Abstract

It is known that a linear filter may be easily compensated with its inverse transfer function. However, it was shown that this approach could also be valid even for such a complex nonlinear system as frequency conversion. As a matter of fact, it is possible to at least partly precompensate for distortions occurring within, or even downstream from, frequency conversion crystals with a simple linear optical filter set upstream. In this paper, we give the theoretical background and derive the optimum precompensation filter from simple analytical formulas even in the case of saturation. We first show the relevance of our approach for Gaussian pulses: the pulse may be short or not and chirped or not, and the same linear precompensation filter may be used as long as saturation is not reached. We then study the case of phase-modulated pulses, as can be found on high power lasers such as lasers for fusion. We show that previous experimental results are in perfect agreement with these calculations. Finally, justified by our simple analytical formulas, we present a rigorous parametrical study giving the distortion reduction for any second and third harmonic generation system in the case of phase-modulated pulses.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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2011 (3)

2010 (1)

Y. Chen, P. Yuan, L. Qian, H. Zhu, and D. Fan, “Numerical study on the efficient generation of 351 nm broadband pulses by frequency mixing of broadband and narrowband Nd:glass lasers,” Opt. Commun. 283, 2737–2741 (2010).
[CrossRef]

2009 (2)

2008 (1)

2006 (1)

2003 (1)

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

1999 (1)

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 (1)

1990 (1)

R. W. Short and S. Skupsky, “Frequency conversion of broad-bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

1989 (1)

Akhmanov, S. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Beck, N.

Bordenave, E.

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]

Chen, Y.

Y. Chen, P. Yuan, L. Qian, H. Zhu, and D. Fan, “Numerical study on the efficient generation of 351 nm broadband pulses by frequency mixing of broadband and narrowband Nd:glass lasers,” Opt. Commun. 283, 2737–2741 (2010).
[CrossRef]

Chirkin, A. S.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Ehrlich, R. B.

Fan, D.

Y. Chen, P. Yuan, L. Qian, H. Zhu, and D. Fan, “Numerical study on the efficient generation of 351 nm broadband pulses by frequency mixing of broadband and narrowband Nd:glass lasers,” Opt. Commun. 283, 2737–2741 (2010).
[CrossRef]

Feng, B.

Garnier, J.

Gleyze, J. F.

Gouédard, C.

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

D. Penninckx, S. Hocquet, and C. Gouédard, “Dispositif de réduction des distorsions temporelles induites dans des impulsions lumineuses par un système convertisseur de fréquence optique non linéaire,” French patent application 08-58954 (2008).

Han, W.

Hocquet, S.

S. Hocquet, G. Lacroix, and D. Penninckx, “Compensation of frequency modulation to amplitude modulation conversion in frequency conversion systems,” Appl. Opt. 48, 2515–2521 (2009).
[CrossRef]

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

D. Penninckx, S. Hocquet, and C. Gouédard, “Dispositif de réduction des distorsions temporelles induites dans des impulsions lumineuses par un système convertisseur de fréquence optique non linéaire,” French patent application 08-58954 (2008).

Jaouën, Y.

Jia, H.

Karazys, D. T.

Lacroix, G.

Li, F.

Li, K.

Luce, J.

Migus, A.

Morice, O.

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

Murray, J. R.

Penninckx, D.

Qian, L.

Y. Chen, P. Yuan, L. Qian, H. Zhu, and D. Fan, “Numerical study on the efficient generation of 351 nm broadband pulses by frequency mixing of broadband and narrowband Nd:glass lasers,” Opt. Commun. 283, 2737–2741 (2010).
[CrossRef]

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]

Short, R. W.

R. W. Short and S. Skupsky, “Frequency conversion of broad-bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

Skupsky, S.

R. W. Short and S. Skupsky, “Frequency conversion of broad-bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

Smith, J. R.

Tan, J.

Thompson, C. E.

Vidal, S.

Videau, L.

Vysloukh, V. A.

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

Wang, F.

Wang, J.

Wang, L.

Wang, W.

Weiland, T. L.

Wilcox, R. B.

Xiang, Y.

Yang, Y.

Yuan, P.

Y. Chen, P. Yuan, L. Qian, H. Zhu, and D. Fan, “Numerical study on the efficient generation of 351 nm broadband pulses by frequency mixing of broadband and narrowband Nd:glass lasers,” Opt. Commun. 283, 2737–2741 (2010).
[CrossRef]

Zhang, X.

Zhao, S.

Zheng, W.

Zhong, W.

Zhou, L.

Zhu, H.

Y. Chen, P. Yuan, L. Qian, H. Zhu, and D. Fan, “Numerical study on the efficient generation of 351 nm broadband pulses by frequency mixing of broadband and narrowband Nd:glass lasers,” Opt. Commun. 283, 2737–2741 (2010).
[CrossRef]

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

R. W. Short and S. Skupsky, “Frequency conversion of broad-bandwidth laser light,” IEEE J. Quantum Electron. 26, 580–588 (1990).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

Y. Chen, P. Yuan, L. Qian, H. Zhu, and D. Fan, “Numerical study on the efficient generation of 351 nm broadband pulses by frequency mixing of broadband and narrowband Nd:glass lasers,” Opt. Commun. 283, 2737–2741 (2010).
[CrossRef]

Opt. Eng. (1)

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

Opt. Lett. (3)

Proc. SPIE (1)

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]

Other (2)

D. Penninckx, S. Hocquet, and C. Gouédard, “Dispositif de réduction des distorsions temporelles induites dans des impulsions lumineuses par un système convertisseur de fréquence optique non linéaire,” French patent application 08-58954 (2008).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of Femtosecond Laser Pulses (American Institute of Physics, 1992).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Ideal Gaussian pulse filtered at 2ω by a Gaussian amplitude filter with σ=7·1021 international system of units (SI) without and with precompensation at 1ω (σcomp=2σ), (b) ideal Gaussian pulse filtered at 2ω by a Gaussian phase filter (σ=i2·1020 SI) without and with precompensation at 1ω (σcomp=2σ), (c) ideal Gaussian pulse filtered at 2ω by a sinc amplitude filter without and with precompensation by a Gaussian filter at 1ω, (d) spectrum of the ideal Gaussian pulse and filtering functions (sinc filtering is represented by the x’s and Gaussian filtering by the plus symbols).

Fig. 2.
Fig. 2.

(a) Ideal phase-modulated constant signal (fm=5GHz and m1ω=6) filtered at 2ω by a Gaussian amplitude filter with σ=2·1022 SI without and with precompensation at 1ω (σcomp=2σ), in the nondepleted regime, (b) same ideal phase-modulated constant signal filtered at 2ω by a Gaussian phase filter (σ=i8·1022 SI) without and with precompensation at 1ω (σcomp=σ), in the nondepleted regime, (c) same ideal phase-modulated constant signal filtered at 2ω by a sinc amplitude filter without and with precompensation by a Gaussian filter at 1ω, (d) spectrum of the ideal phase-modulated constant signal and filtering functions (sinc filtering is represented by the x’s and Gaussian filtering by the plus symbols).

Fig. 3.
Fig. 3.

Evolution of the parameter β with intensity, expressing the saturation of the frequency conversion, in (a) SHG and (b) THG processes.

Tables (4)

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Table 1. Simulations Performed for Amplitude Filtering at 2ω

Tables Icon

Table 2. Simulations Performed for Phase Filtering at 2ω

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Table 3. Parametrical Study in SHGa

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Table 4. Parametrical Study in THGa

Equations (5)

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[E1(ω)Hcomp(ω)E1(ω)Hcomp(ω)]×H(ω)=C(ω),
β·σcompσ=N2,
β·γ2γcomp2=N2,
β·σcompσ=N,
β·φcompφ2ω=N,

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