Abstract

An approach to efficient axially symmetric focusing of a light beam to an extended line segment is studied wherein the on-axis intensity and the scale of transverse intensity distribution can be controlled precisely and simultaneously at any point of the segment. Schematic realization is based on employing two phase-only optical components in tandem, the first of which, with a disk form, performs prior central light beam shaping and marginal correction to smooth the edge slopes, while the second one, with an annular form, is used for the appropriate axicon-type focusing of a light beam to the segment. An instance is given of converting a collimated Gaussian laser beam into an oscillation-free nondiffracting zero-order Bessel beam reproduced on a finite interval.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  3. R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon a CO2–TEA laser beam in a high-pressure gas,” Opt. Commun. 28, 193–196 (1979).
    [CrossRef]
  4. M. Rioux, R. Tremblay, P. A. Bélanger, “Linear, annular, and radial focusing with axicons and applications to laser machining,” Appl. Opt. 17, 1532–1536 (1978).
    [CrossRef] [PubMed]
  5. G. Haüsler, W. Heckel, “Light sectioning with large depth and high resolution,” Appl. Opt. 27, 5165–5169 (1988).
    [CrossRef] [PubMed]
  6. S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).
  7. S. Klewitz, F. Brinkmann, S. Herminghaus, P. Leiderer, “Bessel-beam-pumped turnable distributed-feedback laser,” Appl. Opt. 34, 7670–7673 (1995).
    [CrossRef] [PubMed]
  8. J. A. Davis, D. M. Cottrell, “Range-finding by triangulation with nondiffracting beams,” Appl. Opt. 35, 2159–2161 (1996).
    [CrossRef] [PubMed]
  9. J. A. Kim, K. I. Lee, H. R. Noh, W. Jhe, M. Ohtsu, “Atom trap in an axicon mirror,” Opt. Lett. 22, 117–119 (1997).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  33. S. Yu. Popov, A. T. Friberg, “Apodization of generalized axicons to produce uniform axial line images,” Pure Appl. Opt. 7, 537–548 (1998).
    [CrossRef]
  34. H. Bartelt, “Applications of the tandem component: an element with optimum light efficiency,” Appl. Opt. 24, 3811–3816 (1985).
    [CrossRef] [PubMed]
  35. A. Papoulis, Systems and Transforms with Applications in Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 7.
  36. V. P. Koronkevich, I. A. Mikhaltsova, E. G. Churin, Yu. I. Yurlov, “Lensacon,” Appl. Opt. 34, 5761–5772 (1995).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  39. N. C. Roberts, “Beam shaping by holographic filters,” Appl. Opt. 28, 31–32 (1989).
    [CrossRef] [PubMed]

1998

S. Yu. Popov, A. T. Friberg, “Apodization of generalized axicons to produce uniform axial line images,” Pure Appl. Opt. 7, 537–548 (1998).
[CrossRef]

1997

B. Hafizi, E. Esarey, P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[CrossRef]

J. A. Kim, K. I. Lee, H. R. Noh, W. Jhe, M. Ohtsu, “Atom trap in an axicon mirror,” Opt. Lett. 22, 117–119 (1997).
[CrossRef] [PubMed]

1996

1995

1994

1993

1992

A. J. Cox, J. D’Anna, “Constant-axial-intensity nondiffracting beam,” Opt. Lett. 17, 232–234 (1992).
[CrossRef] [PubMed]

J. Sochacki, S. Bará, Z. Jaroszewicz, A. Kołodziejczyk, “Phase retardation of the uniform-intensity axilens,” Opt. Lett. 31, 5326–5330 (1992).

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

R. M. Herman, T. A. Wiggins, “Apodization of diffractionless beams,” Appl. Opt. 31, 5913–5915 (1992).
[CrossRef] [PubMed]

1991

1989

1988

1987

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

1986

V. V. Korobkin, L. Ya. Polonskii, V. P. Poponin, L. N. Pyatnitskii, “Focusing of Gaussian and super-Gaussian laser beams by axicons to obtain continuous laser sparks,” Sov. J. Quantum Electron. 13, 178–183 (1986).
[CrossRef]

1985

1984

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik 67, 267–278 (1984).

1983

1980

G. Roy, R. Tremblay, “Influence of the divergence of a laser beam on the axial intensity distribution of an axicon,” Opt. Commun. 34, 1–3 (1980).
[CrossRef]

1979

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon a CO2–TEA laser beam in a high-pressure gas,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

1978

1974

1962

1960

1954

Bará, S.

J. Sochacki, S. Bará, Z. Jaroszewicz, A. Kołodziejczyk, “Phase retardation of the uniform-intensity axilens,” Opt. Lett. 31, 5326–5330 (1992).

Bartelt, H.

Bélanger, P. A.

Blanchard, M.

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon a CO2–TEA laser beam in a high-pressure gas,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

Brinkmann, F.

Brinkmann, S.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

Bryngdahl, O.

Churin, E. G.

Cottrell, D. M.

Cox, A. J.

D’Anna, J.

D’Astous, Y.

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon a CO2–TEA laser beam in a high-pressure gas,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

Davidson, N.

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Davis, J. A.

Dibble, D. C.

Dong, B. Z.

Dresel, T.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

Durnin, J.

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

Eberly, J. H.

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

Ersoy, O. K.

Esarey, E.

B. Hafizi, E. Esarey, P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[CrossRef]

Friberg, A. T.

S. Yu. Popov, A. T. Friberg, “Apodization of generalized axicons to produce uniform axial line images,” Pure Appl. Opt. 7, 537–548 (1998).
[CrossRef]

A. T. Friberg, “Stationary-phase analysis of generalized axicons,” J. Opt. Soc. Am. A 13, 743–750 (1996).
[CrossRef]

S. Yu. Popov, A. T. Friberg, “Linear axicons in partially coherent light,” Opt. Eng. 34, 2567–2573 (1995).
[CrossRef]

A. Vasara, J. Turunen, A. T. Friberg, “Realization of general non-diffracting beams with computer-generated holograms,” J. Opt. Soc. Am. A 6, 1748–1754 (1989).
[CrossRef] [PubMed]

Friesem, A. A.

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Fujiwara, S.

Gu, B. Y.

Hafizi, B.

B. Hafizi, E. Esarey, P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[CrossRef]

Han, C.-Y.

Hasman, E.

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Haüsler, G.

Heckel, W.

Herman, R. M.

Herminghaus, S.

Ishii, Y.

Jaroszewicz, Z.

Jhe, W.

Khonina, S. N.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993).
[CrossRef]

Kim, J. A.

Klewitz, S.

Kolodziejczyk, A.

Korobkin, V. V.

V. V. Korobkin, L. Ya. Polonskii, V. P. Poponin, L. N. Pyatnitskii, “Focusing of Gaussian and super-Gaussian laser beams by axicons to obtain continuous laser sparks,” Sov. J. Quantum Electron. 13, 178–183 (1986).
[CrossRef]

Koronkevich, V. P.

V. P. Koronkevich, I. A. Mikhaltsova, E. G. Churin, Yu. I. Yurlov, “Lensacon,” Appl. Opt. 34, 5761–5772 (1995).
[CrossRef] [PubMed]

V. P. Koronkevich, I. G. Palchikova, “Kinoforms with increased depth of focus,” Optik 87, 92–93 (1991).

Kotlyar, V. V.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993).
[CrossRef]

Lee, K. I.

Leiderer, P.

McLeod, J. H.

Miceli, J. J.

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

Mikhaltsova, I. A.

V. P. Koronkevich, I. A. Mikhaltsova, E. G. Churin, Yu. I. Yurlov, “Lensacon,” Appl. Opt. 34, 5761–5772 (1995).
[CrossRef] [PubMed]

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik 67, 267–278 (1984).

Murata, K.

Nalivaiko, V. I.

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik 67, 267–278 (1984).

Noh, H. R.

Ohtsu, M.

Palchikova, I. G.

V. P. Koronkevich, I. G. Palchikova, “Kinoforms with increased depth of focus,” Optik 87, 92–93 (1991).

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 7.

Polonskii, L. Ya.

V. V. Korobkin, L. Ya. Polonskii, V. P. Poponin, L. N. Pyatnitskii, “Focusing of Gaussian and super-Gaussian laser beams by axicons to obtain continuous laser sparks,” Sov. J. Quantum Electron. 13, 178–183 (1986).
[CrossRef]

Poponin, V. P.

V. V. Korobkin, L. Ya. Polonskii, V. P. Poponin, L. N. Pyatnitskii, “Focusing of Gaussian and super-Gaussian laser beams by axicons to obtain continuous laser sparks,” Sov. J. Quantum Electron. 13, 178–183 (1986).
[CrossRef]

Popov, S. Yu.

S. Yu. Popov, A. T. Friberg, “Apodization of generalized axicons to produce uniform axial line images,” Pure Appl. Opt. 7, 537–548 (1998).
[CrossRef]

S. Yu. Popov, A. T. Friberg, “Linear axicons in partially coherent light,” Opt. Eng. 34, 2567–2573 (1995).
[CrossRef]

Pyatnitskii, L. N.

V. V. Korobkin, L. Ya. Polonskii, V. P. Poponin, L. N. Pyatnitskii, “Focusing of Gaussian and super-Gaussian laser beams by axicons to obtain continuous laser sparks,” Sov. J. Quantum Electron. 13, 178–183 (1986).
[CrossRef]

Rioux, M.

Roberts, N. C.

Rosen, J.

Roy, G.

G. Roy, R. Tremblay, “Influence of the divergence of a laser beam on the axial intensity distribution of an axicon,” Opt. Commun. 34, 1–3 (1980).
[CrossRef]

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon a CO2–TEA laser beam in a high-pressure gas,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

Schreiner, R.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

Schwider, J.

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

Sochacki, J.

Soifer, V. A.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993).
[CrossRef]

Soldatenkov, I. S.

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik 67, 267–278 (1984).

Sprangle, P.

B. Hafizi, E. Esarey, P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[CrossRef]

Staronski, L. R.

Tremblay, R.

G. Roy, R. Tremblay, “Influence of the divergence of a laser beam on the axial intensity distribution of an axicon,” Opt. Commun. 34, 1–3 (1980).
[CrossRef]

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon a CO2–TEA laser beam in a high-pressure gas,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

M. Rioux, R. Tremblay, P. A. Bélanger, “Linear, annular, and radial focusing with axicons and applications to laser machining,” Appl. Opt. 17, 1532–1536 (1978).
[CrossRef] [PubMed]

Turunen, J.

Vasara, A.

Wiggins, T. A.

Yang, G. Z.

Yariv, A.

Yurlov, Yu. I.

Appl. Opt.

R. M. Herman, T. A. Wiggins, “High-efficiency diffractionless beams of constant size and intensity,” Appl. Opt. 33, 7297–7306 (1994).
[CrossRef] [PubMed]

S. Klewitz, F. Brinkmann, S. Herminghaus, P. Leiderer, “Bessel-beam-pumped turnable distributed-feedback laser,” Appl. Opt. 34, 7670–7673 (1995).
[CrossRef] [PubMed]

V. P. Koronkevich, I. A. Mikhaltsova, E. G. Churin, Yu. I. Yurlov, “Lensacon,” Appl. Opt. 34, 5761–5772 (1995).
[CrossRef] [PubMed]

J. A. Davis, D. M. Cottrell, “Range-finding by triangulation with nondiffracting beams,” Appl. Opt. 35, 2159–2161 (1996).
[CrossRef] [PubMed]

M. Rioux, R. Tremblay, P. A. Bélanger, “Linear, annular, and radial focusing with axicons and applications to laser machining,” Appl. Opt. 17, 1532–1536 (1978).
[CrossRef] [PubMed]

C.-Y. Han, Y. Ishii, K. Murata, “Reshaping collimated laser beam with Gaussian profile to uniform profiles,” Appl. Opt. 22, 3644–3647 (1983).
[CrossRef] [PubMed]

H. Bartelt, “Applications of the tandem component: an element with optimum light efficiency,” Appl. Opt. 24, 3811–3816 (1985).
[CrossRef] [PubMed]

G. Haüsler, W. Heckel, “Light sectioning with large depth and high resolution,” Appl. Opt. 27, 5165–5169 (1988).
[CrossRef] [PubMed]

N. C. Roberts, “Beam shaping by holographic filters,” Appl. Opt. 28, 31–32 (1989).
[CrossRef] [PubMed]

A. J. Cox, D. C. Dibble, “Holographic reproduction of a diffraction-free beam,” Appl. Opt. 30, 1330–1332 (1991).
[CrossRef] [PubMed]

R. M. Herman, T. A. Wiggins, “Apodization of diffractionless beams,” Appl. Opt. 31, 5913–5915 (1992).
[CrossRef] [PubMed]

J. Mod. Opt.

S. N. Khonina, V. V. Kotlyar, V. A. Soifer, “Calculation of the focusators into a longitudinal line-segment and study of a focal area,” J. Mod. Opt. 40, 761–769 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of nondiffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

R. Tremblay, Y. D’Astous, G. Roy, M. Blanchard, “Laser plasmas optically pumped by focusing with an axicon a CO2–TEA laser beam in a high-pressure gas,” Opt. Commun. 28, 193–196 (1979).
[CrossRef]

G. Roy, R. Tremblay, “Influence of the divergence of a laser beam on the axial intensity distribution of an axicon,” Opt. Commun. 34, 1–3 (1980).
[CrossRef]

Opt. Eng.

S. Yu. Popov, A. T. Friberg, “Linear axicons in partially coherent light,” Opt. Eng. 34, 2567–2573 (1995).
[CrossRef]

Opt. Lett.

Optik

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform axicons,” Optik 67, 267–278 (1984).

V. P. Koronkevich, I. G. Palchikova, “Kinoforms with increased depth of focus,” Optik 87, 92–93 (1991).

S. Brinkmann, T. Dresel, R. Schreiner, J. Schwider, “Axicon-type test interferometer for cylindrical surfaces,” Optik 102, 106–110 (1996).

Phys. Rev. E

B. Hafizi, E. Esarey, P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539–3545 (1997).
[CrossRef]

Phys. Rev. Lett.

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

Pure Appl. Opt.

S. Yu. Popov, A. T. Friberg, “Apodization of generalized axicons to produce uniform axial line images,” Pure Appl. Opt. 7, 537–548 (1998).
[CrossRef]

Sov. J. Quantum Electron.

V. V. Korobkin, L. Ya. Polonskii, V. P. Poponin, L. N. Pyatnitskii, “Focusing of Gaussian and super-Gaussian laser beams by axicons to obtain continuous laser sparks,” Sov. J. Quantum Electron. 13, 178–183 (1986).
[CrossRef]

Other

A. Papoulis, Systems and Transforms with Applications in Optics, 1st ed. (McGraw-Hill, New York, 1968), Chap. 7.

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