Abstract

We demonstrate that when a partially coherent beam with a Gaussian intensity distribution is focused by a lens, the desired partially coherent flat-topped intensity distribution or doughnut-shaped intensity distribution at the geometrical focus can be generated by choice of appropriate form of spectral degree of coherence. We provide a novel approach to beam shaping of a partially coherent beam and offer new schemes for their potential applications such as material processing, optical therapy, and optical tweezers.

© 2004 Optical Society of America

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References

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    [Crossref]
  6. R. Gase, “The multimode laser radiation as a Gaussian Schell model beam,” J. Mod. Opt. 38, 1107–1116 (1991).
    [Crossref]
  7. Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
    [Crossref]
  8. J. Turunen, E. Tervonen, A. T. Friberg, “Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,” J. Appl. Phys. 67, 49–59 (1990).
    [Crossref]
  9. E. Tervonen, A. T. Friberg, J. Turunen, “Gaussian Schell-model beams generated with synthetic acousto-optic holograms,” J. Opt. Soc. Am. A 9, 796–803 (1992).
    [Crossref]
  10. Here the Fresnel number of GSM beam is defined as Nw = w20/λf, which is independent of the coherence of the GSM beam. The strict definition for the Fresnel number of the GSM beam has been given by J. Pu, “Waist location and Rayleigh range for Gaussian Schell-model beams,” J. Opt. (Paris) 22, 157–159 (1991).
  11. J. Pu, S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36, 1407–1411 (2000).
    [Crossref]
  12. S. Anand, B. K. Yadav, H. C. Kandpal, “Experimental study of the phenomenon of 1 × N spectral switch due to diffraction of partially coherent light,” J. Opt. Soc. Am. A 19, 2223–2228 (2002).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  15. G. Gbur, T. D. Visser, “Can spatial coherence effects produce a local minimum of intensity at focus,” Opt. Lett. 28, 1627–1629 (2003).
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    [Crossref]
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    [Crossref]

2003 (2)

2002 (1)

2001 (1)

2000 (1)

J. Pu, S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36, 1407–1411 (2000).
[Crossref]

1999 (2)

1998 (1)

1996 (2)

1992 (2)

E. Tervonen, A. T. Friberg, J. Turunen, “Gaussian Schell-model beams generated with synthetic acousto-optic holograms,” J. Opt. Soc. Am. A 9, 796–803 (1992).
[Crossref]

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[Crossref] [PubMed]

1991 (2)

Here the Fresnel number of GSM beam is defined as Nw = w20/λf, which is independent of the coherence of the GSM beam. The strict definition for the Fresnel number of the GSM beam has been given by J. Pu, “Waist location and Rayleigh range for Gaussian Schell-model beams,” J. Opt. (Paris) 22, 157–159 (1991).

R. Gase, “The multimode laser radiation as a Gaussian Schell model beam,” J. Mod. Opt. 38, 1107–1116 (1991).
[Crossref]

1990 (1)

J. Turunen, E. Tervonen, A. T. Friberg, “Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,” J. Appl. Phys. 67, 49–59 (1990).
[Crossref]

1988 (1)

1986 (1)

1984 (1)

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[Crossref]

Anand, S.

Arinaga, S.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[Crossref]

Ashkin, A.

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[Crossref] [PubMed]

Churin, E. G.

Dickey, F. M.

Dixit, S. N.

Feit, M. D.

Friberg, A. T.

Gase, R.

R. Gase, “The multimode laser radiation as a Gaussian Schell model beam,” J. Mod. Opt. 38, 1107–1116 (1991).
[Crossref]

Gbur, G.

Kandpal, H. C.

Kato, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[Crossref]

Kitagawa, Y.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[Crossref]

Lohmann, A. W.

Mendlovic, D.

Mima, K.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[Crossref]

Miyanaga, N.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[Crossref]

Nakatsuka, M.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[Crossref]

Nemoto, S.

J. Pu, S. Nemoto, “Anomalous behaviors of the Fraunhofer diffraction patterns for a class of partially coherent light,” Opt. Express 11, 339–346 (2003), http://www.opticsexpress.org .
[Crossref] [PubMed]

J. Pu, S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36, 1407–1411 (2000).
[Crossref]

Ohtsuka, Y.

Perry, M. D.

Popov, S. Y.

Powell, H. T.

Pu, J.

J. Pu, S. Nemoto, “Anomalous behaviors of the Fraunhofer diffraction patterns for a class of partially coherent light,” Opt. Express 11, 339–346 (2003), http://www.opticsexpress.org .
[Crossref] [PubMed]

J. Pu, S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36, 1407–1411 (2000).
[Crossref]

Here the Fresnel number of GSM beam is defined as Nw = w20/λf, which is independent of the coherence of the GSM beam. The strict definition for the Fresnel number of the GSM beam has been given by J. Pu, “Waist location and Rayleigh range for Gaussian Schell-model beams,” J. Opt. (Paris) 22, 157–159 (1991).

Romero, L. A.

Schafer, D.

Shabtay, G.

Tervonen, E.

E. Tervonen, A. T. Friberg, J. Turunen, “Gaussian Schell-model beams generated with synthetic acousto-optic holograms,” J. Opt. Soc. Am. A 9, 796–803 (1992).
[Crossref]

J. Turunen, E. Tervonen, A. T. Friberg, “Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,” J. Appl. Phys. 67, 49–59 (1990).
[Crossref]

Turunen, J.

Visser, T. D.

Yadav, B. K.

Yamanaka, C.

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[Crossref]

Biophys. J. (1)

A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime,” Biophys. J. 61, 569–582 (1992).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

J. Pu, S. Nemoto, “Spectral shifts and spectral switches in diffraction of partially coherent light by a circular aperture,” IEEE J. Quantum Electron. 36, 1407–1411 (2000).
[Crossref]

J. Appl. Phys. (1)

J. Turunen, E. Tervonen, A. T. Friberg, “Acousto-optic control and modulation of optical coherence by electronically synthesized holographic gratings,” J. Appl. Phys. 67, 49–59 (1990).
[Crossref]

J. Mod. Opt. (1)

R. Gase, “The multimode laser radiation as a Gaussian Schell model beam,” J. Mod. Opt. 38, 1107–1116 (1991).
[Crossref]

J. Opt. (Paris) (1)

Here the Fresnel number of GSM beam is defined as Nw = w20/λf, which is independent of the coherence of the GSM beam. The strict definition for the Fresnel number of the GSM beam has been given by J. Pu, “Waist location and Rayleigh range for Gaussian Schell-model beams,” J. Opt. (Paris) 22, 157–159 (1991).

J. Opt. Soc. Am. A (6)

Opt. Express (1)

Opt. Lett. (5)

Phys. Rev. Lett. (1)

Y. Kato, K. Mima, N. Miyanaga, S. Arinaga, Y. Kitagawa, M. Nakatsuka, C. Yamanaka, “Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression,” Phys. Rev. Lett. 53, 1057–1060 (1984).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1

(a) Spectral degree of coherence of the partially coherent beam at the lens plane and (b) intensity distribution at the geometrical focus when the incident partially coherent beam is a GSM beam of α = σ/w 0 = 0.3 (dashed curve) and α = σ/w 0 = 1 (solid curve). The Fresnel number of the GSM beam is N w = w 0 2f = 100.

Fig. 2
Fig. 2

(a) Spectral degree of coherence of the partially coherent beam at the lens plane and (b) intensity distribution at the geometrical focus when the spatially coherent function of the incident partially coherent beam is given by Eq. (5). N w = w 0 2f = 100, ∊ = 0.0, w 0/ = 1.5, f = 1 m, and λ = 632.8 nm. The dotted curve represents the super-Gaussian profile exp[-(r/ r 0)14] with r 0 = 0.0095w 0.

Fig. 3
Fig. 3

(a) Spectral degree of coherence of the partially coherent beam at the lens plane and (b) intensity distribution at the geometrical focus when the spatially coherent function of the incident partially coherent beam is given by Eq. (5). N w = w 0 2f = 100, ∊ = 0.0, w 0/ = 2, f = 1 m, and λ = 632.8 nm. The dotted curve represents the super-Gaussian profile exp[-(r/ r 0)18] with r 0 = 0.0126w 0.

Fig. 4
Fig. 4

(a) Spectral degree of coherence of the partially coherent beam at the lens plane and (b) intensity distribution at the geometrical focus when the spatially coherent function of the incident partially coherent beam is given by Eq. (5). N w = w 0 2f = 100, ∊ = 0.0, w 0/ = 3, f = 1 m, and λ = 632.8 nm. The dotted curve represents the super-Gaussian profile exp[-(r/ r 0)32] with r 0 = 0.0185w 0.

Fig. 5
Fig. 5

(a) Spectral degree of coherence of the partially coherent beam at the lens plane and (b) intensity distribution (solid curve) at the geometrical focus when the spatially coherent function of the incident partially coherent beam is given by Eq. (5). N w = w 0 2f = 100, ∊ = 0.4, w 0/ = 1, f = 1 m, and λ = 632.8 nm. The dotted curve in (b) is the intensity distribution of TEM01 mode I(r) = I 0(r/ r 0)2exp[-2(r/ r 0)2] with r 0 = 0.006w 0.

Fig. 6
Fig. 6

(a) Spectral degree of coherence of the partially coherent beam at the lens plane and (b) intensity distribution at the geometrical focus when the spatially coherent function of the incident partially coherent beam is given by Eq. (5). N w = w 0 2f = 100, ∊ = 0.2, w 0/ = 1, f = 1 m, and λ = 632.8 nm.

Equations (6)

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W0r1, r2, ω=I0r1, ωI0r2, ω1/2μ0r2-r1, ω,
I0r, ω=W0r, r, ω=I0 exp-r2/2w02
Ir, ω=k2πf2  W0r1, r2, ωexpikfr · r1-r2dr1dr2,
μ0Δr, ω=exp-Δr2/2σ2,
μ0Δr, ω=11-2Be sinck|Δr|b-21-2Be sinck|Δr|b,
μ0Δr, ω=Be sinc3.832|Δr|L¯=2J13.832|Δr|/L¯3.832|Δr|/L¯.

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