J. F. Nye, M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Padgett, M. J.

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” Progress in Optics, Vol. XXXIX, E. Wolf, ed. (Elsevier, 1999), Chap. IV.

Popiolek-Masajada, A.

A. Popiołek-Masajada, M. Borwińska, E. Fra¸czek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
[CrossRef]

Rozas, D.

Sacks, Z. S.

Saffman, M.

A. V. Mamaev, M. Saffman, A. A. Zazulya, “Propagation of dark stripe beams in nonlinear media; snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef] [PubMed]

Servín, M.

D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998).

Shinkaryev, V. V.

S. N. Khonina, V. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Soifer, V. A.

S. N. Khonina, V. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

Staliunas, K.

M. Vasnetsov, K. Staliunas, Optical Vortices (Nova Science, 1999).

Swartzlander, G. A.

Takeda, M.

Uspleniev, G. V.

S. N. Khonina, V. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

van Duijl, A.

Vasnetsov, M.

M. Vasnetsov, K. Staliunas, Optical Vortices (Nova Science, 1999).

Wada, A.

Wang, W.

Woerdman, J. P.

G. P. Karman, M. W. Beijersbergen, A. van Duijl, J. P. Woerdman, “Creation and annihilation of phase singularities in a focal field,” Opt. Lett. 22, 1503–1505 (1997).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Yokozei, T.

Zazulya, A. A.

A. V. Mamaev, M. Saffman, A. A. Zazulya, “Propagation of dark stripe beams in nonlinear media; snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef] [PubMed]

J. Mod. Opt.

S. N. Khonina, V. V. Shinkaryev, V. A. Soifer, G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992).
[CrossRef]

J. Opt. Soc. Am. B

Meas. Sci. Technol.

A. Popiołek-Masajada, M. Borwińska, E. Fra¸czek, “Testing a new method for small-angle rotation measurements with the optical vortex interferometer,” Meas. Sci. Technol. 17, 653–658 (2006).
[CrossRef]

Opt. Commun.

J. Masajada, B. Dubik, “Optical vortex generation by three plane wave interference,” Opt. Commun. 198, 21–26 (2001).
[CrossRef]

T. Ackemann, E. Kriege, W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapour,” Opt. Commun. 155, 339–346 (1995).
[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman “Helical-wavefront laser beam produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

J. Masajada, “Synthetics holograms for optical vortices generation—image evaluation,” Optik 110, 554–558 (1999).

Phys. Rev. Lett.

A. V. Mamaev, M. Saffman, A. A. Zazulya, “Propagation of dark stripe beams in nonlinear media; snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef] [PubMed]

Proc. R. Soc. London Ser. A

J. F. Nye, M. V. Berry, “Dislocation in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Other

M. Vasnetsov, K. Staliunas, Optical Vortices (Nova Science, 1999).

L. Allen, M. J. Padgett, M. Babiker, “The orbital angular momentum of light,” Progress in Optics, Vol. XXXIX, E. Wolf, ed. (Elsevier, 1999), Chap. IV.

D. Malacara, M. Servín, Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998).

Ch. Brosseau, Fundamentals of Polarized Light: A Statistical Optics Approach (Wiley-Interscience, 1998), pp. 332–333.

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 (5)

Fig. 1
Fig. 1

Scheme of the interferometer setup and orientation of coordinate axes: P, polarizer; WP, Wollaston prism; A, analyzer; F, transmission filter; BS1, BS2, BS3, BS4, four beam splitters.

Fig. 2
Fig. 2

Results of numerical analysis: intensity (gray levels) and phase distributions (curves) in the interference image for different values of intensity coefficient I: (a) I = 0.25 ; (b) I = 0.5 ; (c) I = 0.75 ; (d) I = 1 (see detailed description in text).

Fig. 3
Fig. 3

Lines of phase distribution in the interference image for the intensity coefficient I = 0.5 around the optical vortex (enlarged); numbers denote phases in degrees.

Fig. 4
Fig. 4

Scheme of the experimental setup: P, polarizer; WP, Wollaston prism; A, analyzer; BS1, BS2, BS3, BS4, four beam splitters; P r 1 , P o 1 , polarizers used to change the intensities of the light in reference and object arms, respectively; P r 2 , P o 2 , polarizers used to obtain the s- or p-polarization states on beam splitters; C, CCD camera connected to the computer; M, additional mirror to obtain the forks (angles and distances between the elements are not preserved).

Fig. 5
Fig. 5

(left) Intensity distributions in the interference image for two different relative intensities I of the reference and object waves; the circles mark the points in which the minimum intensities have been founded; (right) same after adding an additional plane wave: (a) I nearly equals the ideal value of 0.5; characteristic forklike fringes in the right figure; (b) I too far from the ideal value of 0.5; no forks.

Equations (23)

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

a A o A r .
E r ln = A r [ 1 0 ] .
J WP = 1 2 [ 1 + e i δ r 1 e i δ r 1 e i δ r 1 + e i δ r ] .
E r Out = 1 2 [ 1 + e i δ r 1 e i δ r 1 e i δ r 1 + e i δ r ] A r [ 1 0 ] = 1 2 A r [ 1 + e i δ r 1 e i δ r ] .
E r Out = A r e i δ r / 2 [ cos   δ r 2 sin   δ r 2 e i π / 2 ] .
E o Out = A o [ e i δ o 0 ] ,
J A = [ 1 0 0 0 ] .
E Out = J A ( E r Out + E o Out ) ,
E Out = 1 2 A r [ 1 + e i δ r + 2 a e i δ o 0 ] .
I Out = E Out E Out * = 0 ,
Re ( E Out ) = 0 ,
Im ( E Out ) = 0 ,
1 + cos   δ r + 2 a   cos   δ o = 0 ,
sin   δ r + 2 a   sin   δ o = 0.
cos   δ o = a , cos   δ r 2 = a , cos   δ o = a , cos   δ r 2 = + a .
δ o a = 1 1 a 2 .
δ o I = δ o a a I = 1 1 I 1 2 1 I = 1 2 I ( 1 I ) ,
Δ δ o = δ o I Δ I = 1 2 I ( 1 I ) Δ I ,
Δ δ o ,min = 0.25 Δ I .
Δ δ r = δ r I Δ I = 1 I ( 1 I ) Δ I ,
Δ δ r ,min = 0.5 Δ I .
( Δ I = 1 % Δ I = 0.01 ) { Δ δ r ,min = 0.3 λ 1000 Δ δ o ,min = 0.15 λ 2000 .
E x ,Out 1 + e i δ r + 2 a e i δ o .

Metrics