Abstract

A study of the maximal intensity peaks due to nonlinear holographic images of obstacles such as obscurations or phase defects in a high-power laser system is presented. It is shown that the interference of the high-power plane wave and the converging image wave results in the formation of intensity maximums in the vicinity of the image plane, the values of which significantly exceed the intensity in the image plane itself. For round obstacles, analytical expressions that describe magnitudes and locations of the maxima depending on the radius and the type of obstacle are given. A procedure of numerical modeling that allows estimation of the influence of beam size, medium thickness, type, size, and shape of obstacles onto the properties of nonlinear images is described. It is demonstrated that for a given combination of the nonlinear medium and the high-power beam parameters, there is an intrinsic size of obstacles that is most harmful for the laser system components.

© 2011 Optical Society of America

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References

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  1. J. T. Hunt, K. R. Manes, and P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
    [CrossRef] [PubMed]
  2. W. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes, Rep. UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1996).
  3. C. C. Widmayer, D. Milam, and S. P. Deszoeke, “Nonlinear formation of holographic images of obscurations in laser beams,” Appl. Opt. 36, 9342–9347 (1997).
    [CrossRef]
  4. C. C. Widmayer, M. R. Nickels, and D. Milam, “Nonlinear holographic imaging of phase errors,” Appl. Opt. 37, 4801–4805 (1998).
    [CrossRef]
  5. L. P. Xie, F. Jing, J. L. Zhao, J. Q. Su, W. Y. Wang, and H. S. Peng, “Nonlinear hot-image formation of an intense laser beam in media with gain and loss,” Opt. Commun. 236, 343–348 (2004).
    [CrossRef]
  6. L. P. Xie, J. L. Zhao, and F. Jing, “Second-order hot image from a scatter in high-power laser systems,” Appl. Opt. 44, 2553–2557 (2005).
    [CrossRef] [PubMed]
  7. Y. Wang, S. Wen, L. Zhang, Y. Hu, and D. Fan, “Obscuration size dependence of hot image in laser beam through a Kerr medium slab with gain and loss,” Appl. Opt. 47, 1152–1163 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  11. I. V. Epatko, A. A. Malyutin, R. V. Serov, D. A. Solov'ev, A. D. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28, 697–702 (1998)
    [CrossRef]
  12. I. V. Epatko, R. V. Serov, “Advantage of fast Fourier interpolation for laser modeling,” J. Phys. IV 133, 679–682(2006).
    [CrossRef]

2008 (1)

2007 (1)

2006 (1)

I. V. Epatko, R. V. Serov, “Advantage of fast Fourier interpolation for laser modeling,” J. Phys. IV 133, 679–682(2006).
[CrossRef]

2005 (2)

S. G. Garanin, A. I. Zaretskii, R. I. Il'kaev, G. A. Kirillov, G. G. Kochemasov, R. F. Kurunov, V. M. Murugov, S. A. Sukharev, “Channel of a high-power laser fusion Luch facility emitting 3.3-kJ and 4-ns pulses,” Quantum Electron. 35, 299 (2005).
[CrossRef]

L. P. Xie, J. L. Zhao, and F. Jing, “Second-order hot image from a scatter in high-power laser systems,” Appl. Opt. 44, 2553–2557 (2005).
[CrossRef] [PubMed]

2004 (1)

L. P. Xie, F. Jing, J. L. Zhao, J. Q. Su, W. Y. Wang, and H. S. Peng, “Nonlinear hot-image formation of an intense laser beam in media with gain and loss,” Opt. Commun. 236, 343–348 (2004).
[CrossRef]

1999 (1)

M. L. André, “The French Megajoule Laser Project (LMJ),” Fusion Eng. Des. 44, 43–49, 1999.
[CrossRef]

1998 (2)

I. V. Epatko, A. A. Malyutin, R. V. Serov, D. A. Solov'ev, A. D. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28, 697–702 (1998)
[CrossRef]

C. C. Widmayer, M. R. Nickels, and D. Milam, “Nonlinear holographic imaging of phase errors,” Appl. Opt. 37, 4801–4805 (1998).
[CrossRef]

1997 (1)

1996 (1)

W. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes, Rep. UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1996).

1993 (1)

André, M. L.

M. L. André, “The French Megajoule Laser Project (LMJ),” Fusion Eng. Des. 44, 43–49, 1999.
[CrossRef]

Auerbach, J. M.

Bowers, M. W.

Chulkin, A. D.

I. V. Epatko, A. A. Malyutin, R. V. Serov, D. A. Solov'ev, A. D. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28, 697–702 (1998)
[CrossRef]

Deszoeke, S. P.

Dixit, S. N.

Eimerl, D.

W. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes, Rep. UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1996).

Epatko, I. V.

I. V. Epatko, R. V. Serov, “Advantage of fast Fourier interpolation for laser modeling,” J. Phys. IV 133, 679–682(2006).
[CrossRef]

I. V. Epatko, A. A. Malyutin, R. V. Serov, D. A. Solov'ev, A. D. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28, 697–702 (1998)
[CrossRef]

Erbert, G. V.

Fan, D.

Garanin, S. G.

S. G. Garanin, A. I. Zaretskii, R. I. Il'kaev, G. A. Kirillov, G. G. Kochemasov, R. F. Kurunov, V. M. Murugov, S. A. Sukharev, “Channel of a high-power laser fusion Luch facility emitting 3.3-kJ and 4-ns pulses,” Quantum Electron. 35, 299 (2005).
[CrossRef]

Haynam, C. A.

Heestand, G. M.

Henesian, M. A.

Hermann, M. R.

Hu, Y.

Hunt, J. T.

W. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes, Rep. UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1996).

J. T. Hunt, K. R. Manes, and P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
[CrossRef] [PubMed]

Il'kaev, R. I.

S. G. Garanin, A. I. Zaretskii, R. I. Il'kaev, G. A. Kirillov, G. G. Kochemasov, R. F. Kurunov, V. M. Murugov, S. A. Sukharev, “Channel of a high-power laser fusion Luch facility emitting 3.3-kJ and 4-ns pulses,” Quantum Electron. 35, 299 (2005).
[CrossRef]

Jancaitis, K. S.

Jing, F.

L. P. Xie, J. L. Zhao, and F. Jing, “Second-order hot image from a scatter in high-power laser systems,” Appl. Opt. 44, 2553–2557 (2005).
[CrossRef] [PubMed]

L. P. Xie, F. Jing, J. L. Zhao, J. Q. Su, W. Y. Wang, and H. S. Peng, “Nonlinear hot-image formation of an intense laser beam in media with gain and loss,” Opt. Commun. 236, 343–348 (2004).
[CrossRef]

Kirillov, G. A.

S. G. Garanin, A. I. Zaretskii, R. I. Il'kaev, G. A. Kirillov, G. G. Kochemasov, R. F. Kurunov, V. M. Murugov, S. A. Sukharev, “Channel of a high-power laser fusion Luch facility emitting 3.3-kJ and 4-ns pulses,” Quantum Electron. 35, 299 (2005).
[CrossRef]

Kochemasov, G. G.

S. G. Garanin, A. I. Zaretskii, R. I. Il'kaev, G. A. Kirillov, G. G. Kochemasov, R. F. Kurunov, V. M. Murugov, S. A. Sukharev, “Channel of a high-power laser fusion Luch facility emitting 3.3-kJ and 4-ns pulses,” Quantum Electron. 35, 299 (2005).
[CrossRef]

Kurunov, R. F.

S. G. Garanin, A. I. Zaretskii, R. I. Il'kaev, G. A. Kirillov, G. G. Kochemasov, R. F. Kurunov, V. M. Murugov, S. A. Sukharev, “Channel of a high-power laser fusion Luch facility emitting 3.3-kJ and 4-ns pulses,” Quantum Electron. 35, 299 (2005).
[CrossRef]

Malyutin, A. A.

I. V. Epatko, A. A. Malyutin, R. V. Serov, D. A. Solov'ev, A. D. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28, 697–702 (1998)
[CrossRef]

Manes, K. R.

Marshall, C. D.

Mehta, N. C.

Menapace, J.

Milam, D.

C. C. Widmayer, M. R. Nickels, and D. Milam, “Nonlinear holographic imaging of phase errors,” Appl. Opt. 37, 4801–4805 (1998).
[CrossRef]

C. C. Widmayer, D. Milam, and S. P. Deszoeke, “Nonlinear formation of holographic images of obscurations in laser beams,” Appl. Opt. 36, 9342–9347 (1997).
[CrossRef]

W. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes, Rep. UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1996).

Moses, E.

Murray, J. R.

Murugov, V. M.

S. G. Garanin, A. I. Zaretskii, R. I. Il'kaev, G. A. Kirillov, G. G. Kochemasov, R. F. Kurunov, V. M. Murugov, S. A. Sukharev, “Channel of a high-power laser fusion Luch facility emitting 3.3-kJ and 4-ns pulses,” Quantum Electron. 35, 299 (2005).
[CrossRef]

Nickels, M. R.

Nostrand, M. C.

Orth, C. D.

Patterson, R.

Peng, H. S.

L. P. Xie, F. Jing, J. L. Zhao, J. Q. Su, W. Y. Wang, and H. S. Peng, “Nonlinear hot-image formation of an intense laser beam in media with gain and loss,” Opt. Commun. 236, 343–348 (2004).
[CrossRef]

Renard, P. A.

W. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes, Rep. UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1996).

J. T. Hunt, K. R. Manes, and P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
[CrossRef] [PubMed]

Sacks, R. A.

Serov, R. V.

I. V. Epatko, R. V. Serov, “Advantage of fast Fourier interpolation for laser modeling,” J. Phys. IV 133, 679–682(2006).
[CrossRef]

I. V. Epatko, A. A. Malyutin, R. V. Serov, D. A. Solov'ev, A. D. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28, 697–702 (1998)
[CrossRef]

Shaw, M. J.

Solov'ev, D. A.

I. V. Epatko, A. A. Malyutin, R. V. Serov, D. A. Solov'ev, A. D. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28, 697–702 (1998)
[CrossRef]

Spaeth, M.

Su, J. Q.

L. P. Xie, F. Jing, J. L. Zhao, J. Q. Su, W. Y. Wang, and H. S. Peng, “Nonlinear hot-image formation of an intense laser beam in media with gain and loss,” Opt. Commun. 236, 343–348 (2004).
[CrossRef]

Sukharev, S. A.

S. G. Garanin, A. I. Zaretskii, R. I. Il'kaev, G. A. Kirillov, G. G. Kochemasov, R. F. Kurunov, V. M. Murugov, S. A. Sukharev, “Channel of a high-power laser fusion Luch facility emitting 3.3-kJ and 4-ns pulses,” Quantum Electron. 35, 299 (2005).
[CrossRef]

Sutton, S. B.

Van Wonterghem, B. M.

Wang, W. Y.

L. P. Xie, F. Jing, J. L. Zhao, J. Q. Su, W. Y. Wang, and H. S. Peng, “Nonlinear hot-image formation of an intense laser beam in media with gain and loss,” Opt. Commun. 236, 343–348 (2004).
[CrossRef]

Wang, Y.

Wegner, P. J.

Wen, S.

White, R. K.

Widmayer, C. C.

Williams, W.

W. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes, Rep. UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1996).

Williams, W. H.

Xie, L. P.

L. P. Xie, J. L. Zhao, and F. Jing, “Second-order hot image from a scatter in high-power laser systems,” Appl. Opt. 44, 2553–2557 (2005).
[CrossRef] [PubMed]

L. P. Xie, F. Jing, J. L. Zhao, J. Q. Su, W. Y. Wang, and H. S. Peng, “Nonlinear hot-image formation of an intense laser beam in media with gain and loss,” Opt. Commun. 236, 343–348 (2004).
[CrossRef]

Yang, S. T.

Zaretskii, A. I.

S. G. Garanin, A. I. Zaretskii, R. I. Il'kaev, G. A. Kirillov, G. G. Kochemasov, R. F. Kurunov, V. M. Murugov, S. A. Sukharev, “Channel of a high-power laser fusion Luch facility emitting 3.3-kJ and 4-ns pulses,” Quantum Electron. 35, 299 (2005).
[CrossRef]

Zhang, L.

Zhao, J. L.

L. P. Xie, J. L. Zhao, and F. Jing, “Second-order hot image from a scatter in high-power laser systems,” Appl. Opt. 44, 2553–2557 (2005).
[CrossRef] [PubMed]

L. P. Xie, F. Jing, J. L. Zhao, J. Q. Su, W. Y. Wang, and H. S. Peng, “Nonlinear hot-image formation of an intense laser beam in media with gain and loss,” Opt. Commun. 236, 343–348 (2004).
[CrossRef]

Appl. Opt. (6)

Fusion Eng. Des. (1)

M. L. André, “The French Megajoule Laser Project (LMJ),” Fusion Eng. Des. 44, 43–49, 1999.
[CrossRef]

J. Phys. IV (1)

I. V. Epatko, R. V. Serov, “Advantage of fast Fourier interpolation for laser modeling,” J. Phys. IV 133, 679–682(2006).
[CrossRef]

Opt. Commun. (1)

L. P. Xie, F. Jing, J. L. Zhao, J. Q. Su, W. Y. Wang, and H. S. Peng, “Nonlinear hot-image formation of an intense laser beam in media with gain and loss,” Opt. Commun. 236, 343–348 (2004).
[CrossRef]

Quantum Electron. (2)

S. G. Garanin, A. I. Zaretskii, R. I. Il'kaev, G. A. Kirillov, G. G. Kochemasov, R. F. Kurunov, V. M. Murugov, S. A. Sukharev, “Channel of a high-power laser fusion Luch facility emitting 3.3-kJ and 4-ns pulses,” Quantum Electron. 35, 299 (2005).
[CrossRef]

I. V. Epatko, A. A. Malyutin, R. V. Serov, D. A. Solov'ev, A. D. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28, 697–702 (1998)
[CrossRef]

Other (1)

W. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, “Modeling of self-focusing experiments by beam propagation codes, Rep. UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1996).

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Figures (12)

Fig. 1
Fig. 1

Scheme demonstrating holographic image formation (a) and two-dimensional distributions of intensity and their profiles along the Y-axis (b) from left to right: at the obstacle plane, at the NM input surface, at the IP.

Fig. 2
Fig. 2

Complex amplitudes of waves superposition: A IP is the amplitude in the IP, A R is the amplitude at distances ± z R from the IP, and A max is the maximum amplitude.

Fig. 3
Fig. 3

Complex amplitudes for waves in the case of phase obscuration with the phase shift φ: A 0 is the plane wave and A s is the scattered wave.

Fig. 4
Fig. 4

Evolution of on-axis and peak intensity for opaque disk with diameter 1 mm and sharp edge (smoothing 1 μm ), B = 0.2 rad . The origin is in the IP.

Fig. 5
Fig. 5

Evolution of on-axis intensity for phase obstacles with ± π phase shift, diameter 1 mm , smoothing 1 μm , and B = 0.1 rad .

Fig. 6
Fig. 6

Maximum intensity versus the phase shift. Obscuration is the disk with diameter 0.5 mm and sharp edge (smoothing 0.3 μm ).

Fig. 7
Fig. 7

Comparison of modeling results for infinitely thin NM (open circles) and for NM with the thickness of 3 cm (solid line), z R = 25 cm .

Fig. 8
Fig. 8

Maximum intensity versus obscuration diameter for NM with the reduced thickness of 3 cm .

Fig. 9
Fig. 9

Maximum intensity versus obscuration diameter for infinitely thin NM and NM with reduced thickness of 3 cm .

Fig. 10
Fig. 10

Maximum fluence as a function of the distance from the NM obtained in [4].

Fig. 11
Fig. 11

Maximum fluence for crater defect as a function of the distance from the NM obtained in our simulations.

Fig. 12
Fig. 12

Maximum fluence versus the distance from the NM for the protrusion at 0.3 μm and 30 μm smoothing.

Tables (1)

Tables Icon

Table 1 Ratios of the Maximal Intensity to the High-Power Beam Intensity Obtained During the Simulation for Several Different Shapes of Obscurations, All with an Area of π / 4 mm 2

Equations (19)

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

A 1 ( x , y , 0 ) = i B A S * ( x , y , 2 Z 0 ) exp ( i B ) ,
A 1 ( x , y , 0 ) = i B A 0 ( 1 τ obs ( x , y ) ) exp ( i B ) .
A 0 ( 0 , 0 , z ) + A 1 ( 0 , 0 , z ) = A 0 exp ( i B ) + i B A 0 ( 1 exp ( i k r 2 / 2 z ) ) exp ( i B ) .
I ( z ) = I 0 { [ 1 B sin ( π z R / z ) ] 2 + B 2 [ 1 cos ( π z R / z ) ] 2 } ,
Z max ( m ) = π z R ( 2 m + 1 ) π + arctan ( 1 / B ) ,
I max = I 0 ( 1 + B 2 + B ) 2 .
I ( z ) = I 0 · { ( 1 B sin ( π z R z ) B π · z R 2 Z 0 + z ) 2 + B 2 ( 1 cos ( π z R z ) π · z R 2 Z 0 + z ) 2 } .
I max = I 0 ( ( 1 B π · z R 2 Z 0 ) 2 + ( B π · z R 2 Z 0 ) 2 + B ) 2 .
I max = I 0 ( ( 1 2 B π · z R 2 Z 0 ) 2 + ( 2 B π · z R Z 0 ) 2 + 2 B ) 2 .
I ( z ) = I 0 | 1 + i B ( 1 exp ( i φ ) ) ( 1 exp ( i π z R / z ) ) | 2 .
I max = I 0 [ 1 + 4 B 2 sin 2 ( φ 2 ) 2 B sin ( φ ) + 2 B | sin ( φ 2 ) | ] 2 .
L D b / 0.7.
δ 4.3 D b / N .
θ < 0.7 λ N / D b ,
d obs < D b / 6.
Z 0 D b 2 / ( 0.7 λ N ) .
d c d obs + 12 δ ,
L 2 , 3 d obs + 18 δ .
δ ( 1 18 / N ) d obs / N .

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