Abstract

What we believe to be a new arrangement of an optical vortex interferometer (OVI) is presented. In the proposed configuration the optical vortex lattice is generated in a one-wave setup by use of birefringent elements—Wollaston compensators. The obtained vortex lattice is regular and stable, which is necessary for predicted applications. The new OVI configuration allows the measurement of waves and optical media properties.

© 2007 Optical Society of America

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References

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  1. J. F. Nye and M. V. Berry, "Dislocation in wave trains," Proc. R. Soc. London Ser. A 336, 165-190 (1974).
    [CrossRef]
  2. M. Vasnetsov and K. Staliunas, Optical Vortices (Nova Science, 1999).
  3. G. Foo, D. M. Palacios, and G. A. Swartzlander, Jr., "Optical vortex coronagraph," Opt. Lett. 30, 3308-3310 (2005).
    [CrossRef]
  4. J. Masajada, A. Popiolek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207, 85-93 (2002).
    [CrossRef]
  5. A. Popiolek-Masajada and M. Borwinska, "High-sensitivity wave tilt measurements with optical vortex interferometer," in Proc. SPIE 6189, 6189071-6189077 (2006).
  6. J. Masajada, A. Popiolek-Masajada, E. Frączek, and W. Frączek, "Vortex points localization problem in optical vortices interferometer," Opt. Commun. 234, 23-28 (2004).
    [CrossRef]
  7. J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
    [CrossRef]
  8. K. W. Nicholls and J. F. Nye, "Three-beam model for studying dislocations in wave pulses," J. Phys. A: Math. Gen. 20, 4673-4696 (1987).
    [CrossRef]
  9. K. O'Holleran, M. Padgett, and M. Denis, "Topology of optical vortex lines formed by the interference of three, four, and five plane waves," Opt. Express 14, 3039-3044 (2006).
    [CrossRef] [PubMed]
  10. P. Kurzynowski, W. A. Wozniak, and E. Frączek, "Optical vortices generation using Wollaston prism," Appl. Opt. 45, 7898-7903 (2006).
    [CrossRef] [PubMed]

2006

2005

2004

J. Masajada, A. Popiolek-Masajada, E. Frączek, and W. Frączek, "Vortex points localization problem in optical vortices interferometer," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

2002

J. Masajada, A. Popiolek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207, 85-93 (2002).
[CrossRef]

2001

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[CrossRef]

1987

K. W. Nicholls and J. F. Nye, "Three-beam model for studying dislocations in wave pulses," J. Phys. A: Math. Gen. 20, 4673-4696 (1987).
[CrossRef]

1974

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

Berry, M. V.

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

Borwinska, M.

A. Popiolek-Masajada and M. Borwinska, "High-sensitivity wave tilt measurements with optical vortex interferometer," in Proc. SPIE 6189, 6189071-6189077 (2006).

Denis, M.

Dubik, B.

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[CrossRef]

Foo, G.

Fraczek, E.

P. Kurzynowski, W. A. Wozniak, and E. Frączek, "Optical vortices generation using Wollaston prism," Appl. Opt. 45, 7898-7903 (2006).
[CrossRef] [PubMed]

J. Masajada, A. Popiolek-Masajada, E. Frączek, and W. Frączek, "Vortex points localization problem in optical vortices interferometer," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

Fraczek, W.

J. Masajada, A. Popiolek-Masajada, E. Frączek, and W. Frączek, "Vortex points localization problem in optical vortices interferometer," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

Kurzynowski, P.

Masajada, J.

J. Masajada, A. Popiolek-Masajada, E. Frączek, and W. Frączek, "Vortex points localization problem in optical vortices interferometer," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

J. Masajada, A. Popiolek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207, 85-93 (2002).
[CrossRef]

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[CrossRef]

Nicholls, K. W.

K. W. Nicholls and J. F. Nye, "Three-beam model for studying dislocations in wave pulses," J. Phys. A: Math. Gen. 20, 4673-4696 (1987).
[CrossRef]

Nye, J. F.

K. W. Nicholls and J. F. Nye, "Three-beam model for studying dislocations in wave pulses," J. Phys. A: Math. Gen. 20, 4673-4696 (1987).
[CrossRef]

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

O'Holleran, K.

Padgett, M.

Palacios, D. M.

Popiolek-Masajada, A.

A. Popiolek-Masajada and M. Borwinska, "High-sensitivity wave tilt measurements with optical vortex interferometer," in Proc. SPIE 6189, 6189071-6189077 (2006).

J. Masajada, A. Popiolek-Masajada, E. Frączek, and W. Frączek, "Vortex points localization problem in optical vortices interferometer," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

J. Masajada, A. Popiolek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207, 85-93 (2002).
[CrossRef]

Staliunas, K.

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

Swartzlander, G. A.

Vasnetsov, M.

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

Wieliczka, D.

J. Masajada, A. Popiolek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207, 85-93 (2002).
[CrossRef]

Wozniak, W. A.

Appl. Opt.

J. Phys. A: Math. Gen.

K. W. Nicholls and J. F. Nye, "Three-beam model for studying dislocations in wave pulses," J. Phys. A: Math. Gen. 20, 4673-4696 (1987).
[CrossRef]

Opt. Commun.

J. Masajada, A. Popiolek-Masajada, E. Frączek, and W. Frączek, "Vortex points localization problem in optical vortices interferometer," Opt. Commun. 234, 23-28 (2004).
[CrossRef]

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21-27 (2001).
[CrossRef]

J. Masajada, A. Popiolek-Masajada, and D. Wieliczka, "The interferometric system using optical vortices as phase markers," Opt. Commun. 207, 85-93 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. R. Soc. London Ser. A

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

Other

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

A. Popiolek-Masajada and M. Borwinska, "High-sensitivity wave tilt measurements with optical vortex interferometer," in Proc. SPIE 6189, 6189071-6189077 (2006).

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Figures (5)

Fig. 1
Fig. 1

Interferometer setup: P1, P2, polarizers; M1, M2, mirrors; W1, W2, Wollaston compensators; BS1, BS2, beam splitters; A, analyzer; CCD, camera. (I) Object arm of the interferometer; (II) reference arm.

Fig. 2
Fig. 2

Wollaston compensator setup: the z axis is a wave propagation axis; the δ axis is a main Wollaston axis; arrows indicate the optical axis orientation in the wedges. Lines with constant phase difference introduced by the Wollaston compensator have been marked. For the first Wollaston compensator the angle between the δ axis and the x axis of the Cartesian system is equal to 45°, whereas the second angle is 0°.

Fig. 3
Fig. 3

Main axis orientations of the Wollaston compensators W1 and W2 with regard to the observation Cartesian coordinate (x, y) system.

Fig. 4
Fig. 4

(a), (c) Intensity I and (b), (d) phase Ψ distributions for the exemplary numerically, generated interferograms. (a) and (b) refer to γ 1 / γ 2 = 1 , whereas (c) and (d) refer to γ 1 / γ 2 = 2 . Points that are optical vortices are marked.

Fig. 5
Fig. 5

Experimental interferograms recorded on a CCD camera (a), (c) without the reference beam and (b), (d) with the reference beam added. (a) and (b) refer to γ 1 / γ 2 = 1 , whereas (c) and (d) refer to γ 1 / γ 2 = 2 . Spatial data for the presented cases have been denoted.

Equations (16)

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E o u t [ 1 1 1 1 ] [ 1 0 0 e i δ 2 ] [ 1 + e i δ 1 * 1 e i δ 1 * ] [ 1 0 ] ,
[ 1 0 ]
[ 1 + e i δ 1 * 1 e i δ 1 * ]
[ 1 0 0 e i δ 2 ]
[ 1 1 1 1 ]
E o u t ( δ 1 , δ 2 ) ( 1 + e i δ 1 + e i δ 2 e i δ 1 e i δ 2 ) [ 1 1 ] ,
I o u t ( δ 1 , δ 2 ) = ( E x E x * + E y E y * ) 1 + sin δ 1 sin δ 2 ,
sin δ 1 sin δ 2 = 1 ,
I o u t ( δ 1 , δ 2 ) 1 + sin ( δ 1 + φ 1 ) sin ( δ 2 + φ 2 ) ,
tan φ 1 = tan Δ sin 2 α ,
tan φ 2 = tan Δ cos 2 α ,
tan 2 Δ = tan 2 φ 1 + tan 2 φ 2 ,
tan 2 α = tan φ 1 tan φ 2 .
α = ± 45 ° I 1 + sin δ 2 sin ( δ 1 ± Δ ) ,
α = 0 ° I 1 + sin δ 1 sin ( δ 2 + Δ ) ,
α = 90 ° I 1 + sin δ 1 sin ( δ 2 Δ ) .

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