Abstract

Frequency modulation to amplitude modulation (FM-to-AM) conversion is an important issue that can prevent fusion ignition with high power lasers such as the Laser MegaJoule (LMJ). On LMJ, most of the FM-to-AM conversion is expected in the so-called frequency conversion and focusing system, which is a nonlinear system. However, we propose linear transfer functions to compensate the effect of frequency conversion on FM-to-AM conversion. We show that most of AM distortion can be reduced by practical systems: for beam intensity up to 3GW/cm2, the FM-to-AM conversion level can be divided by at least 2, and we almost cancel intensity modulation for intensities below 1GW/cm2.

© 2009 Optical Society of America

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  1. www-lmj.cea.fr and www.llnl.gov/nif/project.
  2. J. R. Murray, J. Ray Smith, R. B. Ehrlich, D. T. Karazys, C. E. Thompson, T. L. Weiland, and R. B. Wilcox, “Experimental observation and suppression of transverse stimulated Brillouin scattering in large optical components,” J. Opt. Soc. Am. B 6, 2402-2411 (1989).
    [CrossRef]
  3. J. Garnier, L. Videau, C. Gouédard, and A. Migus, “Statistical analysis for beam smoothing and some applications ,” J. Opt. Soc. Am. A 14, 1928-1937 (1997).
  4. J. E. Rothenberg, D. F. Browning, and R. B. Wilcox, “Issue of FM to AM conversion on the National Ignition Facility,” Proc. SPIE 3492, 51-61 (1999).
    [CrossRef]
  5. J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
    [CrossRef]
  6. D. Penninckx, N. Beck, J.-F. Gleyze, and L. Videau, “Signal propagation over polarization-maintaining fibers: problem and solutions,” J. Lightwave Technol. 24, 4197-4207 (2006).
    [CrossRef]
  7. S. Hocquet, D. Penninckx, É. Bordenave, C. Gouédard, and Y. Jaouën, “FM-to-AM conversion in high power lasers,” Appl. Opt. 47, 3338-3349 (2008).
    [CrossRef] [PubMed]
  8. O. Morice, “Miró: Complete modeling and software for pulse amplification and propagation in high-power laser systems,” Opt. Eng. 42, 1530-1541 (2003).
    [CrossRef]
  9. J. R. Carson, “Notes on the theory of modulation,” Proc. IRE 10, 57-64 (1922).
    [CrossRef]
  10. A. Boscheron, “Etude de nouvelles configurations de conversion de fréquence pour l'optimisation des lasers de haute puissance,” Ph.D. dissertation (Université Paris XI, 1996).
  11. S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys 66, 3456-3462 (1989).
    [CrossRef]
  12. V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strishevkii, “Method for compensating the phase-matching dispersion in nonlinear optics,” Sov. J. Quantum Electron. 4, 1090-1098 (1975).
    [CrossRef]
  13. J. Néauport, N. Blanchot, C. Rouyer, and C. Sauteret, “Chromatism compensation of the PETAL multipetawatt high energy laser,” Appl. Opt. 46, 1568-1574(2007).
    [CrossRef] [PubMed]
  14. L. J. Waxer, J. H. Kelly, J. Rothenberg, A. Babushkin, C. Bibeau, A. Bayramian, and S. Payne, “Precision spectral sculpting for narrow-band amplification of broadband frequency-modulated pulses,” Opt. Lett. 27, 1427-1429(2002).
    [CrossRef]
  15. “Multiple-FM smoothing by spectral dispersion--an augmented laser speckle smoothing scheme,” Lab. Laser Energetics Rev. 114, 73-80 (2008).

2008

“Multiple-FM smoothing by spectral dispersion--an augmented laser speckle smoothing scheme,” Lab. Laser Energetics Rev. 114, 73-80 (2008).

S. Hocquet, D. Penninckx, É. Bordenave, C. Gouédard, and Y. Jaouën, “FM-to-AM conversion in high power lasers,” Appl. Opt. 47, 3338-3349 (2008).
[CrossRef] [PubMed]

2007

2006

2004

J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
[CrossRef]

2003

O. Morice, “Miró: Complete modeling and software for pulse amplification and propagation in high-power laser systems,” Opt. Eng. 42, 1530-1541 (2003).
[CrossRef]

2002

1999

J. E. Rothenberg, D. F. Browning, and R. B. Wilcox, “Issue of FM to AM conversion on the National Ignition Facility,” Proc. SPIE 3492, 51-61 (1999).
[CrossRef]

1997

J. Garnier, L. Videau, C. Gouédard, and A. Migus, “Statistical analysis for beam smoothing and some applications ,” J. Opt. Soc. Am. A 14, 1928-1937 (1997).

1989

J. R. Murray, J. Ray Smith, R. B. Ehrlich, D. T. Karazys, C. E. Thompson, T. L. Weiland, and R. B. Wilcox, “Experimental observation and suppression of transverse stimulated Brillouin scattering in large optical components,” J. Opt. Soc. Am. B 6, 2402-2411 (1989).
[CrossRef]

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys 66, 3456-3462 (1989).
[CrossRef]

1975

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strishevkii, “Method for compensating the phase-matching dispersion in nonlinear optics,” Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

1922

J. R. Carson, “Notes on the theory of modulation,” Proc. IRE 10, 57-64 (1922).
[CrossRef]

Amedt, P.

J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
[CrossRef]

Babushkin, A.

Bayramian, A.

Beck, N.

Berger, R. H.

J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
[CrossRef]

Bibeau, C.

Blanchot, N.

Bordenave, É.

Boscheron, A.

A. Boscheron, “Etude de nouvelles configurations de conversion de fréquence pour l'optimisation des lasers de haute puissance,” Ph.D. dissertation (Université Paris XI, 1996).

Browning, D. F.

J. E. Rothenberg, D. F. Browning, and R. B. Wilcox, “Issue of FM to AM conversion on the National Ignition Facility,” Proc. SPIE 3492, 51-61 (1999).
[CrossRef]

Carson, J. R.

J. R. Carson, “Notes on the theory of modulation,” Proc. IRE 10, 57-64 (1922).
[CrossRef]

Craxton, R. S.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys 66, 3456-3462 (1989).
[CrossRef]

Ehrlich, R. B.

Garnier, J.

J. Garnier, L. Videau, C. Gouédard, and A. Migus, “Statistical analysis for beam smoothing and some applications ,” J. Opt. Soc. Am. A 14, 1928-1937 (1997).

Glendinning, S. G.

J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
[CrossRef]

Glenzer, S. H.

J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
[CrossRef]

Gleyze, J.-F.

Gouédard, C.

S. Hocquet, D. Penninckx, É. Bordenave, C. Gouédard, and Y. Jaouën, “FM-to-AM conversion in high power lasers,” Appl. Opt. 47, 3338-3349 (2008).
[CrossRef] [PubMed]

J. Garnier, L. Videau, C. Gouédard, and A. Migus, “Statistical analysis for beam smoothing and some applications ,” J. Opt. Soc. Am. A 14, 1928-1937 (1997).

Hann, S. W.

J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
[CrossRef]

Hocquet, S.

Jaouën, Y.

Karazys, D. T.

Karpenko, S. G.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strishevkii, “Method for compensating the phase-matching dispersion in nonlinear optics,” Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Kelly, J. H.

Kessler, T.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys 66, 3456-3462 (1989).
[CrossRef]

Kornienko, N. E.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strishevkii, “Method for compensating the phase-matching dispersion in nonlinear optics,” Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Landen, R. L.

J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
[CrossRef]

Letzring, S.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys 66, 3456-3462 (1989).
[CrossRef]

Lindl, J. D.

J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
[CrossRef]

Migus, A.

J. Garnier, L. Videau, C. Gouédard, and A. Migus, “Statistical analysis for beam smoothing and some applications ,” J. Opt. Soc. Am. A 14, 1928-1937 (1997).

Morice, O.

O. Morice, “Miró: Complete modeling and software for pulse amplification and propagation in high-power laser systems,” Opt. Eng. 42, 1530-1541 (2003).
[CrossRef]

Murray, J. R.

Néauport, J.

Payne, S.

Penninckx, D.

Rothenberg, J.

Rothenberg, J. E.

J. E. Rothenberg, D. F. Browning, and R. B. Wilcox, “Issue of FM to AM conversion on the National Ignition Facility,” Proc. SPIE 3492, 51-61 (1999).
[CrossRef]

Rouyer, C.

Sauteret, C.

Short, R. W.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys 66, 3456-3462 (1989).
[CrossRef]

Skupsky, S.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys 66, 3456-3462 (1989).
[CrossRef]

Smith, J. Ray

Soures, J. M.

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys 66, 3456-3462 (1989).
[CrossRef]

Strishevkii, V. L.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strishevkii, “Method for compensating the phase-matching dispersion in nonlinear optics,” Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Suter, L. J.

J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
[CrossRef]

Thompson, C. E.

Videau, L.

D. Penninckx, N. Beck, J.-F. Gleyze, and L. Videau, “Signal propagation over polarization-maintaining fibers: problem and solutions,” J. Lightwave Technol. 24, 4197-4207 (2006).
[CrossRef]

J. Garnier, L. Videau, C. Gouédard, and A. Migus, “Statistical analysis for beam smoothing and some applications ,” J. Opt. Soc. Am. A 14, 1928-1937 (1997).

Volosov, V. D.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strishevkii, “Method for compensating the phase-matching dispersion in nonlinear optics,” Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Waxer, L. J.

Weiland, T. L.

Wilcox, R. B.

Appl. Opt.

J. Appl. Phys

S. Skupsky, R. W. Short, T. Kessler, R. S. Craxton, S. Letzring, and J. M. Soures, “Improved laser-beam uniformity using the angular dispersion of frequency-modulated light,” J. Appl. Phys 66, 3456-3462 (1989).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Lab. Laser Energetics Rev.

“Multiple-FM smoothing by spectral dispersion--an augmented laser speckle smoothing scheme,” Lab. Laser Energetics Rev. 114, 73-80 (2008).

Opt. Eng.

O. Morice, “Miró: Complete modeling and software for pulse amplification and propagation in high-power laser systems,” Opt. Eng. 42, 1530-1541 (2003).
[CrossRef]

Opt. Lett.

Phys. Plasmas

J. D. Lindl, P. Amedt, R. H. Berger, S. G. Glendinning, S. H. Glenzer, S. W. Hann, R. L. Landen, and L. J. Suter, “The physics basis for ignition using indirect-drive targets on National Ignition Facility,” Phys. Plasmas 11, 339-491(2004).
[CrossRef]

Proc. IRE

J. R. Carson, “Notes on the theory of modulation,” Proc. IRE 10, 57-64 (1922).
[CrossRef]

Proc. SPIE

J. E. Rothenberg, D. F. Browning, and R. B. Wilcox, “Issue of FM to AM conversion on the National Ignition Facility,” Proc. SPIE 3492, 51-61 (1999).
[CrossRef]

Sov. J. Quantum Electron.

V. D. Volosov, S. G. Karpenko, N. E. Kornienko, and V. L. Strishevkii, “Method for compensating the phase-matching dispersion in nonlinear optics,” Sov. J. Quantum Electron. 4, 1090-1098 (1975).
[CrossRef]

Statistical analysis for beam smoothing and some applications

J. Garnier, L. Videau, C. Gouédard, and A. Migus, “Statistical analysis for beam smoothing and some applications ,” J. Opt. Soc. Am. A 14, 1928-1937 (1997).

Other

A. Boscheron, “Etude de nouvelles configurations de conversion de fréquence pour l'optimisation des lasers de haute puissance,” Ph.D. dissertation (Université Paris XI, 1996).

www-lmj.cea.fr and www.llnl.gov/nif/project.

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Figures (5)

Fig. 1
Fig. 1

Simple description of frequency conversion and focusing system (SCF) on LMJ. Crystals convert IR into UV thanks to KDP (thickness of 14 mm ) and DKDP ( 10 mm ) crystals with a type I–type II configuration. The plane grating (density grooves of 802.7 mm 1 with an incident angle of 25 ° ) improves efficiency conversion by dispersion: phase mismatch over the spectrum is considerably lowered. The focusing grating separates UV light from first and second harmonics; it also focuses the beam to the target.

Fig. 2
Fig. 2

(a) Spectral acceptance at 3 ω for the frequency conversion system at 2 GW / cm 2 . It filters the phase-modulated optical spectrum (only the smoothing modulation spectrum is represented, f m = 14.25 GHz with m = 15 rad ). (b) Evolution with intensity of the acceptance spectral parameter γ;the higher the intensity, the thinner the filter is. (c) Evolution of β defined by I 3 ω I 1 ω β expressing saturation of frequency conversion. At very low intensity β = 3 . (d) Effect of grating and crystals on FM-to-AM conversion: evolution with the intensity.

Fig. 3
Fig. 3

FM-to-AM conversion distortion criterion α for a different compensation function from Eq. (6) considering only the effect of grating angular dispersion (spectral acceptance is set to have a perfect phase matching over the whole spectrum). For any intensity there is an optimized value that almost cancels intensity modulation.

Fig. 4
Fig. 4

FM-to-AM conversion distortion criterion α for a different compensation function from Eq. (7) considering only the effect of spectral acceptance. For any intensity there is an optimized value that minimizes intensity modulation. The higher the intensity, the less efficient the compensation.

Fig. 5
Fig. 5

FM-to-AM conversion distortion criterion α for different intensities: (Diamond-shaped points) Intensity modulation for initial system without compensation. (Cross-shaped points) Intensity modulation for optimized compensation systems with a second order transfer function in modulus. (Star-shaped points) Intensity modulation for optimized compensation systems with a realistic system: results are better than a second order system, and reduction is almost complete for intensity below 1.5 GW / cm 2 ( α < 5 % ) and reduces most of FM-to-AM conversion for intensities up to 3 GW / cm 2 . (Square points) FM-to-AM conversion for a SCF with a compensation system optimized at 0.2 GW / cm 2 . At high intensity, intensity modulation are slightly reduced. (Triangle points) FM-to-AM conversion for a SCF with a compensation system optimized at 2.5 GW / cm 2 . At low intensity, intensity modulations are worse than without compensation.

Equations (12)

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a 0 ( t ) = exp { i [ m 1 sin ( 2 π f m 1 t ) + m 2 sin ( 2 π f m 2 t ) ] } .
α = 2 I max I min I max + I min .
H c ( f ) s inc ( γ f ) 1 γ 2 6 f 2 ,
φ ( f ) = φ 0 + φ 1 f + 1 2 φ 2 f 2 + ο [ f 2 ] .
H d ( f ) exp [ i 2 φ 2 f 2 ] ,
H d   comp ( f ) = exp [ i 2 φ 2 comp f 2 ] ,
H c   comp ( f ) = 1 + γ comp 2 6 f 2 ,
H d , comp real ( f ) = exp [ i π λ 0 2 D c f 2 ] .
φ 2 comp = 2 π λ 0 2 D c .
H c   real ( f ) = 1 + A exp [ i ( 2 π f Δ τ + ψ ) ] ,
| H c   real ( f ) | 2 = ( 1 + A 2 ) + 2 A cos ψ ( 1 ( 2 π f Δ τ ) 2 2 ) 2 A sin ψ ( 2 π f Δ τ ) + o [ f 2 ] .
| H c   real ( f ) | 2 = ( 1 A ) 2 + A ( 2 π Δ τ ) 2 f 2 + o [ f 2 ] .

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