Abstract

Based on the restraining effect that spatial filtering has on the frequency spectrum of a beam, from the small-scale focusing theory of Bespalov and Talanov (B-T theory) we derive an expression for the pinhole diameter of the spatial filter corresponding to the fastest growing frequency. Then, compared with the theoretical pinhole diameter of the spatial filter, the restraining effect of the spatial filter on a hot image with different pinhole diameters is numerically investigated. The numerical results show that, if the pinhole diameter is larger than the theoretical one, the hot-image intensity will remain steady; once the pinhole diameter becomes smaller than the theoretical one, the hot-image intensity will begin to decrease. Moreover, as the pinhole diameter decreases, a more prominent restraining effect can be obtained. But reducing the diameter of the spatial filter would lead to greater beam energy loss. The parameters of the spatial filter must be chosen to guarantee that the scheme fulfills the demand for low beam energy loss and a satisfactory restraining effect simultaneously.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  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. H. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, "Modeling of self-focusing experiments by beam propagation codes," in ICF Quarterly Report October-December 1995, UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1995), pp. 1-8.
  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. L. Xie, J. Zhao, J. Su, F. Jing, W. Wang, and H. Peng, "Theoretical analysis of hot image effect from phase scatterer," Acta Phys. Sin. 53, 2175-2179 (2004) (in Chinese).
  5. L. Xie, J. Su, F. Jing, J. Zhao, W. Wang, X. Wang, and Z. Peng, "Nonlinear hot holographic image in high power solid-state laser systems," High Power Laser Part. Beams 16, 547-550 (2004) (in Chinese).
  6. L. Xie, F. Jing, J. Zhao, J. Su, W. Wang, and H. Peng, "Nonlinear hot-image formation of an intense laser beam in media with gain and loss," Opt. Commun. 236, 343-348 (2004).
    [CrossRef]
  7. L. Xie, J. Zhao, and F. Jing, "Second-order hot-image from a scaterer in high-power laser system," Appl. Opt. 44, 2553-2557 (2005).
    [CrossRef] [PubMed]
  8. V. I. Bespalov and V. I. Talanov, "Filamentary structure of light beams in nonlinear liquids," JETP Lett. 3, 307-310 (1966).
  9. A. J. Campillo, S. L. Shapiro, and B. R. Suydam, "Periodic breakup of optical beams due to self-focusing," Appl. Phys. Lett. 13, 628-630 (1973).
    [CrossRef]
  10. J. A. Fleck, J. R. Morris, and E. S. Bliss, "Small-scale self-focusing effect in a high power glass laser amplifier," IEEE J. Quantum Electron. QE-14, 353-363 (1978).
    [CrossRef]

2005 (1)

2004 (3)

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

L. Xie, J. Su, F. Jing, J. Zhao, W. Wang, X. Wang, and Z. Peng, "Nonlinear hot holographic image in high power solid-state laser systems," High Power Laser Part. Beams 16, 547-550 (2004) (in Chinese).

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

1997 (1)

1993 (1)

1978 (1)

J. A. Fleck, J. R. Morris, and E. S. Bliss, "Small-scale self-focusing effect in a high power glass laser amplifier," IEEE J. Quantum Electron. QE-14, 353-363 (1978).
[CrossRef]

1973 (1)

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, "Periodic breakup of optical beams due to self-focusing," Appl. Phys. Lett. 13, 628-630 (1973).
[CrossRef]

1966 (1)

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

Bespalov, V. I.

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

Bliss, E. S.

J. A. Fleck, J. R. Morris, and E. S. Bliss, "Small-scale self-focusing effect in a high power glass laser amplifier," IEEE J. Quantum Electron. QE-14, 353-363 (1978).
[CrossRef]

Campillo, A. J.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, "Periodic breakup of optical beams due to self-focusing," Appl. Phys. Lett. 13, 628-630 (1973).
[CrossRef]

deSzoeke, S. P.

Eimerl, D.

W. H. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, "Modeling of self-focusing experiments by beam propagation codes," in ICF Quarterly Report October-December 1995, UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1995), pp. 1-8.

Fleck, J. A.

J. A. Fleck, J. R. Morris, and E. S. Bliss, "Small-scale self-focusing effect in a high power glass laser amplifier," IEEE J. Quantum Electron. QE-14, 353-363 (1978).
[CrossRef]

Hunt, J. T.

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

W. H. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, "Modeling of self-focusing experiments by beam propagation codes," in ICF Quarterly Report October-December 1995, UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1995), pp. 1-8.

Jing, F.

L. Xie, J. Zhao, and F. Jing, "Second-order hot-image from a scaterer in high-power laser system," Appl. Opt. 44, 2553-2557 (2005).
[CrossRef] [PubMed]

L. Xie, J. Su, F. Jing, J. Zhao, W. Wang, X. Wang, and Z. Peng, "Nonlinear hot holographic image in high power solid-state laser systems," High Power Laser Part. Beams 16, 547-550 (2004) (in Chinese).

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

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

Manes, K. R.

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

W. H. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, "Modeling of self-focusing experiments by beam propagation codes," in ICF Quarterly Report October-December 1995, UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1995), pp. 1-8.

Milam, D.

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. H. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, "Modeling of self-focusing experiments by beam propagation codes," in ICF Quarterly Report October-December 1995, UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1995), pp. 1-8.

Morris, J. R.

J. A. Fleck, J. R. Morris, and E. S. Bliss, "Small-scale self-focusing effect in a high power glass laser amplifier," IEEE J. Quantum Electron. QE-14, 353-363 (1978).
[CrossRef]

Peng, H.

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

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

Peng, Z.

L. Xie, J. Su, F. Jing, J. Zhao, W. Wang, X. Wang, and Z. Peng, "Nonlinear hot holographic image in high power solid-state laser systems," High Power Laser Part. Beams 16, 547-550 (2004) (in Chinese).

Renard, P. A.

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

W. H. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, "Modeling of self-focusing experiments by beam propagation codes," in ICF Quarterly Report October-December 1995, UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1995), pp. 1-8.

Shapiro, S. L.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, "Periodic breakup of optical beams due to self-focusing," Appl. Phys. Lett. 13, 628-630 (1973).
[CrossRef]

Su, J.

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

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

L. Xie, J. Su, F. Jing, J. Zhao, W. Wang, X. Wang, and Z. Peng, "Nonlinear hot holographic image in high power solid-state laser systems," High Power Laser Part. Beams 16, 547-550 (2004) (in Chinese).

Suydam, B. R.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, "Periodic breakup of optical beams due to self-focusing," Appl. Phys. Lett. 13, 628-630 (1973).
[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).

Wang, W.

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

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

L. Xie, J. Su, F. Jing, J. Zhao, W. Wang, X. Wang, and Z. Peng, "Nonlinear hot holographic image in high power solid-state laser systems," High Power Laser Part. Beams 16, 547-550 (2004) (in Chinese).

Wang, X.

L. Xie, J. Su, F. Jing, J. Zhao, W. Wang, X. Wang, and Z. Peng, "Nonlinear hot holographic image in high power solid-state laser systems," High Power Laser Part. Beams 16, 547-550 (2004) (in Chinese).

Widmayer, C. C.

Williams, W. H.

W. H. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, "Modeling of self-focusing experiments by beam propagation codes," in ICF Quarterly Report October-December 1995, UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1995), pp. 1-8.

Xie, L.

L. Xie, J. Zhao, and F. Jing, "Second-order hot-image from a scaterer in high-power laser system," Appl. Opt. 44, 2553-2557 (2005).
[CrossRef] [PubMed]

L. Xie, J. Su, F. Jing, J. Zhao, W. Wang, X. Wang, and Z. Peng, "Nonlinear hot holographic image in high power solid-state laser systems," High Power Laser Part. Beams 16, 547-550 (2004) (in Chinese).

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

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

Zhao, J.

L. Xie, J. Zhao, and F. Jing, "Second-order hot-image from a scaterer in high-power laser system," Appl. Opt. 44, 2553-2557 (2005).
[CrossRef] [PubMed]

L. Xie, J. Su, F. Jing, J. Zhao, W. Wang, X. Wang, and Z. Peng, "Nonlinear hot holographic image in high power solid-state laser systems," High Power Laser Part. Beams 16, 547-550 (2004) (in Chinese).

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

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

Acta Phys. Sin. (1)

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

Appl. Opt. (3)

Appl. Phys. Lett. (1)

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, "Periodic breakup of optical beams due to self-focusing," Appl. Phys. Lett. 13, 628-630 (1973).
[CrossRef]

High Power Laser Part. Beams (1)

L. Xie, J. Su, F. Jing, J. Zhao, W. Wang, X. Wang, and Z. Peng, "Nonlinear hot holographic image in high power solid-state laser systems," High Power Laser Part. Beams 16, 547-550 (2004) (in Chinese).

IEEE J. Quantum Electron. (1)

J. A. Fleck, J. R. Morris, and E. S. Bliss, "Small-scale self-focusing effect in a high power glass laser amplifier," IEEE J. Quantum Electron. QE-14, 353-363 (1978).
[CrossRef]

JETP Lett. (1)

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

Opt. Commun. (1)

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

Other (1)

W. H. Williams, P. A. Renard, K. R. Manes, D. Milam, J. T. Hunt, and D. Eimerl, "Modeling of self-focusing experiments by beam propagation codes," in ICF Quarterly Report October-December 1995, UCRL-LR-105821-96-1 (Lawrence Livermore National Laboratory, 1995), pp. 1-8.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Principle of restraining a hot-image by using a spatial filter system.

Fig. 2
Fig. 2

Configuration of the spatial filter system.

Fig. 3
Fig. 3

Program flow chart for the spatial filtering system.

Fig. 4
Fig. 4

Beam peak intensity with different pinhole diameters of the spatial filters.

Fig. 5
Fig. 5

Intensity distribution in the hot-image plane with different pinhole diameters of the spatial filters.

Fig. 6
Fig. 6

Beam intensity distribution at the front surface of the nonlinear medium with different pinhole diameters of the spatial filters.

Fig. 7
Fig. 7

Beam peak intensity for the spatial filter system at different positions between the scatterer and the front surface of the nonlinear medium.

Fig. 8
Fig. 8

Intensity distribution in the hot-image plane for the spatial filter system in different positions between the scatterer and the front surface of the nonlinear medium.

Fig. 9
Fig. 9

Restraining effects on the hot image with the same pinhole diameter of the spatial filter but different sizes of scatterers. Curves 1, 3, 5 refer to the scatterer radii of 0.15, 0.2, and 0.3 cm, respectively, with no spatial filter; curves 2, 4, 6 refer to the same scatterers when the pinhole diameter is 0.5 cm.

Equations (9)

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

k x = k 0 sin θ ,
k x = k 0 θ .
θ m = k m / k 0 .
θ vac = n 0 θ med ,
θ c = d / 2 f 1 ,
θ c θ vac = n 0 θ med = n 0 θ m .
d ( 2 f 1 / k vac ) k m ,
k m 2 = k 0 2 n 2 n 0 | A | 2 = 2 k 0 2 n 2 I 0 n 0 2 c ε 0 = 2 k vac 2 n 2 I 0 c ε 0 = k vac 2 n 0 γ I 0 ,
d 2 f 1 k vac k m = 2 f 1 k vac k vac 2 n 0 γ I 0 = 2 f 1 n 0 γ I 0 .

Metrics