Abstract

A pair of axicons with an adjustable separation between them is used to generate a variable diameter ring beam with high efficiency. This beam illuminates a lens to produce quasi-diffraction-free beams with a tunable spot size and depth of field. We studied the generated beam characteristics while changing either the ring diameter or its thickness. Such a scheme has applications in adjustable imaging, including nondiffracting beam microscopy, material processing with an irradiance above a certain threshold value, and particle trapping/manipulation.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (1)

L. Begel and T. Galstian, “Dynamic tuning of non-diffracting beams by using an electrically variable liquid crystal lens,” Opt. Commun. 441, 127–131 (2019).
[Crossref]

2018 (3)

2016 (1)

2015 (3)

V. Wang, W. Qu, L. Jian, and Y. Zhang, “Generation and control of Bessel beams based on annular reflection,” Appl. Phys. B 119, 241–245 (2015).
[Crossref]

S. K. Tiwari, S. P. Ram, K. H. Rao, S. R. Mishra, and H. S. Rawat, “Generation and focusing of a collimated hollow beam,” Opt. Eng. 54, 115111 (2015).
[Crossref]

U. Fuchs and S. Wickenhagen, “Modular optical design for flexible beam expansion,” Proc. SPIE 9580, 958007 (2015).
[Crossref]

2013 (3)

2012 (2)

2011 (1)

2010 (1)

B. Chebbi, S. Minko, N. Al-Akwaa, and I. Golub, “Remote control of extended depth of field focusing,” Opt. Commun. 283, 1678–1683 (2010).
[Crossref]

2009 (1)

S. Akturk, C. L. Arnold, B. Prade, and A. Mysyrowicz, “Generation of high quality tunable Bessel beams using a liquid-immersion axicon,” Opt. Commun. 282, 3206–3209 (2009).
[Crossref]

2008 (1)

G. Milne, G. D. M. Jeffries, and D. T. Chu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101 (2008).
[Crossref]

2007 (1)

2006 (1)

I. Golub, “Fresnel axicon,” Opt. Lett. 31, 890–892 (2006).
[Crossref]

2003 (1)

V. Vaičaitis and S. Paulkas, “Formation of Bessel beams with continuously variable cone angle,” Opt. Quantum Electron. 35, 1065–1071 (2003).
[Crossref]

2001 (1)

1995 (1)

1992 (1)

1990 (1)

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Akturk, S.

S. Akturk, C. L. Arnold, B. Prade, and A. Mysyrowicz, “Generation of high quality tunable Bessel beams using a liquid-immersion axicon,” Opt. Commun. 282, 3206–3209 (2009).
[Crossref]

Al-Akwaa, N.

B. Chebbi, S. Minko, N. Al-Akwaa, and I. Golub, “Remote control of extended depth of field focusing,” Opt. Commun. 283, 1678–1683 (2010).
[Crossref]

Arnold, C. L.

S. Akturk, C. L. Arnold, B. Prade, and A. Mysyrowicz, “Generation of high quality tunable Bessel beams using a liquid-immersion axicon,” Opt. Commun. 282, 3206–3209 (2009).
[Crossref]

Begel, L.

L. Begel and T. Galstian, “Dynamic tuning of non-diffracting beams by using an electrically variable liquid crystal lens,” Opt. Commun. 441, 127–131 (2019).
[Crossref]

Billet, C.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).

Boucher, P.

Brinkmann, F.

Brown, D. L.

Chebbi, B.

K. Gourley, I. Golub, and B. Chebbi, “Demonstration of a Fresnel axicon,” Appl. Opt. 50, 303–306 (2011).
[Crossref]

B. Chebbi, S. Minko, N. Al-Akwaa, and I. Golub, “Remote control of extended depth of field focusing,” Opt. Commun. 283, 1678–1683 (2010).
[Crossref]

Chu, D. T.

G. Milne, G. D. M. Jeffries, and D. T. Chu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101 (2008).
[Crossref]

Courvoisier, F.

De Koninck, Y.

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Eberly, J. H.

Fuchs, U.

U. Fuchs and S. Wickenhagen, “Modular optical design for flexible beam expansion,” Proc. SPIE 9580, 958007 (2015).
[Crossref]

S. Kiontke and U. Fuchs, “Arrangement of optical elements for focusing approximately collimated beams,” U.S. patent9625623 (April18, 2017).

Galstian, T.

L. Begel and T. Galstian, “Dynamic tuning of non-diffracting beams by using an electrically variable liquid crystal lens,” Opt. Commun. 441, 127–131 (2019).
[Crossref]

Golub, I.

Gong, L.

Gourley, K.

Grulkowski, I.

Herminghaus, S.

Hoyo, J. D.

Huang, H.

Jeffries, G. D. M.

G. Milne, G. D. M. Jeffries, and D. T. Chu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101 (2008).
[Crossref]

Ji, N.

Jian, L.

V. Wang, W. Qu, L. Jian, and Y. Zhang, “Generation and control of Bessel beams based on annular reflection,” Appl. Phys. B 119, 241–245 (2015).
[Crossref]

Khalil, D.

Khonina, S. N.

Kiontke, S.

S. Kiontke and U. Fuchs, “Arrangement of optical elements for focusing approximately collimated beams,” U.S. patent9625623 (April18, 2017).

Klewitz, S.

Koyama, M.

Labroille, G.

Leiderer, P.

Li, Y.

Y. Li, Q. Yu, Z. Yang, and J. Ma, “Tunable Bessel and annular beams generated by a unimorph deformable mirror,” Opt. Eng. 57, 106107 (2018).
[Crossref]

Li, Y. M.

Lin, Y.

Lu, R.

Ma, J.

Y. Li, Q. Yu, Z. Yang, and J. Ma, “Tunable Bessel and annular beams generated by a unimorph deformable mirror,” Opt. Eng. 57, 106107 (2018).
[Crossref]

Mahmoud, M. A.

McCarthy, N.

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Milne, G.

G. Milne, G. D. M. Jeffries, and D. T. Chu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101 (2008).
[Crossref]

Minko, S.

B. Chebbi, S. Minko, N. Al-Akwaa, and I. Golub, “Remote control of extended depth of field focusing,” Opt. Commun. 283, 1678–1683 (2010).
[Crossref]

Mishra, S. R.

S. K. Tiwari, S. P. Ram, K. H. Rao, S. R. Mishra, and H. S. Rawat, “Generation and focusing of a collimated hollow beam,” Opt. Eng. 54, 115111 (2015).
[Crossref]

S. K. Tiwari, S. R. Mishra, S. P. Ram, and H. S. Rawat, “Generation of a Bessel beam of variable spot size,” Appl. Opt. 51, 3718–3725 (2012).
[Crossref]

Mysyrowicz, A.

S. Akturk, C. L. Arnold, B. Prade, and A. Mysyrowicz, “Generation of high quality tunable Bessel beams using a liquid-immersion axicon,” Opt. Commun. 282, 3206–3209 (2009).
[Crossref]

Paulkas, S.

V. Vaičaitis and S. Paulkas, “Formation of Bessel beams with continuously variable cone angle,” Opt. Quantum Electron. 35, 1065–1071 (2003).
[Crossref]

Pinel, O.

Prade, B.

S. Akturk, C. L. Arnold, B. Prade, and A. Mysyrowicz, “Generation of high quality tunable Bessel beams using a liquid-immersion axicon,” Opt. Commun. 282, 3206–3209 (2009).
[Crossref]

Qu, W.

V. Wang, W. Qu, L. Jian, and Y. Zhang, “Generation and control of Bessel beams based on annular reflection,” Appl. Phys. B 119, 241–245 (2015).
[Crossref]

Ram, S. P.

S. K. Tiwari, S. P. Ram, K. H. Rao, S. R. Mishra, and H. S. Rawat, “Generation and focusing of a collimated hollow beam,” Opt. Eng. 54, 115111 (2015).
[Crossref]

S. K. Tiwari, S. R. Mishra, S. P. Ram, and H. S. Rawat, “Generation of a Bessel beam of variable spot size,” Appl. Opt. 51, 3718–3725 (2012).
[Crossref]

Rao, K. H.

S. K. Tiwari, S. P. Ram, K. H. Rao, S. R. Mishra, and H. S. Rawat, “Generation and focusing of a collimated hollow beam,” Opt. Eng. 54, 115111 (2015).
[Crossref]

Rawat, H. S.

S. K. Tiwari, S. P. Ram, K. H. Rao, S. R. Mishra, and H. S. Rawat, “Generation and focusing of a collimated hollow beam,” Opt. Eng. 54, 115111 (2015).
[Crossref]

S. K. Tiwari, S. R. Mishra, S. P. Ram, and H. S. Rawat, “Generation of a Bessel beam of variable spot size,” Appl. Opt. 51, 3718–3725 (2012).
[Crossref]

Ren, Y. X.

Savaryn, V.

Seka, W.

Shalaby, M. Y.

Szulzycki, K.

Taguchi, M.

Tanaka, K.

Tanaka, T.

Tanimoto, M.

Theriault, G.

Tiwari, S. K.

S. K. Tiwari, S. P. Ram, K. H. Rao, S. R. Mishra, and H. S. Rawat, “Generation and focusing of a collimated hollow beam,” Opt. Eng. 54, 115111 (2015).
[Crossref]

S. K. Tiwari, S. R. Mishra, S. P. Ram, and H. S. Rawat, “Generation of a Bessel beam of variable spot size,” Appl. Opt. 51, 3718–3725 (2012).
[Crossref]

Tremblay, R.

Vaicaitis, V.

V. Vaičaitis and S. Paulkas, “Formation of Bessel beams with continuously variable cone angle,” Opt. Quantum Electron. 35, 1065–1071 (2003).
[Crossref]

Wang, Q. C.

Wang, V.

V. Wang, W. Qu, L. Jian, and Y. Zhang, “Generation and control of Bessel beams based on annular reflection,” Appl. Phys. B 119, 241–245 (2015).
[Crossref]

Wang, Z. Q.

Wickenhagen, S.

U. Fuchs and S. Wickenhagen, “Modular optical design for flexible beam expansion,” Proc. SPIE 9580, 958007 (2015).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).

Xue, G. S.

Yang, Z.

Y. Li, Q. Yu, Z. Yang, and J. Ma, “Tunable Bessel and annular beams generated by a unimorph deformable mirror,” Opt. Eng. 57, 106107 (2018).
[Crossref]

Yu, Q.

Y. Li, Q. Yu, Z. Yang, and J. Ma, “Tunable Bessel and annular beams generated by a unimorph deformable mirror,” Opt. Eng. 57, 106107 (2018).
[Crossref]

Zhang, Y.

V. Wang, W. Qu, L. Jian, and Y. Zhang, “Generation and control of Bessel beams based on annular reflection,” Appl. Phys. B 119, 241–245 (2015).
[Crossref]

Zhong, M. C.

Zhou, J. H.

Appl. Opt. (7)

Appl. Phys. B (1)

V. Wang, W. Qu, L. Jian, and Y. Zhang, “Generation and control of Bessel beams based on annular reflection,” Appl. Phys. B 119, 241–245 (2015).
[Crossref]

Appl. Phys. Lett. (1)

G. Milne, G. D. M. Jeffries, and D. T. Chu, “Tunable generation of Bessel beams with a fluidic axicon,” Appl. Phys. Lett. 92, 261101 (2008).
[Crossref]

Biomed. Opt. Express (1)

J. Opt. Soc. Am. A (2)

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

Opt. Commun. (3)

S. Akturk, C. L. Arnold, B. Prade, and A. Mysyrowicz, “Generation of high quality tunable Bessel beams using a liquid-immersion axicon,” Opt. Commun. 282, 3206–3209 (2009).
[Crossref]

L. Begel and T. Galstian, “Dynamic tuning of non-diffracting beams by using an electrically variable liquid crystal lens,” Opt. Commun. 441, 127–131 (2019).
[Crossref]

B. Chebbi, S. Minko, N. Al-Akwaa, and I. Golub, “Remote control of extended depth of field focusing,” Opt. Commun. 283, 1678–1683 (2010).
[Crossref]

Opt. Eng. (2)

Y. Li, Q. Yu, Z. Yang, and J. Ma, “Tunable Bessel and annular beams generated by a unimorph deformable mirror,” Opt. Eng. 57, 106107 (2018).
[Crossref]

S. K. Tiwari, S. P. Ram, K. H. Rao, S. R. Mishra, and H. S. Rawat, “Generation and focusing of a collimated hollow beam,” Opt. Eng. 54, 115111 (2015).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

V. Vaičaitis and S. Paulkas, “Formation of Bessel beams with continuously variable cone angle,” Opt. Quantum Electron. 35, 1065–1071 (2003).
[Crossref]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[Crossref]

Proc. SPIE (1)

U. Fuchs and S. Wickenhagen, “Modular optical design for flexible beam expansion,” Proc. SPIE 9580, 958007 (2015).
[Crossref]

Other (2)

S. Kiontke and U. Fuchs, “Arrangement of optical elements for focusing approximately collimated beams,” U.S. patent9625623 (April18, 2017).

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975).

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Figures (12)

Fig. 1.
Fig. 1. Experimental setup block diagram for tunable diameter ring beam generation and its focusing. The optional insert with a beam expander and an aperture is used in the second part of the experiments.
Fig. 2.
Fig. 2. Focused beam with a 10 µm scale for calibration.
Fig. 3.
Fig. 3. FWHM of the focal spot versus distance between the axicons. The solid line is plotted using Eq. (3).
Fig. 4.
Fig. 4. Transverse intensity profile of the generated focal spot for a 1 mm aperture.
Fig. 5.
Fig. 5. Peak intensity of the focused beam and FWHM of its spot size versus distance from the lens focus for a 1 mm aperture. The continuous line is a numerical simulation of longitudinal intensity distribution.
Fig. 6.
Fig. 6. Transverse intensity profile of the generated focal spot for a 3 mm aperture.
Fig. 7.
Fig. 7. Peak intensity of the focused beam and FWHM of its spot size versus distance from the lens focus for a 3 mm aperture. The continuous line is numerical simulation of longitudinal intensity distribution.
Fig. 8.
Fig. 8. Transverse intensity profile of the generated focal spot for an open aperture.
Fig. 9.
Fig. 9. Peak intensity of the focused beam and FWHM of its spot size versus distance from the lens focus for a fully open aperture. The continuous line is numerical simulation of longitudinal intensity distribution.
Fig. 10.
Fig. 10. Transverse intensity profile of a lens-only generated focal spot.
Fig. 11.
Fig. 11. Peak intensity of the focused beam and FWHM of its spot size versus distance from the lens focus for a case with a lens only.
Fig. 12.
Fig. 12. Transverse intensity profiles of the beam at different positions along the optical axis ${z}$ for a 1 mm aperture case. (a) ${z} = {650}\;\unicode{x00B5}{\rm m}$, (b) ${ z} = {400}\;\unicode{x00B5}{\rm m}$, (c) ${z} = {0}$, (d) ${z} = - {400}\;\unicode{x00B5}{\rm m}$, and (e) ${z} = - {650}\;\unicode{x00B5}{\rm m}$.

Equations (4)

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

| E 0 ( ρ ) | 2 | 0 R J 0 ( k r ρ f ) r d r | 2 f 2 R 2 k 2 ρ 2 J 1 2 ( k ρ R f ) .
| E 0 ( ρ ) | 2 | R δ R J 0 ( k r ρ f ) r d r | 2 R 2 δ 2 J 0 2 ( k ρ R f ) .
F W H M = 0.36 N A λ .
D O F = 2.8 f 2 ( R a v k Δ R ) ,