Abstract

We report on the interesting effect observed with the diffractive binary element, which matches the property of an axicon and vortex lens. Binary phase coding simplifies the manufacturing process and gives additional advantages for metrology purposes. Under laser beam illumination, our element produces two waves: converging and diverging. Both waves carry a single optical vortex. We show that this special diffractive element can be used to set up a simple surface profilometer.

© 2013 Optical Society of America

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References

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2013

J. Masajada, A. Popiolek-Masajada, and I. Augustyniak, Proc. SPIE 8550, 85503B (2013).

A. Popiolek-Masajada, M. Borwinska, T. Przerwa-Tetmajer, and P. Kurzynowski, Opt. Laser Technol. 48, 503 (2013).
[CrossRef]

2009

2008

2006

2001

1993

1992

J. Sochacki, A. Kolodziejczyk, Z. Jaroszewicz, and S. Bara, Appl. Opt. 31, 5326 (1992).
[CrossRef]

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

1982

1954

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics, E. Wolf, ed. (Elsevier, 1999), Vol. 39, Chap. IV, pp. 291–372.

Augustyniak, I.

J. Masajada, A. Popiolek-Masajada, and I. Augustyniak, Proc. SPIE 8550, 85503B (2013).

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics, E. Wolf, ed. (Elsevier, 1999), Vol. 39, Chap. IV, pp. 291–372.

Bara, S.

Borwinska, M.

A. Popiolek-Masajada, M. Borwinska, T. Przerwa-Tetmajer, and P. Kurzynowski, Opt. Laser Technol. 48, 503 (2013).
[CrossRef]

Drobczynski, S.

Gomez, V.

Ina, H.

Jankowska, E.

Jaroszewicz, Z.

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Kobayashi, S.

Kolodziejczyk, A.

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Kress, B.

Kurzynowski, P.

A. Popiolek-Masajada, M. Borwinska, T. Przerwa-Tetmajer, and P. Kurzynowski, Opt. Laser Technol. 48, 503 (2013).
[CrossRef]

Leniec, M.

Masajada, J.

McLeod, J. H.

Ottevaere, H.

Padgett, M. J.

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics, E. Wolf, ed. (Elsevier, 1999), Vol. 39, Chap. IV, pp. 291–372.

Popiolek-Masajada, A.

J. Masajada, A. Popiolek-Masajada, and I. Augustyniak, Proc. SPIE 8550, 85503B (2013).

A. Popiolek-Masajada, M. Borwinska, T. Przerwa-Tetmajer, and P. Kurzynowski, Opt. Laser Technol. 48, 503 (2013).
[CrossRef]

Przerwa-Tetmajer, T.

A. Popiolek-Masajada, M. Borwinska, T. Przerwa-Tetmajer, and P. Kurzynowski, Opt. Laser Technol. 48, 503 (2013).
[CrossRef]

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Sochacki, J.

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Staronski, L. R.

Swartzlander, G. A.

Takeda, M.

Thienpont, H.

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

Appl. Opt.

J. Mod. Opt.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, J. Mod. Opt. 39, 1147 (1992).
[CrossRef]

J. Opt. Soc. Am.

Opt. Express

Opt. Laser Technol.

A. Popiolek-Masajada, M. Borwinska, T. Przerwa-Tetmajer, and P. Kurzynowski, Opt. Laser Technol. 48, 503 (2013).
[CrossRef]

Opt. Lett.

Proc. SPIE

J. Masajada, A. Popiolek-Masajada, and I. Augustyniak, Proc. SPIE 8550, 85503B (2013).

Other

L. Allen, M. J. Padgett, and M. Babiker, Progress in Optics, E. Wolf, ed. (Elsevier, 1999), Vol. 39, Chap. IV, pp. 291–372.

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Figures (12)

Fig. 1.
Fig. 1.

When illuminated by Gaussian beam, the AV element produces a diverging and a converging beam. Both beams carry the optical vortex.

Fig. 2.
Fig. 2.

Measurements of the AV element of m=1. (a) A photograph of the central part of the plate seen with an optical microscope. (b) An AFM scan of a fragment of the structure (the center of the scanned fragment is located approximately 3.14 mm from the center of the element). (c) A profile of the scanned fragment.

Fig. 3.
Fig. 3.

AV element manufactured as kinoform will generate only the converging beam. Figure shows the numerical simulations; z denotes the distance between the element and the observation plane.

Fig. 4.
Fig. 4.

Binary AV element for m=1 will produce converging and diverging beams. This effect is easily visible in the area where both beams have a comparable radius of curvature, i.e., close (z=20mm) and far from the AV element (z=80mm). At z=20mm and z=80mm, the amplitude and phase distribution reveals characteristic features for the overlapping vortex beams. Figure shows the numerical simulations.

Fig. 5.
Fig. 5.

Binary AV element for m=2 works in a similar way as the element shown in Fig. 4. However, now we can see characteristic features for the overlapping vortex beams having double topological charge (for z=20 and z=80mm).

Fig. 6.
Fig. 6.

Binary AV element of charge m=1. The experimental results reveal the same features as the numerical simulations (Fig. 4).

Fig. 7.
Fig. 7.

Binary AV element of charge m=2. The experimental results reveal the same features as the numerical simulations (Fig. 5).

Fig. 8.
Fig. 8.

Measurement system is based on the Mach–Zehnder interferometer scheme.

Fig. 9.
Fig. 9.

Phase distribution and interferograms measured while scanning through the phase step, which introduces a phase shift of 3π. (a) The beam center is positioned 5μm from the step. (b) The beam center is positioned at the step. (c) The beam center is positioned 5 μm from the step. There are characteristic fork-like fringes indicating the presence of optical vortices in the interferograms (a) and (c). These fork-like fringes disappear in the interferogram (b).

Fig. 10.
Fig. 10.

Phase distributions at the plane positioned 50 mm behind the focal plane of the FV element, where the phase step was introduced. The Δ parameter denotes the distance between the phase-step and z axis. The h parameter denotes the phase difference introduced by the step.

Fig. 11.
Fig. 11.

Phase maps measured while scanning the damaged optical wedge. The wedge was shifted by 2 μm for each next measurement. The scanning beam center lies at the area of the valley. It is well seen that vortices come apart while scanning the wedge.

Fig. 12.
Fig. 12.

Phase distributions at the plane positioned 50 mm after the focal plane of the FV element, where the phase valley was introduced. The Δ parameter denotes the distance between the center of the valley and z axis.

Equations (3)

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φ(r)=2πλ·r2·(f22f12)/R2+f12(f22f12)/R2.
φ(θ)=imθ.
φ(r)=348611mm2·r2+7941mm·r4,485

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