Abstract

High-power lasers, such as the Laser MegaJoule (LMJ), have to be phase modulated to avoid stimulated Brillouin scattering (SBS) that may strongly damage optics at the end of the laser chain. Current spectral broadening on LMJ is performed with a sinusoidal phase modulation. This pure sinusoidal phase modulation leads to inhomogeneous spectral power densities (SPD). Thus, for a same SBS power threshold, the sinusoidal phase-modulated spectrum has to be larger than the equivalent ideal SPD with isoenergetic peaks. We present in this paper a technique to generate energy-balanced Dirac peaks spectra thanks to nonsinusoidal phase modulations. Thus, we can build a narrower spectrum with a nonsinusoidal phase modulation that has the same SBS threshold as a sinusoidal phase modulation, and we show that FM-to-AM conversion can be strongly reduced, which is of great interest for LMJ laser performance, with reductions up to 40%.

© 2010 Optical Society of America

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References

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  1. www-lmj.cea.fr.
  2. www.llnl.gov/nif/project.
  3. J. R. Murray, J. R. 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]
  4. 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).
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  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. R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2002).
  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. G. W. Faris, L. E. Jusinski, and A. P. Hickman, “High-resolution stimulated Brillouin gain spectroscopy in glasses and crystals,” J. Opt. Soc. Am. B 10, 587-599 (1993).
    [CrossRef]
  9. J. R. Carson, “Notes on the theory of modulation,” Proc. IRE 10, 57-64 (1922).
    [CrossRef]
  10. R. W. Gerchberg and W. O. Saxton, Optik (Jena) 35, 237 (1972).
  11. S. K. Korotky, “Multifrequency lightwave source using phase modulation for suppressing stimulated Brillouin scattering in optical fibers,” U.S. patent 5,566,381 (15 Oct. 1996).
  12. R. T. Logan and R. D. Li, “Method and apparatus for optimizing SBS performance in an optical communication system using at least two phase modulation tones,” U.S. patent 6,282,003 (28 Aug. 2001).
  13. S. Hocquet and D. Penninckx, patent application FR 08 56475.
  14. Y. Dong, Z. Lu, Q. Li, and Y. Liu, “Broadband Brillouin slow light based on multifrequency phase modulation in optical fibers,” J. Opt. Soc. Am. B 25, C109-C115 (2008).
    [CrossRef]
  15. G. P. Agrawal, Non-Linear Fiber Optics, 3rd ed. (Academic, 2001).
  16. M. O. Van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode Fibers,” J. Lightwave Technol. 12, 585-590 (1994).
    [CrossRef]
  17. S. Hocquet, G. Lacroix, and D. Penninckx, “Compensation of FM-to-AM conversion in frequency conversion systems,” Appl. Opt. 48, 2515-2521 (2009).
    [CrossRef] [PubMed]

2009

2008

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]

1997

1994

M. O. Van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode Fibers,” J. Lightwave Technol. 12, 585-590 (1994).
[CrossRef]

1993

1989

1972

R. W. Gerchberg and W. O. Saxton, Optik (Jena) 35, 237 (1972).

1922

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

Agrawal, G. P.

G. P. Agrawal, Non-Linear Fiber Optics, 3rd ed. (Academic, 2001).

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]

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]

Boot, A. J.

M. O. Van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode Fibers,” J. Lightwave Technol. 12, 585-590 (1994).
[CrossRef]

Bordenave, É.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2002).

Carson, J. R.

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

Dong, Y.

Ehrlich, R. B.

Faris, G. W.

Garnier, J.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, Optik (Jena) 35, 237 (1972).

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]

Gouédard, C.

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]

Hickman, A. P.

Hocquet, S.

Jaouën, Y.

Jusinski, L. E.

Karazys, D. T.

Korotky, S. K.

S. K. Korotky, “Multifrequency lightwave source using phase modulation for suppressing stimulated Brillouin scattering in optical fibers,” U.S. patent 5,566,381 (15 Oct. 1996).

Lacroix, G.

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]

Li, Q.

Li, R. D.

R. T. Logan and R. D. Li, “Method and apparatus for optimizing SBS performance in an optical communication system using at least two phase modulation tones,” U.S. patent 6,282,003 (28 Aug. 2001).

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]

Liu, Y.

Logan, R. T.

R. T. Logan and R. D. Li, “Method and apparatus for optimizing SBS performance in an optical communication system using at least two phase modulation tones,” U.S. patent 6,282,003 (28 Aug. 2001).

Lu, Z.

Migus, A.

Murray, J. R.

Penninckx, D.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, Optik (Jena) 35, 237 (1972).

Smith, J. R.

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.

Van Deventer, M. O.

M. O. Van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode Fibers,” J. Lightwave Technol. 12, 585-590 (1994).
[CrossRef]

Videau, L.

Weiland, T. L.

Wilcox, R. B.

Appl. Opt.

J. Lightwave Technol.

M. O. Van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode Fibers,” J. Lightwave Technol. 12, 585-590 (1994).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Optik (Jena)

R. W. Gerchberg and W. O. Saxton, Optik (Jena) 35, 237 (1972).

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]

Other

G. P. Agrawal, Non-Linear Fiber Optics, 3rd ed. (Academic, 2001).

R. W. Boyd, Nonlinear Optics, 2nd ed. (Academic, 2002).

www-lmj.cea.fr.

www.llnl.gov/nif/project.

S. K. Korotky, “Multifrequency lightwave source using phase modulation for suppressing stimulated Brillouin scattering in optical fibers,” U.S. patent 5,566,381 (15 Oct. 1996).

R. T. Logan and R. D. Li, “Method and apparatus for optimizing SBS performance in an optical communication system using at least two phase modulation tones,” U.S. patent 6,282,003 (28 Aug. 2001).

S. Hocquet and D. Penninckx, patent application FR 08 56475.

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Figures (13)

Fig. 1
Fig. 1

Different optical spectra obtained by sinusoidal phase modulation. (a) Energy-balanced spectra with three peaks for m = 1.43 rad ( f m = 2 GHz ). (b) Normalized spectral power of density of LMJ anti-Brillouin function sinusoidal phase modulation at 3 ω : f m = 2 GHz and m = 21 rad .

Fig. 2
Fig. 2

SPD to achieve anti-Brillouin function. (a) Sine phase modulation SPD at 3 ω ( m = 21 , f m = 2 GHz ). (b) Ideal energy-balanced spectrum with same value of maximum of SPD (about 6% of the total energy).

Fig. 3
Fig. 3

(a) Illustration for the definition of the error function ε used when we are looking for an ideal 25-peak energy-balanced spectrum. (b) Results of gradient algorithm optimization for nonsinusoidal phase modulation for different values of the number of harmonics: the higher N is, the lower the error function is. However, most of the gain is obtained for N = 3 , which is simple enough for practical realization.

Fig. 4
Fig. 4

Error function for nonsinusoidal phase modulation with N = 3 for any values of phases φ 2 and φ 3 . In that example, the ideal spectrum considered is a 25-peak spectrum and m 1 = 1.4 , m 2 = 5.6 , and m 3 = 0.4 . Minima of error function are symmetry positions for SPD.

Fig. 5
Fig. 5

Importance of phase control. Particular operating point for a nonsinusoidal phase modulation composed of two harmonics: f m = 2 GHz and 3 f m = 6 GHz with the same modulation index m = 1.4 . Two U.S. patents [11, 12] assume that the SPD associated is composed of nine energy-balanced peaks. However, (a) if φ 3 = 0 , as presented in patent from [12], SPD is not energy balanced. (b) Energy-balanced spectrum is performed only for a good choice of the relative phase: φ 3 = π / 2 [π]. (c) Evolution of error function in the case of an ideal energy-balanced spectrum with nine peaks for different values of φ 3 .

Fig. 6
Fig. 6

Modulation indexes for optimized three-harmonic-signal solutions. ( m 1 , m 3 ) are almost constant and m 2 increases with the spectrum width. Exceptions are presented in contrasting shades.

Fig. 7
Fig. 7

(a) Nonsinusoidal phase modulation scheme: the harmonic combination and phase control is performed directly with the HF signal. Optical components remain the same. (b) HF multiharmonic generator at 2 4 6 GHz used in our different setups.

Fig. 8
Fig. 8

Top line: different nonsinusoidal phase modulation SPD [(a)  m = 2.4 , (b)  m = 5.1 , (c)  m = 7 ]. Bottom line: Sinusoidal phase modulation SPD with equivalent bandwidth [(d)  m 2 = 1.8 , (e)  m 2 = 2.05 , (f)  m 2 = 3.3 , m 1 = 1.4 ± 0.1 , m 3 = 0.4 ± 0.2 , φ 2 = 90 ° and φ 3 = 180 ° ]. Vertical scale is the same for both lines: nonsinusoidal phase modulation SPD maxima are below equivalent sinusoidal phase modulation SPD maxima.

Fig. 9
Fig. 9

(a) Experimental measurements. (b) Power P inj required to observe SBS in function of SBS threshold for a not-broadened spectrum using Eq. (8). Discrepancies between (a) experiments and (b) simulations are small and equivalent between sinusoidal and nonsinusoidal cases. The letters (a) to (f) in the figure refer to the spectra in Fig. 8.

Fig. 10
Fig. 10

Setup of SBS measurement experiment. Laser is pulsed but shape controlled: gain of the amplifier is constant to prevent temporal deformation; power lever is set with a variable attenuator before injection in the long fiber. The phase modulation used is either sinusoidal or nonsinusoidal. SBS measurements are made with two photodiodes synchronized for both original and back SBS signals: we consider that the SBS threshold is reached when back SBS appears with always the same level.

Fig. 11
Fig. 11

Parametrical optical filter using birefringence in PMF: impacts of the different parameters on the transfer function. The second wave plate is useful to get back the linear polarization on a fiber axis.

Fig. 12
Fig. 12

Distortion criterion for different symmetrical amplitude filters. Comparison between sinusoidal (squares) and nonsinusoidal (circles) phase modulation with the same anti-Brillouin efficiency. We added numerical simulations with MATLAB.

Fig. 13
Fig. 13

Left column: temporal shape measured after filtering ( f 3 dB = 20 GHz ) for both sinusoidal (bottom line) and nonsinusoidal (upper line) phase modulation. Right column: AM spectra associated. Data points concentrated at the frequency axis represent the measurement noise filtered for the results. In insert, we give numerical simulations obtained with MATLAB.

Equations (26)

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a ( t ) = I ( t ) · exp ( i [ 2 π f 0 t + m sin ( 2 π f m t ) ] ) ,
a mod ( t ) = exp ( i m sin ( 2 π f m t ) ) .
a ˜ mod ( f ) = n = + J n ( m ) δ ( f n f m ) ,
SPD ( f ) = | a ˜ mod ( f ) | 2 = n = + | J n ( m ) | 2 δ ( f n f m ) .
a opt ( t ) = exp ( i n = 1 m n sin ( 2 π n f m t + φ n ) ) ,
a opt ( t ) = exp ( i n = 1 N m n sin ( 2 π n f m t + φ n ) ) .
ε ( SPD ) = k = + ( SPD ( k f m ) SPD ideal ( k f m ) ) 2 .
P inj = P Threshold SPD max ,
k g b P Threshold L eff / A eff 21 ,
L eff = [ 1 exp ( α L ) ] / α .
α = 2 · I max I min I max + I min .
H 0 ( f ) 1 + A exp ( i ( 2 π f Δ τ + Ψ ) ) .
| H o ( f ) | 2 1 + C cos ( 2 π f Δ τ ) ,
SPD ( f ) = 1 2 M + 1 k = M M δ ( f k f m ) .
A ˜ ( f ) = 1 2 M + 1 k = M M e i ϕ k δ ( f k f m ) ,
A ( t ) = 1 2 M + 1 k = M M exp ( i ( 2 π k f m t + ϕ k ) ) .
I ( t ) = A ( t ) · A * ( t ) = 1 2 M + 1 [ ( 2 M + 1 ) + [ k = 1 2 M 1 a k cos ( ( 2 π k f m t + γ k ) ) ] + cos ( ( 2 π · 2 M · f m t + ϕ N + ϕ N ) ) ] .
[ k = 1 2 M 1 a k cos ( ( 2 π k f m t + γ k ) ) ] + cos ( ( 2 π · 2 M · f m t + ϕ N + ϕ N ) ) = 0.
a mod ( t ) = exp ( i [ m 1 sin ( ω n t ) + m 2 sin ( 2 ω n t + φ 2 ) ] ) .
a ˜ mod ( ω ) = [ n J n ( m 1 ) δ ( ω n ω n ) ] * [ k J k ( m 2 ) e i k φ 2 δ ( ω 2 k ω n ) ] .
a ˜ mod ( ω ) = [ n [ k J n 2 k ( m 1 ) · J k ( m 2 ) e i k φ 2 ] δ ( ω n ω n ) ] .
a ˜ mod ( l ω n ) = [ k J l 2 k ( m 1 ) · J k ( m 2 ) e i k φ 2 ] and a ˜ mod ( l ω n ) = ( 1 ) l [ k J l 2 k ( m 1 ) · J k ( m 2 ) ( 1 ) k e i k φ 2 ] .
a ˜ mod ( l ω n ) = e i θ ( l ω n ) a ˜ mod ( l ω n ) .
( 1 ) l ( 1 ) k e i k φ 2 = e i θ ( l ω n ) e i k φ 2 .
a ˜ mod ( t ) = exp ( i [ m 1 sin ( ω n t ) + m 2 sin ( 2 ω n t + φ 2 ) + m 3 sin ( 3 ω n t + φ 3 ) ] ) .
( 1 ) h ( e i φ 2 ) k ( e i φ 3 ) l = e i θ ( h ω n ) ( e i φ 2 ) k ( e i φ 3 ) l .

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