Abstract

A type of nondiffracting narrow light beam that propagates across a long range with a narrow beamwidth is presented. This beam is formed by a distorted concave spherical wave front that can be generated by a Galilean transmitting telescope with an eyepiece that has a spherical aberration. We observed an unusual image with a striped pattern in the laser beam’s atmospheric backscatter that provided an opportunity to examine this effect. We demonstrate the mechanism of the generation and the characteristics of the long-range nondiffracting beam. The results show that a nondiffracting core beam with a width of the order of millimeters with a propagation distance of the order of a kilometer is generated by a 10-cm-diameter laser beam.

© 1997 Optical Society of America

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References

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  1. V. E. Zuev, Propagation of Visible and Infrared Radiation in the Atmosphere (Wiley, New York, 1974), Chap. 11, p. 348.
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    [CrossRef]
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  7. T. Aruga, K. Araki, T. Igarashi, F. Imai, Y. Yamamoto, H. Sakagami, “Earth-to-space laser beam transmission for space craft attitude measurement,” Appl. Opt. 23, 143–147 (1984).
    [CrossRef]
  8. Special Issue on Intersatellite Links, Int. J. Satellite Commun. 6, 77–238 (1988).
  9. L. A. Tompson, C. S. Gardner, “Experiment on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature London 328, 229–231 (1987).
    [CrossRef]
  10. H. Mcleod, “The axicon: a new type of optical element,” J. Opt. Soc. Am. 44, 592–597 (1954).
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    [CrossRef] [PubMed]
  13. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  14. K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1988).
    [CrossRef]
  15. A. J. Cox, D. C. Dibble, “Constant-axial-intensity nondiffracting beam,” J. Opt. Soc.Am. A 9, 282–286 (1992).
    [CrossRef]
  16. A. J. Cox, J. D’Anna, “Nondiffracting beam from a spatially filtered Fabry–Perot resonator,” Opt. Lett. 17, 232–234 (1992).
    [CrossRef] [PubMed]
  17. J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3961 (1988).
    [CrossRef] [PubMed]
  18. A. Vasara, J. Turunen, A. T. Friberg, “Realization of general nondiffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
    [CrossRef] [PubMed]
  19. T. Aruga, “Methods and instruments for generation of long-range nondiffracting narrow light beams,” Japanese patent8-23379 (17January1996).
  20. A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).
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    [CrossRef]
  24. M. Born, E. Wolf, Principle of Optics (Pergamon, Oxford, UK, 1975), Chap. 8, p. 370.
  25. N. G. Van Kampen, “The method of stationary phase and the method of Fresnel zones,” Physica 24, 437–444 (1958).
    [CrossRef]
  26. K. Kanda, Shinwa Koki Company, Fuchu, Tokyo, Japan; Y. Miho, Kenko Company, Iruma, Saitama, Japan (personal communications, 1995).

1992 (2)

A. J. Cox, D. C. Dibble, “Constant-axial-intensity nondiffracting beam,” J. Opt. Soc.Am. A 9, 282–286 (1992).
[CrossRef]

A. J. Cox, J. D’Anna, “Nondiffracting beam from a spatially filtered Fabry–Perot resonator,” Opt. Lett. 17, 232–234 (1992).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

1988 (4)

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1988).
[CrossRef]

F. Roddier, “Curvature sensing and compensation: a new concept in adaptive optics,” Appl. Opt. 27, 1223–1225 (1988).
[CrossRef] [PubMed]

J. Turunen, A. Vasara, A. T. Friberg, “Holographic generation of diffraction-free beams,” Appl. Opt. 27, 3959–3961 (1988).
[CrossRef] [PubMed]

Special Issue on Intersatellite Links, Int. J. Satellite Commun. 6, 77–238 (1988).

1987 (3)

L. A. Tompson, C. S. Gardner, “Experiment on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature London 328, 229–231 (1987).
[CrossRef]

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

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

1986 (1)

1984 (1)

1977 (1)

1972 (1)

1970 (1)

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

1965 (1)

1963 (1)

G. Fiocco, L. D. Smullin, “Determination ofscattering layers in the upper atmosphere (60–140 km) by optical radar,” Nature London 199, 1275–1276 (1963).
[CrossRef]

1962 (1)

1958 (1)

N. G. Van Kampen, “The method of stationary phase and the method of Fresnel zones,” Physica 24, 437–444 (1958).
[CrossRef]

1954 (1)

Araki, K.

Aruga, T.

T. Aruga, K. Araki, T. Igarashi, F. Imai, Y. Yamamoto, H. Sakagami, “Earth-to-space laser beam transmission for space craft attitude measurement,” Appl. Opt. 23, 143–147 (1984).
[CrossRef]

T. Aruga, “Methods and instruments for generation of long-range nondiffracting narrow light beams,” Japanese patent8-23379 (17January1996).

Born, M.

M. Born, E. Wolf, Principle of Optics (Pergamon, Oxford, UK, 1975), Chap. 8, p. 370.

Bufton, J. L.

Cox, A. J.

A. J. Cox, D. C. Dibble, “Constant-axial-intensity nondiffracting beam,” J. Opt. Soc.Am. A 9, 282–286 (1992).
[CrossRef]

A. J. Cox, J. D’Anna, “Nondiffracting beam from a spatially filtered Fabry–Perot resonator,” Opt. Lett. 17, 232–234 (1992).
[CrossRef] [PubMed]

D’Anna, J.

Dibble, D. C.

A. J. Cox, D. C. Dibble, “Constant-axial-intensity nondiffracting beam,” J. Opt. Soc.Am. A 9, 282–286 (1992).
[CrossRef]

Durnin, J.

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

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

Eberly, H. J.

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

Fiocco, G.

G. Fiocco, L. D. Smullin, “Determination ofscattering layers in the upper atmosphere (60–140 km) by optical radar,” Nature London 199, 1275–1276 (1963).
[CrossRef]

Fontanella, J. C.

Friberg, A. T.

Fried, D. L.

Fujiwara, S.

Gardner, C. S.

L. A. Tompson, C. S. Gardner, “Experiment on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature London 328, 229–231 (1987).
[CrossRef]

Igarashi, T.

Imai, F.

Kikuchi, H.

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1988).
[CrossRef]

Labeyrie, A.

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Mcleod, H.

Menzies, R. T.

Miceli, J. J.

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

Minott, P. O.

Primot, J.

Roddier, F.

Rousset, G.

Sakagami, H.

Smullin, L. D.

G. Fiocco, L. D. Smullin, “Determination ofscattering layers in the upper atmosphere (60–140 km) by optical radar,” Nature London 199, 1275–1276 (1963).
[CrossRef]

Tompson, L. A.

L. A. Tompson, C. S. Gardner, “Experiment on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature London 328, 229–231 (1987).
[CrossRef]

Turunen, J.

Uehara, K.

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1988).
[CrossRef]

Van Kampen, N. G.

N. G. Van Kampen, “The method of stationary phase and the method of Fresnel zones,” Physica 24, 437–444 (1958).
[CrossRef]

Vasara, A.

Wolf, E.

M. Born, E. Wolf, Principle of Optics (Pergamon, Oxford, UK, 1975), Chap. 8, p. 370.

Yamamoto, Y.

Zuev, V. E.

V. E. Zuev, Propagation of Visible and Infrared Radiation in the Atmosphere (Wiley, New York, 1974), Chap. 11, p. 348.

Appl. Opt. (5)

Appl. Phys. B (1)

K. Uehara, H. Kikuchi, “Generation of nearly diffraction-free laser beams,” Appl. Phys. B 48, 125–129 (1988).
[CrossRef]

Astron. Astrophys. (1)

A. Labeyrie, “Attainment of diffraction-limited resolution in large telescopes by Fourier analyzing speckle patterns in star images,” Astron. Astrophys. 6, 85–87 (1970).

Int. J. Satellite Commun. (1)

Special Issue on Intersatellite Links, Int. J. Satellite Commun. 6, 77–238 (1988).

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (3)

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

A. J. Cox, D. C. Dibble, “Constant-axial-intensity nondiffracting beam,” J. Opt. Soc.Am. A 9, 282–286 (1992).
[CrossRef]

Nature London (2)

L. A. Tompson, C. S. Gardner, “Experiment on laser guide stars at Mauna Kea Observatory for adaptive imaging in astronomy,” Nature London 328, 229–231 (1987).
[CrossRef]

G. Fiocco, L. D. Smullin, “Determination ofscattering layers in the upper atmosphere (60–140 km) by optical radar,” Nature London 199, 1275–1276 (1963).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

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

Physica (1)

N. G. Van Kampen, “The method of stationary phase and the method of Fresnel zones,” Physica 24, 437–444 (1958).
[CrossRef]

Other (5)

K. Kanda, Shinwa Koki Company, Fuchu, Tokyo, Japan; Y. Miho, Kenko Company, Iruma, Saitama, Japan (personal communications, 1995).

M. Born, E. Wolf, Principle of Optics (Pergamon, Oxford, UK, 1975), Chap. 8, p. 370.

T. Aruga, “Methods and instruments for generation of long-range nondiffracting narrow light beams,” Japanese patent8-23379 (17January1996).

V. E. Zuev, Propagation of Visible and Infrared Radiation in the Atmosphere (Wiley, New York, 1974), Chap. 11, p. 348.

See, for example, Proceedings of the Fifth International Workshop on Laser Ranging Instrumentation, Royal Greenwich Observatory, UK, 1984 (U. Bonn, Geodetic Institute, Bonn, Germany, 1984).

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Figures (13)

Fig. 1
Fig. 1

Block diagram of the equipment used in the experiment. The concept of laser beam transmission and the reception of scattered light from the atmosphere are shown.

Fig. 2
Fig. 2

Image of laser beam transmission in the atmosphere with a very small beam divergence angle. This image was taken by a Cassegrain telescope of 50-cm diameter. One frame (1/30-s) image of the IIT camera is shown.

Fig. 3
Fig. 3

Same image as in Fig. 2 with a very small beam convergence angle. The striped pattern is formed only by a very narrow light beam that corresponds to a continuous point source of long range.

Fig. 4
Fig. 4

Concept of the formation of the striped pattern shown in Fig. 3. The striped pattern is formed by a longitudinal combination of bright spots.

Fig. 5
Fig. 5

Spherical aberration of a typical negative eyepiece. The dotted curve shows a model of the spherical aberration used for calculation.

Fig. 6
Fig. 6

Example of wave-front shapes at the aperture of light beam emission. Distortion results from the eyepiece’s spherical aberration of the model in Fig. 5. Wave fronts 1–3 are formed by changing the separation between the objective and the eyepiece of the transmitting telescope. The dotted curves show spherical wave fronts, assuming that there are no aberrations.

Fig. 7
Fig. 7

Example of the nondiffracting light beam propagation over a long range. A uniform intensity profile is assumed for transmitting light beams: (a) for emitting the wave front of case 1 in Fig. 6, (b) for emitting the wave front of case 2 in Fig. 6.

Fig. 8
Fig. 8

Intensity profile of the propagating laser beam: (a) beam profile at 1 km for the propagation in Fig. 7(a), (b) beam profile at 0.5 km for the propagation in Fig. 7(b).

Fig. 9
Fig. 9

Focused light beam profile at 1 km given a spherical wave.

Fig. 10
Fig. 10

Example of the nondiffracting light beam propagation for Gaussian laser beam emission (truncated at 1/e 2 in the aperture). The same condition as in Fig. 7(a) is assumed.

Fig. 11
Fig. 11

Intensity profile of the propagating laser beam in Fig. 10 at 1 km.

Fig. 12
Fig. 12

Example of a wave-front shape for a telescope of 50-cm diameter. The same condition for the eyepiece’s spherical aberration shown in Fig. 5 is assumed.

Fig. 13
Fig. 13

Light beam propagation for the wave front in Fig. 12.

Equations (14)

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

1R=Δf2.
θρ=ρR.
θρ=s+s1gρρa, ρa=aρ,
s=sf2, s1=s1f2.
hρ=01θρdρ.
uP=c Aξ, ηexp-iklξ, ηdξdη,
IP=uP2.
l=z+x2+y22z-xξ+yη+zζz+ξ2+η2+ζ22z,
ζ=hρ.
uP=2πa2c 01AaρJ0rkzaρ×exp-ik2za2ρ2-kζρdρ,
gρ=c1ρ2 for ρ<0.5,  c2ρ-1 c3 for ρ  0.5,
w1=λDz,
w0=1.125 λzπρa.
w0=2.25πλDzfor ρaa.

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