Abstract

The formation of nonlinear holographic images behind a multislab amplifier is studied. The analytical expressions describing magnitudes and locations of intensity maxima depending on the corresponding image number are derived. Comparison with numerical calculations results is given. On the basis of numerical modeling, analysis of gain saturation, slab thickness, and slab aberrations influence is carried out.

© 2012 Optical Society of America

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References

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  1. V. I. Talanov, “On self-focusing of electromagnetic waves in a nonlinear medium,” Izv. Vuzov, Radiophysica 7, 564–565 (1964).
  2. V. I. Bespalov, and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–309 (1966).
  3. J. T. Hunt, K. R. Manes, and P. A. Renard, “Hot images from obscurations,” Appl. Opt. 32, 5973–5982 (1993).
    [CrossRef]
  4. S. G. Garanin, I. V. Epatko, R. I. Istomin, L. V. L’vov, A. A. Malyutin, V. R. Serov, and S. A. Sukharev, “Risky intensity peaks resulting from nonlinear holographic imaging,” Appl. Opt. 50, 3733–3741 (2011).
    [CrossRef]
  5. M. D. Feit, C. C. Widmayer, W. H. Williams, R. A. Sachs, P. A. Renard, and M. A. Henessian, “The NIF’s assessment of the optical damage threat for flat-in-time pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.
  6. M. D. Feit, W. H. Williams, C. C. Widmayer, R. A. Sacks, P. A. Renard, and M. A. Henesian, “The NIF’s assessment of the optical damage threat for shaped ICF pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.
  7. D. Li, J. Zhao, T. Peng, and Z. Ye, “Hot images induced by arrayed mechanical defects in high-power laser system with cascaded medium,” Opt. Eng. 47, 114202 (2008).
    [CrossRef]
  8. Y. Wang, S. Wen, K. You, Z. Tang, J. Deng, L. Zhang, and D. Fan, “Multiple hot images from an obscuration in an intense laser beam through cascaded Kerr medium disks,” Appl. Opt. 47, 5668–5681 (2008).
    [CrossRef]
  9. T. Peng, J. Zhao, and D. Li, “Theoretical analysis of hot-image effect in a high-power laser system with cascaded nonlinear medium,” Opt. Lasers Eng. 49, 972–978 (2011).
    [CrossRef]
  10. I. V. Epatko, A. A. Malyutin, R. V. Serov, and D. A. Solov’ev, “Inclusion of aberrations of a tilted plane-parallel plate in diffraction calculations of the propagation of radiation,” Quantum Electron. 28, 703–706 (1998).
    [CrossRef]
  11. R. A. Sacks, M. A. Henesian, S. W. Haney, and J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Annual Report, UCRL-LR-105821-96, 1996, p. 207.
  12. I. V. Epatko and R. V. Serov, “Advantage of fast Fourier interpolation for laser modeling,” J. Phys. IV France 133, 679–682 (2006).
    [CrossRef]

2011 (2)

S. G. Garanin, I. V. Epatko, R. I. Istomin, L. V. L’vov, A. A. Malyutin, V. R. Serov, and S. A. Sukharev, “Risky intensity peaks resulting from nonlinear holographic imaging,” Appl. Opt. 50, 3733–3741 (2011).
[CrossRef]

T. Peng, J. Zhao, and D. Li, “Theoretical analysis of hot-image effect in a high-power laser system with cascaded nonlinear medium,” Opt. Lasers Eng. 49, 972–978 (2011).
[CrossRef]

2008 (2)

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

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

2006 (1)

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

1998 (1)

I. V. Epatko, A. A. Malyutin, R. V. Serov, and D. A. Solov’ev, “Inclusion of aberrations of a tilted plane-parallel plate in diffraction calculations of the propagation of radiation,” Quantum Electron. 28, 703–706 (1998).
[CrossRef]

1993 (1)

1966 (1)

V. I. Bespalov, and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–309 (1966).

1964 (1)

V. I. Talanov, “On self-focusing of electromagnetic waves in a nonlinear medium,” Izv. Vuzov, Radiophysica 7, 564–565 (1964).

Bespalov, V. I.

V. I. Bespalov, and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–309 (1966).

Deng, J.

Epatko, I. V.

S. G. Garanin, I. V. Epatko, R. I. Istomin, L. V. L’vov, A. A. Malyutin, V. R. Serov, and S. A. Sukharev, “Risky intensity peaks resulting from nonlinear holographic imaging,” Appl. Opt. 50, 3733–3741 (2011).
[CrossRef]

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

I. V. Epatko, A. A. Malyutin, R. V. Serov, and D. A. Solov’ev, “Inclusion of aberrations of a tilted plane-parallel plate in diffraction calculations of the propagation of radiation,” Quantum Electron. 28, 703–706 (1998).
[CrossRef]

Fan, D.

Feit, M. D.

M. D. Feit, C. C. Widmayer, W. H. Williams, R. A. Sachs, P. A. Renard, and M. A. Henessian, “The NIF’s assessment of the optical damage threat for flat-in-time pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

M. D. Feit, W. H. Williams, C. C. Widmayer, R. A. Sacks, P. A. Renard, and M. A. Henesian, “The NIF’s assessment of the optical damage threat for shaped ICF pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

Garanin, S. G.

Haney, S. W.

R. A. Sacks, M. A. Henesian, S. W. Haney, and J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Annual Report, UCRL-LR-105821-96, 1996, p. 207.

Henesian, M. A.

R. A. Sacks, M. A. Henesian, S. W. Haney, and J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Annual Report, UCRL-LR-105821-96, 1996, p. 207.

M. D. Feit, W. H. Williams, C. C. Widmayer, R. A. Sacks, P. A. Renard, and M. A. Henesian, “The NIF’s assessment of the optical damage threat for shaped ICF pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

Henessian, M. A.

M. D. Feit, C. C. Widmayer, W. H. Williams, R. A. Sachs, P. A. Renard, and M. A. Henessian, “The NIF’s assessment of the optical damage threat for flat-in-time pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

Hunt, J. T.

Istomin, R. I.

L’vov, L. V.

Li, D.

T. Peng, J. Zhao, and D. Li, “Theoretical analysis of hot-image effect in a high-power laser system with cascaded nonlinear medium,” Opt. Lasers Eng. 49, 972–978 (2011).
[CrossRef]

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

Malyutin, A. A.

S. G. Garanin, I. V. Epatko, R. I. Istomin, L. V. L’vov, A. A. Malyutin, V. R. Serov, and S. A. Sukharev, “Risky intensity peaks resulting from nonlinear holographic imaging,” Appl. Opt. 50, 3733–3741 (2011).
[CrossRef]

I. V. Epatko, A. A. Malyutin, R. V. Serov, and D. A. Solov’ev, “Inclusion of aberrations of a tilted plane-parallel plate in diffraction calculations of the propagation of radiation,” Quantum Electron. 28, 703–706 (1998).
[CrossRef]

Manes, K. R.

Peng, T.

T. Peng, J. Zhao, and D. Li, “Theoretical analysis of hot-image effect in a high-power laser system with cascaded nonlinear medium,” Opt. Lasers Eng. 49, 972–978 (2011).
[CrossRef]

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

Renard, P. A.

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

M. D. Feit, C. C. Widmayer, W. H. Williams, R. A. Sachs, P. A. Renard, and M. A. Henessian, “The NIF’s assessment of the optical damage threat for flat-in-time pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

M. D. Feit, W. H. Williams, C. C. Widmayer, R. A. Sacks, P. A. Renard, and M. A. Henesian, “The NIF’s assessment of the optical damage threat for shaped ICF pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

Sachs, R. A.

M. D. Feit, C. C. Widmayer, W. H. Williams, R. A. Sachs, P. A. Renard, and M. A. Henessian, “The NIF’s assessment of the optical damage threat for flat-in-time pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

Sacks, R. A.

M. D. Feit, W. H. Williams, C. C. Widmayer, R. A. Sacks, P. A. Renard, and M. A. Henesian, “The NIF’s assessment of the optical damage threat for shaped ICF pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

R. A. Sacks, M. A. Henesian, S. W. Haney, and J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Annual Report, UCRL-LR-105821-96, 1996, p. 207.

Serov, R. V.

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

I. V. Epatko, A. A. Malyutin, R. V. Serov, and D. A. Solov’ev, “Inclusion of aberrations of a tilted plane-parallel plate in diffraction calculations of the propagation of radiation,” Quantum Electron. 28, 703–706 (1998).
[CrossRef]

Serov, V. R.

Solov’ev, D. A.

I. V. Epatko, A. A. Malyutin, R. V. Serov, and D. A. Solov’ev, “Inclusion of aberrations of a tilted plane-parallel plate in diffraction calculations of the propagation of radiation,” Quantum Electron. 28, 703–706 (1998).
[CrossRef]

Sukharev, S. A.

Talanov, V. I.

V. I. Bespalov, and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–309 (1966).

V. I. Talanov, “On self-focusing of electromagnetic waves in a nonlinear medium,” Izv. Vuzov, Radiophysica 7, 564–565 (1964).

Tang, Z.

Trenholme, J. B.

R. A. Sacks, M. A. Henesian, S. W. Haney, and J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Annual Report, UCRL-LR-105821-96, 1996, p. 207.

Wang, Y.

Wen, S.

Widmayer, C. C.

M. D. Feit, W. H. Williams, C. C. Widmayer, R. A. Sacks, P. A. Renard, and M. A. Henesian, “The NIF’s assessment of the optical damage threat for shaped ICF pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

M. D. Feit, C. C. Widmayer, W. H. Williams, R. A. Sachs, P. A. Renard, and M. A. Henessian, “The NIF’s assessment of the optical damage threat for flat-in-time pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

Williams, W. H.

M. D. Feit, C. C. Widmayer, W. H. Williams, R. A. Sachs, P. A. Renard, and M. A. Henessian, “The NIF’s assessment of the optical damage threat for flat-in-time pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

M. D. Feit, W. H. Williams, C. C. Widmayer, R. A. Sacks, P. A. Renard, and M. A. Henesian, “The NIF’s assessment of the optical damage threat for shaped ICF pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

Ye, Z.

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

You, K.

Zhang, L.

Zhao, J.

T. Peng, J. Zhao, and D. Li, “Theoretical analysis of hot-image effect in a high-power laser system with cascaded nonlinear medium,” Opt. Lasers Eng. 49, 972–978 (2011).
[CrossRef]

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

Appl. Opt. (3)

Izv. Vuzov, Radiophysica (1)

V. I. Talanov, “On self-focusing of electromagnetic waves in a nonlinear medium,” Izv. Vuzov, Radiophysica 7, 564–565 (1964).

J. Phys. IV France (1)

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

JETP Lett. (1)

V. I. Bespalov, and V. I. Talanov, “Filamentary structure of light beams in nonlinear liquids,” JETP Lett. 3, 307–309 (1966).

Opt. Eng. (1)

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

Opt. Lasers Eng. (1)

T. Peng, J. Zhao, and D. Li, “Theoretical analysis of hot-image effect in a high-power laser system with cascaded nonlinear medium,” Opt. Lasers Eng. 49, 972–978 (2011).
[CrossRef]

Quantum Electron. (1)

I. V. Epatko, A. A. Malyutin, R. V. Serov, and D. A. Solov’ev, “Inclusion of aberrations of a tilted plane-parallel plate in diffraction calculations of the propagation of radiation,” Quantum Electron. 28, 703–706 (1998).
[CrossRef]

Other (3)

R. A. Sacks, M. A. Henesian, S. W. Haney, and J. B. Trenholme, “The PROP92 Fourier beam propagation code,” ICF Annual Report, UCRL-LR-105821-96, 1996, p. 207.

M. D. Feit, C. C. Widmayer, W. H. Williams, R. A. Sachs, P. A. Renard, and M. A. Henessian, “The NIF’s assessment of the optical damage threat for flat-in-time pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

M. D. Feit, W. H. Williams, C. C. Widmayer, R. A. Sacks, P. A. Renard, and M. A. Henesian, “The NIF’s assessment of the optical damage threat for shaped ICF pulses,” presented at the 3rd International Conference on Solid-state Lasers for Applications to Inertial Confinement Fusion, Monterey, California, USA, June 1998.

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Figures (11)

Fig. 1.
Fig. 1.

Sketch of the NHI formation for the SPLNM. Only first-order waves are considered. The thin ascending arrow represents the scattered wave at the input of SPLNM. The thick arrow is the amplified diverging wave at the output of SPLNM. The descending dotted arrows represent the first-order waves focusing in the appropriate NHI.

Fig. 2.
Fig. 2.

Sketch of the second-order waves focusing in the jth NHI for the SPLNM. Grey rhombuses mark planes where the new waves are generated according to Eq. (1).

Fig. 3.
Fig. 3.

Sketch of the fifth-order waves generation as the addition to the third-order wave focusing in the j-th NHI.

Fig. 4.
Fig. 4.

Peak intensity evolution for the system of nine NM and opaque disk obstacles. Along Z axis the distance from the last (the ninth) NM is represented. The roman numerals show the NHI plane number. The peak intensity means the biggest intensity in some plane, and the maximum intensity means the biggest intensity that is reached in the vicinity of the corresponding image plane.

Fig. 5.
Fig. 5.

2D intensity distributions and their cross sections for two different distances Z=220cm (a) and Z=860cm (b) from the last NM. The length of square side for a and b is 4 mm. The obstacle diameter is 0.4 mm.

Fig. 6.
Fig. 6.

Peak intensity evolution in the vicinity of the first and the second NHI. Black triangles and open squares mark the points calculated under Eq. (9) when Eqs. (5) and (7) were used for phase and amplitude.

Fig. 7.
Fig. 7.

Peak intensity evolution for the system of nine NM with finite thickness.

Fig. 8.
Fig. 8.

Maximal intensities in the vicinity of the appropriate NHI when the obstacle size is 0.2 mm. The white (open) bars correspond to the constant increment of B-integral per slab and the shaded bars for increasing increment of B-integral in MSA (see Table 2).

Fig. 9.
Fig. 9.

Input (dashed line) and output (solid line) temporal shapes.

Fig. 10.
Fig. 10.

Calculated maximal fluence in the vicinity of the appropriate NHI for MSA. The results calculated allow for the pulse temporal shape evolution compared to the results for the pulse with constant rectangular temporal shape. Obstacle size is 0.2 mm.

Fig. 11.
Fig. 11.

Influence of astigmatism aberration that appears when diverging and converging scattered beams propagate through the system of tilted slabs. The obstacle size is 0.2 mm.

Tables (2)

Tables Icon

Table 1. Magnitudes of Amplitude and Phase in the NHI planes, Maximum Intensity in the Vicinity of the Corresponding NHI According to Eq. (8)

Tables Icon

Table 2. B-integral Increment for Different Slabs

Equations (15)

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

As(x,y)=A0[τobsexp(iψobs)1]=|As|exp(iψs),
|As|=|A0|(τobs2sin2(ψobs)+(τobscos(ψobs)1)2)0.5
ψs=arctan(τobssin(ψobs)/(τobscos(ψobs)1))+π.
A1=iBAS*.
ASout=(1iB)AS.
Aj(1)=(1iB)Kj(iB)((1iB)j1As)*=iB(1iB)Kj(1+iB)j1As*.
|Aj(1)|=|As|B(1+B2)(K1)/2,
ψj=(ψs+π/2)+(2jK1)arctan(B).
|Aj(3)|=|As|B(1+B2)(K1)/2[1+(B2/(1+B2))(j1)(Kj)].
|Aj|=|As|B(1+B2)(K1)/2[1+l=1[(K1)/2]((B2l/(1+B2)l)m=1l(jm)l!m=1l(K+1jm)l!)],
Ijmax=(|A0+Aj|+|Aj|)2.
Ijmax=(|A0+Aj+im=1,mjKAmπzR2L(jm)+iAS(1+B2)K/2πzR2Z0+2(j1)Lexp(iKarctan(B))|+|Aj|)2,zR=d2/4λ.
Qout(i)=τ·Qsatln(1+g(i)(exp(τ·Qin(i)/Qsat)1)),
g(i+1)=g(i)exp(τ·Qin(i)/Qsat)[1+g(i)(exp(τ·Qin(i)/Qsat)1)]1,g(1)=g(x,y).
B(i)=kγ(Iin(i)/n)Δz(G(i)1)/ln(G(i)),

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