Abstract

The evolution of an image with a local intensity minimum (LIM image) during hot image formation caused by translucent obscuration is theoretically and numerically investigated for the first time to our knowledge. The existence of the LIM image is proved, and the functional relationship describing the intensity of the LIM image is derived by using transfer matrix theory. Furthermore, the influences of the parameters of the obscuration and the nonlinear medium on the intensity of the LIM image are also discussed. The results show that the intensity of the LIM image increases with the increase of the amplitude coefficients of the obscuration, but declines with increasing the thickness of the non linear medium within a certain scope. We also found that the distance from the rear surface of the nonlinear medium to the LIM image plane is approximately equal to that from the obscuration plane to the rear surface of the nonlinear medium.

© 2009 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  6. S. G. Lukishova, Y. V. Senatsky, N. E. Bykovsky, and A. S. Scheulin, “Beam shaping and suppression of self-focusing in high-peak power Nd:glass laser systems,” in Self-Focusing: Past and Present. Fundamentals and Prospects, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., Vol. 114 of Spinger Series in Topics in Applied Physics (Springer, 2008), Chap. 8, pp. 191-229.
    [CrossRef]
  7. Y. W. Wang, J. Q. Deng, L. Z. Chen, S. C. Wen, and K. M. You, “Formation of hot-images in laser beams through a self-defocusing Kerr medium slab,” Chin. Phys. Lett. 26, 024205-1-4 (2009).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. L. P. Xie, J. L. Zhao, and F. Jing, “Second-order hot image from a scatterer in high-power laser systems,” Appl. Opt. 44, 2553-2557 (2005).
    [CrossRef] [PubMed]
  12. T. Peng, J. L. Zhao, D. Li, L. P. Xie, and Z. J. Ye, “Simulation analysis of the evolution of the hot-images induced by coplanar multi-scatterers,” Chin. Phys. 18, 1884-1890(2009).
    [CrossRef]
  13. D. Li, J. L. Zhao, T. Peng, and Z. J. Ye, “Hot images induced by arrayed mechanical defects in high-power laser system with cascaded medium,” Opt. Eng. 47, 114202 (2008).
    [CrossRef]
  14. T. Peng, J. L. Zhao, L. P. Xie, Z. J. Ye, H. H. Wei, J. Q. Su, and J. P. Zhao, “Simulation analysis of the restraining effect of a spatial filter on a hot image,” Appl. Opt. 46, 3205-3209(2007).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2009

Y. W. Wang, J. Q. Deng, L. Z. Chen, S. C. Wen, and K. M. You, “Formation of hot-images in laser beams through a self-defocusing Kerr medium slab,” Chin. Phys. Lett. 26, 024205-1-4 (2009).

T. Peng, J. L. Zhao, D. Li, L. P. Xie, and Z. J. Ye, “Simulation analysis of the evolution of the hot-images induced by coplanar multi-scatterers,” Chin. Phys. 18, 1884-1890(2009).
[CrossRef]

2008

2007

2005

2004

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]

L. P. Xie, J. L. Zhao, J. Q. Su, F. Jing, W. Y. Wang, and H. S. Peng, “Theoretical analysis of hot-image effect from phase scatterer,” Acta Phys. Sin. 53, 2175-2179 (2004) (in Chinese).

1998

1997

1993

1975

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel'dovich, and Y. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362-1366 (1975).
[CrossRef]

1966

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307-310(1966).

Baranova, N. B.

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel'dovich, and Y. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362-1366 (1975).
[CrossRef]

Bespalov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307-310(1966).

Bykovskii, N. E.

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel'dovich, and Y. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362-1366 (1975).
[CrossRef]

Bykovsky, N. E.

S. G. Lukishova, Y. V. Senatsky, N. E. Bykovsky, and A. S. Scheulin, “Beam shaping and suppression of self-focusing in high-peak power Nd:glass laser systems,” in Self-Focusing: Past and Present. Fundamentals and Prospects, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., Vol. 114 of Spinger Series in Topics in Applied Physics (Springer, 2008), Chap. 8, pp. 191-229.
[CrossRef]

Campillo, A. J.

A. J. Campillo, “Small-scale self-focusing,” in Self-Focusing: Past and Present. Fundamentals and Prospects, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., Vol. 114 of Spinger Series in Topics in Applied Physics (Springer , 2008), Chap. 6, pp. 157-173.

Chen, L. Z.

Y. W. Wang, J. Q. Deng, L. Z. Chen, S. C. Wen, and K. M. You, “Formation of hot-images in laser beams through a self-defocusing Kerr medium slab,” Chin. Phys. Lett. 26, 024205-1-4 (2009).

Deng, J. Q.

Y. W. Wang, J. Q. Deng, L. Z. Chen, S. C. Wen, and K. M. You, “Formation of hot-images in laser beams through a self-defocusing Kerr medium slab,” Chin. Phys. Lett. 26, 024205-1-4 (2009).

Y. W. Wang, S. C. Wen, K. M. You, Z. X. Tang, J. Q. Deng, L. F. Zhang, and D. Y. Fan, “Multiple hot images from an obscuration in an intense laser beam through cascaded Kerr medium disks,” Appl. Opt. 47, 5668-5681 (2008).
[CrossRef] [PubMed]

deSzoeke, S. P.

Fan, D. Y.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), pp. 55-58.

Hu, Y. H.

Hunt, J. T.

Jing, F.

L. P. Xie, J. L. Zhao, and F. Jing, “Second-order hot image from a scatterer 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]

L. P. Xie, J. L. Zhao, J. Q. Su, F. Jing, W. Y. Wang, and H. S. Peng, “Theoretical analysis of hot-image effect from phase scatterer,” Acta Phys. Sin. 53, 2175-2179 (2004) (in Chinese).

Li, D.

T. Peng, J. L. Zhao, D. Li, L. P. Xie, and Z. J. Ye, “Simulation analysis of the evolution of the hot-images induced by coplanar multi-scatterers,” Chin. Phys. 18, 1884-1890(2009).
[CrossRef]

D. Li, J. L. Zhao, T. Peng, and Z. J. Ye, “Hot images induced by arrayed mechanical defects in high-power laser system with cascaded medium,” Opt. Eng. 47, 114202 (2008).
[CrossRef]

Lukishova, S. G.

S. G. Lukishova, Y. V. Senatsky, N. E. Bykovsky, and A. S. Scheulin, “Beam shaping and suppression of self-focusing in high-peak power Nd:glass laser systems,” in Self-Focusing: Past and Present. Fundamentals and Prospects, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., Vol. 114 of Spinger Series in Topics in Applied Physics (Springer, 2008), Chap. 8, pp. 191-229.
[CrossRef]

Manes, K. R.

Milam, D.

Nickels, M. 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]

L. P. Xie, J. L. Zhao, J. Q. Su, F. Jing, W. Y. Wang, and H. S. Peng, “Theoretical analysis of hot-image effect from phase scatterer,” Acta Phys. Sin. 53, 2175-2179 (2004) (in Chinese).

Peng, T.

T. Peng, J. L. Zhao, D. Li, L. P. Xie, and Z. J. Ye, “Simulation analysis of the evolution of the hot-images induced by coplanar multi-scatterers,” Chin. Phys. 18, 1884-1890(2009).
[CrossRef]

D. Li, J. L. Zhao, T. Peng, and Z. J. Ye, “Hot images induced by arrayed mechanical defects in high-power laser system with cascaded medium,” Opt. Eng. 47, 114202 (2008).
[CrossRef]

T. Peng, J. L. Zhao, L. P. Xie, Z. J. Ye, H. H. Wei, J. Q. Su, and J. P. Zhao, “Simulation analysis of the restraining effect of a spatial filter on a hot image,” Appl. Opt. 46, 3205-3209(2007).
[CrossRef] [PubMed]

Renard, P. A.

Scheulin, A. S.

S. G. Lukishova, Y. V. Senatsky, N. E. Bykovsky, and A. S. Scheulin, “Beam shaping and suppression of self-focusing in high-peak power Nd:glass laser systems,” in Self-Focusing: Past and Present. Fundamentals and Prospects, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., Vol. 114 of Spinger Series in Topics in Applied Physics (Springer, 2008), Chap. 8, pp. 191-229.
[CrossRef]

Senatskii, Y. V.

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel'dovich, and Y. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362-1366 (1975).
[CrossRef]

Senatsky, Y. V.

S. G. Lukishova, Y. V. Senatsky, N. E. Bykovsky, and A. S. Scheulin, “Beam shaping and suppression of self-focusing in high-peak power Nd:glass laser systems,” in Self-Focusing: Past and Present. Fundamentals and Prospects, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., Vol. 114 of Spinger Series in Topics in Applied Physics (Springer, 2008), Chap. 8, pp. 191-229.
[CrossRef]

Su, J. Q.

T. Peng, J. L. Zhao, L. P. Xie, Z. J. Ye, H. H. Wei, J. Q. Su, and J. P. Zhao, “Simulation analysis of the restraining effect of a spatial filter on a hot image,” Appl. Opt. 46, 3205-3209(2007).
[CrossRef] [PubMed]

L. P. Xie, J. L. Zhao, J. Q. Su, F. Jing, W. Y. Wang, and H. S. Peng, “Theoretical analysis of hot-image effect from phase scatterer,” Acta Phys. Sin. 53, 2175-2179 (2004) (in Chinese).

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]

Talanov, V. I.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307-310(1966).

Tang, Z. X.

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]

L. P. Xie, J. L. Zhao, J. Q. Su, F. Jing, W. Y. Wang, and H. S. Peng, “Theoretical analysis of hot-image effect from phase scatterer,” Acta Phys. Sin. 53, 2175-2179 (2004) (in Chinese).

Wang, X.

X. Wang, “On the beam intensity irregularities induced by the 3rd order nonlinear effect in ICF drivers,” Master's thesis (Sichuan University, 2003), pp. 39-40 (in Chinese).

Wang, Y. W.

Wei, H. H.

Wen, S. C.

Widmayer, C. C.

Xie, L. P.

T. Peng, J. L. Zhao, D. Li, L. P. Xie, and Z. J. Ye, “Simulation analysis of the evolution of the hot-images induced by coplanar multi-scatterers,” Chin. Phys. 18, 1884-1890(2009).
[CrossRef]

T. Peng, J. L. Zhao, L. P. Xie, Z. J. Ye, H. H. Wei, J. Q. Su, and J. P. Zhao, “Simulation analysis of the restraining effect of a spatial filter on a hot image,” Appl. Opt. 46, 3205-3209(2007).
[CrossRef] [PubMed]

L. P. Xie, J. L. Zhao, and F. Jing, “Second-order hot image from a scatterer 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]

L. P. Xie, J. L. Zhao, J. Q. Su, F. Jing, W. Y. Wang, and H. S. Peng, “Theoretical analysis of hot-image effect from phase scatterer,” Acta Phys. Sin. 53, 2175-2179 (2004) (in Chinese).

Ye, Z. J.

T. Peng, J. L. Zhao, D. Li, L. P. Xie, and Z. J. Ye, “Simulation analysis of the evolution of the hot-images induced by coplanar multi-scatterers,” Chin. Phys. 18, 1884-1890(2009).
[CrossRef]

D. Li, J. L. Zhao, T. Peng, and Z. J. Ye, “Hot images induced by arrayed mechanical defects in high-power laser system with cascaded medium,” Opt. Eng. 47, 114202 (2008).
[CrossRef]

T. Peng, J. L. Zhao, L. P. Xie, Z. J. Ye, H. H. Wei, J. Q. Su, and J. P. Zhao, “Simulation analysis of the restraining effect of a spatial filter on a hot image,” Appl. Opt. 46, 3205-3209(2007).
[CrossRef] [PubMed]

You, K. M.

Y. W. Wang, J. Q. Deng, L. Z. Chen, S. C. Wen, and K. M. You, “Formation of hot-images in laser beams through a self-defocusing Kerr medium slab,” Chin. Phys. Lett. 26, 024205-1-4 (2009).

Y. W. Wang, S. C. Wen, K. M. You, Z. X. Tang, J. Q. Deng, L. F. Zhang, and D. Y. Fan, “Multiple hot images from an obscuration in an intense laser beam through cascaded Kerr medium disks,” Appl. Opt. 47, 5668-5681 (2008).
[CrossRef] [PubMed]

Zel'dovich, B. Ya.

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel'dovich, and Y. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362-1366 (1975).
[CrossRef]

Zhang, L. F.

Zhao, J. L.

T. Peng, J. L. Zhao, D. Li, L. P. Xie, and Z. J. Ye, “Simulation analysis of the evolution of the hot-images induced by coplanar multi-scatterers,” Chin. Phys. 18, 1884-1890(2009).
[CrossRef]

D. Li, J. L. Zhao, T. Peng, and Z. J. Ye, “Hot images induced by arrayed mechanical defects in high-power laser system with cascaded medium,” Opt. Eng. 47, 114202 (2008).
[CrossRef]

T. Peng, J. L. Zhao, L. P. Xie, Z. J. Ye, H. H. Wei, J. Q. Su, and J. P. Zhao, “Simulation analysis of the restraining effect of a spatial filter on a hot image,” Appl. Opt. 46, 3205-3209(2007).
[CrossRef] [PubMed]

L. P. Xie, J. L. Zhao, and F. Jing, “Second-order hot image from a scatterer 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]

L. P. Xie, J. L. Zhao, J. Q. Su, F. Jing, W. Y. Wang, and H. S. Peng, “Theoretical analysis of hot-image effect from phase scatterer,” Acta Phys. Sin. 53, 2175-2179 (2004) (in Chinese).

Zhao, J. P.

Acta Phys. Sin.

L. P. Xie, J. L. Zhao, J. Q. Su, F. Jing, W. Y. Wang, and H. S. Peng, “Theoretical analysis of hot-image effect from phase scatterer,” Acta Phys. Sin. 53, 2175-2179 (2004) (in Chinese).

Appl. Opt.

Chin. Phys.

T. Peng, J. L. Zhao, D. Li, L. P. Xie, and Z. J. Ye, “Simulation analysis of the evolution of the hot-images induced by coplanar multi-scatterers,” Chin. Phys. 18, 1884-1890(2009).
[CrossRef]

Chin. Phys. Lett.

Y. W. Wang, J. Q. Deng, L. Z. Chen, S. C. Wen, and K. M. You, “Formation of hot-images in laser beams through a self-defocusing Kerr medium slab,” Chin. Phys. Lett. 26, 024205-1-4 (2009).

JETP Lett.

V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307-310(1966).

Opt. Commun.

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]

Opt. Eng.

D. Li, J. L. Zhao, T. Peng, and Z. J. Ye, “Hot images induced by arrayed mechanical defects in high-power laser system with cascaded medium,” Opt. Eng. 47, 114202 (2008).
[CrossRef]

Sov. J. Quantum Electron.

N. B. Baranova, N. E. Bykovskii, B. Ya. Zel'dovich, and Y. V. Senatskii, “Diffraction and self-focusing during amplification of high-power light pulses,” Sov. J. Quantum Electron. 4, 1362-1366 (1975).
[CrossRef]

Other

S. G. Lukishova, Y. V. Senatsky, N. E. Bykovsky, and A. S. Scheulin, “Beam shaping and suppression of self-focusing in high-peak power Nd:glass laser systems,” in Self-Focusing: Past and Present. Fundamentals and Prospects, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., Vol. 114 of Spinger Series in Topics in Applied Physics (Springer, 2008), Chap. 8, pp. 191-229.
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968), pp. 55-58.

A. J. Campillo, “Small-scale self-focusing,” in Self-Focusing: Past and Present. Fundamentals and Prospects, R. W. Boyd, S. G. Lukishova, and Y. R. Shen, eds., Vol. 114 of Spinger Series in Topics in Applied Physics (Springer , 2008), Chap. 6, pp. 157-173.

X. Wang, “On the beam intensity irregularities induced by the 3rd order nonlinear effect in ICF drivers,” Master's thesis (Sichuan University, 2003), pp. 39-40 (in Chinese).

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Figures (6)

Fig. 1
Fig. 1

Formation mechanism of the LIM image.

Fig. 2
Fig. 2

Intensity distributions on (a) the LIM image plane and (b) the hot image plane.

Fig. 3
Fig. 3

Relative intensity on the LIM image plane versus the amplitude modulation coefficient of the obscuration.

Fig. 4
Fig. 4

Relative intensity on the LIM image plane versus the thickness of the nonlinear medium.

Fig. 5
Fig. 5

LIM image distance d 1 versus the obscuration distance d 0 .

Fig. 6
Fig. 6

Intensity of the laser beam at different distances from the rear surface of the nonlinear medium.

Equations (7)

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

E ( x , y , 0 ) = A 0 [ 1 τ 1 ( x , y ) ] exp ( i k z ) = E 1 ( x , y , 0 ) + E 2 ( x , y , 0 ) ,
τ 0 ( x , y ) = 1 τ 1 ( x , y ) = { τ exp ( i θ ) inside the obscuration 1 outside the obscuration ,
[ u v ] = exp [ ( β α ) 2 L ] [ cos θ 2 sin θ 2 sin θ 2 cos θ 2 ] × [ cosh ( g L ) q 2 2 k 0 g sinh ( g L ) 2 k 0 g q 2 sinh ( g L ) cosh ( g L ) ] [ cos θ 1 sin θ 1 sin θ 1 cos θ 1 ] [ u 0 ( q x , q y , 0 ) v 0 ( q x , q y , 0 ) ] ,
g = q 2 ( q c 2 q 2 ) / 4 k 2 ,
E 2 ( x , y , z ) = F { u + i v } = exp [ ( β α ) 2 L ] F { i [ ( k 0 g q 2 + q 2 4 k 0 g ) sinh ( g L ) ] ( u 0 i v 0 ) e i ( θ 2 θ 1 ) + [ ( cosh ( g L ) + i ( k 0 g q 2 q 2 4 k 0 g ) sinh ( g L ) ) ] ( u 0 + i v 0 ) e i ( θ 1 + θ 2 ) } ,
I = exp [ ( β α ) L ] | 1 + F { [ cosh ( g L ) + i ( k 0 g q 2 q 2 4 k 0 g ) sinh ( g L ) ] ( u 0 + i v 0 ) } | 2 I 0 .
I = exp [ ( β α ) L ] | 1 + [ cosh ( g m L ) + i ( k 0 g m ( q ) m 2 ( q ) m 2 4 k 0 g m ) sinh ( g m L ) ] τ 1 * ( x , y ) | 2 I 0 = exp [ ( β α ) L ] { 1 + cosh 2 [ B e ( β α ) L 1 ( β α ) L ] ( 1 + τ 2 2 τ cos θ ) 2 ( 1 τ cos θ ) cosh [ B e ( β α ) L 1 ( β α ) L ] } I 0 ,

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