Abstract

We report on an experimental characterization of Bessel beams with finite apertures. We show that real Bessel beams can be generated with intensity profiles that closely resemble the ideal Jo2 transverse-intensity distribution of Bessel beams. We also show interferometrically that these beams have planar phase fronts with π-phase shifts from one Bessel ring to the next. We report tolerance conditions for Bessel beam generation and give an example of this generation that uses an unstable resonator as the light source.

© 1992 Optical Society of America

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  1. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  2. J. Durnin, J. J. Miceli, J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13, 79–80 (1988).
    [CrossRef] [PubMed]
  3. P. Sprangle, B. Hafizi, “Critique of nondiffracting beams,” Phys. Rev. Lett. 66, 837 (1991).
    [CrossRef] [PubMed]
  4. J. Dun-in, J. J. Miceli, J. H. Eberly, “Reply to comment by Sprangle and Hafizi,” Phys. Rev. Lett. 66, 838 (1991).
  5. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  6. J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3962 (1988).
    [CrossRef] [PubMed]
  7. G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6, 150–152 (1989).
    [CrossRef]
  8. F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987); L. Vicari, “Truncation of nondiffracting beams,” Opt. Commun. 70, 263–266 (1989); M. Zahid, M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70, 361–364 (1989); É. A. Iolynkina, E. A. Lbragimov, T. Usmanov, “Diffraction convergence of freely propagating beams,” Sov. J. Quantum Electron. 18, 1509–1510 (1988).
    [CrossRef]
  9. K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125 (1989).
    [CrossRef]
  10. K. Thewes, M. A. Karim, A. A. S. Awwal, “Refractive solutions for a diffraction-free beam,” in 1990 Annual Meeting Digest, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper ThRR4; “Diffraction-free beam generation using refracting systems,” Opt. Laser Technol. 23, 105 (1991).
  11. D. R. MacQuigg, “Film calibration method for the analysis of laser light energy distribution,” Appl. Opt. 16, 2028 (1977).
    [CrossRef] [PubMed]
  12. A similar technique was used by S. Skupsky, T. Kessler, “A source of hot spots in frequency-tripled laser light,” Opt. Commun. 70, 123 (1989).
    [CrossRef]
  13. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Chap. 9, p. 463. One of the reviewers drew our attention to this.
  14. Laboratory for Laser Energetics, “High-power laser interferometry,” in 1987 Annual Report, Rep. DOE/DP/40200-64 (University of Rochester, Rochester, N.Y., 1987), pp. 114–123.
  15. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), p. 901.
  16. D. Y. Park, W. Seka, Y. Lin, D. L. Brown, “Operational characteristics of an imaging, unstable ring resonator using Nd:YLF as active medium,” in Proceedings of the International Conference on LASERS ’89, D. G. Harris, T. M. Shay, eds. (STS, McLean, Va., 1990), pp. 449–456.

1991

P. Sprangle, B. Hafizi, “Critique of nondiffracting beams,” Phys. Rev. Lett. 66, 837 (1991).
[CrossRef] [PubMed]

J. Dun-in, J. J. Miceli, J. H. Eberly, “Reply to comment by Sprangle and Hafizi,” Phys. Rev. Lett. 66, 838 (1991).

1989

G. Indebetouw, “Nondiffracting optical fields: some remarks on their analysis and synthesis,” J. Opt. Soc. Am. A 6, 150–152 (1989).
[CrossRef]

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125 (1989).
[CrossRef]

A similar technique was used by S. Skupsky, T. Kessler, “A source of hot spots in frequency-tripled laser light,” Opt. Commun. 70, 123 (1989).
[CrossRef]

1988

1987

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

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

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987); L. Vicari, “Truncation of nondiffracting beams,” Opt. Commun. 70, 263–266 (1989); M. Zahid, M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70, 361–364 (1989); É. A. Iolynkina, E. A. Lbragimov, T. Usmanov, “Diffraction convergence of freely propagating beams,” Sov. J. Quantum Electron. 18, 1509–1510 (1988).
[CrossRef]

1977

Awwal, A. A. S.

K. Thewes, M. A. Karim, A. A. S. Awwal, “Refractive solutions for a diffraction-free beam,” in 1990 Annual Meeting Digest, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper ThRR4; “Diffraction-free beam generation using refracting systems,” Opt. Laser Technol. 23, 105 (1991).

Born, M.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Chap. 9, p. 463. One of the reviewers drew our attention to this.

Brown, D. L.

D. Y. Park, W. Seka, Y. Lin, D. L. Brown, “Operational characteristics of an imaging, unstable ring resonator using Nd:YLF as active medium,” in Proceedings of the International Conference on LASERS ’89, D. G. Harris, T. M. Shay, eds. (STS, McLean, Va., 1990), pp. 449–456.

Dun-in, J.

J. Dun-in, J. J. Miceli, J. H. Eberly, “Reply to comment by Sprangle and Hafizi,” Phys. Rev. Lett. 66, 838 (1991).

Durnin, J.

Eberly, J. H.

J. Dun-in, J. J. Miceli, J. H. Eberly, “Reply to comment by Sprangle and Hafizi,” Phys. Rev. Lett. 66, 838 (1991).

J. Durnin, J. J. Miceli, J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13, 79–80 (1988).
[CrossRef] [PubMed]

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

Friberg, A. T.

Gori, F.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987); L. Vicari, “Truncation of nondiffracting beams,” Opt. Commun. 70, 263–266 (1989); M. Zahid, M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70, 361–364 (1989); É. A. Iolynkina, E. A. Lbragimov, T. Usmanov, “Diffraction convergence of freely propagating beams,” Sov. J. Quantum Electron. 18, 1509–1510 (1988).
[CrossRef]

Guattari, G.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987); L. Vicari, “Truncation of nondiffracting beams,” Opt. Commun. 70, 263–266 (1989); M. Zahid, M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70, 361–364 (1989); É. A. Iolynkina, E. A. Lbragimov, T. Usmanov, “Diffraction convergence of freely propagating beams,” Sov. J. Quantum Electron. 18, 1509–1510 (1988).
[CrossRef]

Hafizi, B.

P. Sprangle, B. Hafizi, “Critique of nondiffracting beams,” Phys. Rev. Lett. 66, 837 (1991).
[CrossRef] [PubMed]

Indebetouw, G.

Karim, M. A.

K. Thewes, M. A. Karim, A. A. S. Awwal, “Refractive solutions for a diffraction-free beam,” in 1990 Annual Meeting Digest, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper ThRR4; “Diffraction-free beam generation using refracting systems,” Opt. Laser Technol. 23, 105 (1991).

Kessler, T.

A similar technique was used by S. Skupsky, T. Kessler, “A source of hot spots in frequency-tripled laser light,” Opt. Commun. 70, 123 (1989).
[CrossRef]

Kikuchi, H.

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125 (1989).
[CrossRef]

Lin, Y.

D. Y. Park, W. Seka, Y. Lin, D. L. Brown, “Operational characteristics of an imaging, unstable ring resonator using Nd:YLF as active medium,” in Proceedings of the International Conference on LASERS ’89, D. G. Harris, T. M. Shay, eds. (STS, McLean, Va., 1990), pp. 449–456.

MacQuigg, D. R.

Miceli, J. J.

J. Dun-in, J. J. Miceli, J. H. Eberly, “Reply to comment by Sprangle and Hafizi,” Phys. Rev. Lett. 66, 838 (1991).

J. Durnin, J. J. Miceli, J. H. Eberly, “Comparison of Bessel and Gaussian beams,” Opt. Lett. 13, 79–80 (1988).
[CrossRef] [PubMed]

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

Padovani, C.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987); L. Vicari, “Truncation of nondiffracting beams,” Opt. Commun. 70, 263–266 (1989); M. Zahid, M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70, 361–364 (1989); É. A. Iolynkina, E. A. Lbragimov, T. Usmanov, “Diffraction convergence of freely propagating beams,” Sov. J. Quantum Electron. 18, 1509–1510 (1988).
[CrossRef]

Park, D. Y.

D. Y. Park, W. Seka, Y. Lin, D. L. Brown, “Operational characteristics of an imaging, unstable ring resonator using Nd:YLF as active medium,” in Proceedings of the International Conference on LASERS ’89, D. G. Harris, T. M. Shay, eds. (STS, McLean, Va., 1990), pp. 449–456.

Seka, W.

D. Y. Park, W. Seka, Y. Lin, D. L. Brown, “Operational characteristics of an imaging, unstable ring resonator using Nd:YLF as active medium,” in Proceedings of the International Conference on LASERS ’89, D. G. Harris, T. M. Shay, eds. (STS, McLean, Va., 1990), pp. 449–456.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), p. 901.

Skupsky, S.

A similar technique was used by S. Skupsky, T. Kessler, “A source of hot spots in frequency-tripled laser light,” Opt. Commun. 70, 123 (1989).
[CrossRef]

Sprangle, P.

P. Sprangle, B. Hafizi, “Critique of nondiffracting beams,” Phys. Rev. Lett. 66, 837 (1991).
[CrossRef] [PubMed]

Thewes, K.

K. Thewes, M. A. Karim, A. A. S. Awwal, “Refractive solutions for a diffraction-free beam,” in 1990 Annual Meeting Digest, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper ThRR4; “Diffraction-free beam generation using refracting systems,” Opt. Laser Technol. 23, 105 (1991).

Turunen, J.

Uehara, K.

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125 (1989).
[CrossRef]

Vasara, A.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Chap. 9, p. 463. One of the reviewers drew our attention to this.

Appl. Opt.

Appl. Phys. B

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125 (1989).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

F. Gori, G. Guattari, C. Padovani, “Bessel–Gauss beams,” Opt. Commun. 64, 491–495 (1987); L. Vicari, “Truncation of nondiffracting beams,” Opt. Commun. 70, 263–266 (1989); M. Zahid, M. S. Zubairy, “Directionality of partially coherent Bessel-Gauss beams,” Opt. Commun. 70, 361–364 (1989); É. A. Iolynkina, E. A. Lbragimov, T. Usmanov, “Diffraction convergence of freely propagating beams,” Sov. J. Quantum Electron. 18, 1509–1510 (1988).
[CrossRef]

A similar technique was used by S. Skupsky, T. Kessler, “A source of hot spots in frequency-tripled laser light,” Opt. Commun. 70, 123 (1989).
[CrossRef]

Opt. Lett.

Phys. Rev. Lett.

P. Sprangle, B. Hafizi, “Critique of nondiffracting beams,” Phys. Rev. Lett. 66, 837 (1991).
[CrossRef] [PubMed]

J. Dun-in, J. J. Miceli, J. H. Eberly, “Reply to comment by Sprangle and Hafizi,” Phys. Rev. Lett. 66, 838 (1991).

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

Other

K. Thewes, M. A. Karim, A. A. S. Awwal, “Refractive solutions for a diffraction-free beam,” in 1990 Annual Meeting Digest, Vol. 15 of OSA 1990 Technical Digest Series (Optical Society of America, Washington, D.C., 1990), paper ThRR4; “Diffraction-free beam generation using refracting systems,” Opt. Laser Technol. 23, 105 (1991).

M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, Oxford, 1970), Chap. 9, p. 463. One of the reviewers drew our attention to this.

Laboratory for Laser Energetics, “High-power laser interferometry,” in 1987 Annual Report, Rep. DOE/DP/40200-64 (University of Rochester, Rochester, N.Y., 1987), pp. 114–123.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986), p. 901.

D. Y. Park, W. Seka, Y. Lin, D. L. Brown, “Operational characteristics of an imaging, unstable ring resonator using Nd:YLF as active medium,” in Proceedings of the International Conference on LASERS ’89, D. G. Harris, T. M. Shay, eds. (STS, McLean, Va., 1990), pp. 449–456.

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Figures (10)

Fig. 1
Fig. 1

Schematic setup for generating Bessel beams after Ref. 1.

Fig. 2
Fig. 2

Typical Bessel beam photograph obtained with a ring aperture of 12.1-mm diameter and 0.1-mm ring width, illuminated by a 1-ns, 1.054-μm, collimated laser pulse from a mode-locker ND:YLF laser. The photograph is taken at 1 m from the 1-m focal length lens (see Fig. 1).

Fig. 3
Fig. 3

Transverse intensity profile of the Bessel beam in Fig. 2 obtained from azimuthally averaging the digitized data Figs. 2 and 3.

Fig. 4
Fig. 4

Intensity distribution of the central Bessel lobe along the direction of propagation for the Bessel beam shown in Fig. 3. The intensity at large distances is determined primarily by the limited extent of the diffraction pattern of the ring mask rather than by the dimension of the lens. Also shown are the predicted intensity distribution based on Fresnel diffraction calculations and the longitudinal intensity distribution for a Gaussian beam of equal FWHM at the lens.

Fig. 5
Fig. 5

Longitudinal intensity distribution of the central Bessel lobe for lens-limited Bessel beams with equal lens and ring diameters (12.1 mm) and ring widths of (a) 25 μm, (b) 50 μm, and (c) 100 μm. The focal length of the lens is f = 1 m at λ = 1 μm.

Fig. 6
Fig. 6

Comparison of theoretical and experimental Bessel ring energies at various distances along the Bessel beam propagation. The Bessel beam is the same as that shown in Fig. 2. The systematic deficiency in the experimental energy content of the center lobe is primarily caused by limited film MTF.

Fig. 7
Fig. 7

Measured phase-front distortions (λ/40 contours at λ = 1 μm) of the Bessel ring substrate showing (a) three-lobed distortion (0.3 λ peak to valley at λ = 1 μm), probably caused by cutting of the substrate during fabrication; simulated far-field (b) intensity distribution for a ring mask with λ/4 rms high-frequency noise (~ 25 μm scale size), leading to clearly identifiable speckle structure in the rings outside the center lobe; (c) and (d) distributions of Bessel beams generated with the measured phase front shown in (a) and scaled for λ = 1 μm and 0.5 μm, respectively.

Fig. 8
Fig. 8

Transverse intensity distribution of a Bessel beam generated with the same mask as used for Fig. 1 but at λ = 0.51 μm (cw Ar+). The clearly visible triangular distortion was observed to rotate with the mask. This intensity distortion is attributed to the measured phase distortion shown in Fig. 7(a). The simulated Bessel beam in Fig. 7(d) closely resembles this figure.

Fig. 9
Fig. 9

Mach–Zehnder interferograms of Bessel beams: (a) numerical simulation corresponding to experimental data shown in (b). Note the clearly visible π-phase jumps when crossing the Bessel beam minima. High-accuracy interferometry of the central spot using spatial synchronous phase detection has yielded a planar phase front of ≤ λ/80 rms. The small circles in (b) are a consequence of dust inside the imaging objective.

Fig. 10
Fig. 10

Transverse-intensity distribution of a Bessel beam generated by using the ring-shaped output from an unstable ring Nd:YLF resonator. The Jo2 distribution shown corresponds to the parameters of the experimental data. The Bessel beam generation efficiency for this setup is ~ 50% and could be further improved in an optimized setup.

Equations (1)

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E ( r , ϕ , z , t ) = a exp i ( - ω t + k z ) J 0 ( k r ) ,

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