Abstract

We developed an improved approach to calculate the Fourier transform of signals with arbitrary large quadratic phase which can be efficiently implemented in numerical simulations utilizing Fast Fourier transform. The proposed algorithm significantly reduces the computational cost of Fourier transform of a highly chirped and stretched pulse by splitting it into two separate transforms of almost transform limited pulses, thereby reducing the required grid size roughly by a factor of the pulse stretching. The application of our improved Fourier transform algorithm in the split-step method for numerical modeling of CPA and OPCPA shows excellent agreement with standard algorithms.

© 2016 Optical Society of America

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References

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  1. G. P. Agarwal, Nonlinear Fiber Optics (Fourth Edition) (Academic, San Diego, 2006).
  2. J. O. Smith, Mathematics of the Discrete Fourier Transform (DFT) (W3K Publishing, 2007).
  3. I. Epatko, A. A. Malyutin, R. V. Serov, D. Solov’ev, and A. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28(8), 697 (1998).
    [Crossref]
  4. O. Morice, “Miró: complete modeling and software for pulse amplification and propagation in high-power laser systems,” Opt. Engineering 42(6), 1530–1541 (2003).
    [Crossref]
  5. B. Jaskorzynska, J. Nilsson, A. Sergeev, and E. Vanin, “Time-frame transformation for efficient simulation of chirped pulse compression in an optical fiber,” Opt. Lett.,  20(20), 2123–2124 (1995).
    [Crossref] [PubMed]
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  7. W.L. Katw, “Phase-Sensitive Amplification of Pulses in Nonlinear Optical Fibers”, in book Computational Wave Propagation, T. Hagstrom, B. Engquist, and G.A. Kriegsmann, eds. (Springer-VerlagNew York, 1996).
  8. S. N. Vlasov, E. V. Koposova, and G. I. Freidman, “Interaction of frequency-modulated light beams in multistage parametric amplifiers at the maximum gain bandwidth,” Quantum Electron. 39(5), 393 (2009).
    [Crossref]
  9. A. Andrianov, E. Anashkina, A. Kim, I. Meyerov, S. Lebedev, A. Sergeev, and G. Mourou, “Three-dimensional modeling of cpa to the multimillijoule level in tapered Yb-doped fibers for coherent combining systems,” Opt. Express 22(23), 28256–28269 (2014).
    [Crossref] [PubMed]
  10. N. Didenko, A. Konyashchenko, A. Lutsenko, and S. Y. Tenyakov, “Contrast degradation in a chirped-pulse amplifier due to generation of prepulses by postpulses,” Opt. Express 16(5), 3178–3190 (2008).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  12. X. Liu, A. P. Shreenath, M. Kimmel, R. Trebino, A. V. Smith, and S. Link, “Numerical simulations of optical parametric amplification cross-correlation frequency-resolved optical gating,” J. Opt. Soc. Am. B 23(2), 318–325 (2006).
    [Crossref]
  13. J. Wang, P. Yuan, J. Ma, Y. Wang, G. Xie, and L. Qian, “Surface-reflection-initiated pulse-contrast degradation in an optical parametric chirped-pulse amplifier,” Opt. Express 21(13), 15580–15594 (2013).
    [Crossref] [PubMed]

2014 (1)

2013 (1)

2009 (1)

S. N. Vlasov, E. V. Koposova, and G. I. Freidman, “Interaction of frequency-modulated light beams in multistage parametric amplifiers at the maximum gain bandwidth,” Quantum Electron. 39(5), 393 (2009).
[Crossref]

2008 (2)

2006 (1)

2003 (1)

O. Morice, “Miró: complete modeling and software for pulse amplification and propagation in high-power laser systems,” Opt. Engineering 42(6), 1530–1541 (2003).
[Crossref]

1998 (1)

I. Epatko, A. A. Malyutin, R. V. Serov, D. Solov’ev, and A. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28(8), 697 (1998).
[Crossref]

1995 (1)

Agarwal, G. P.

G. P. Agarwal, Nonlinear Fiber Optics (Fourth Edition) (Academic, San Diego, 2006).

Anashkina, E.

Andrianov, A.

Chulkin, A.

I. Epatko, A. A. Malyutin, R. V. Serov, D. Solov’ev, and A. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28(8), 697 (1998).
[Crossref]

Didenko, N.

Epatko, I.

I. Epatko, A. A. Malyutin, R. V. Serov, D. Solov’ev, and A. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28(8), 697 (1998).
[Crossref]

Freidman, G. I.

S. N. Vlasov, E. V. Koposova, and G. I. Freidman, “Interaction of frequency-modulated light beams in multistage parametric amplifiers at the maximum gain bandwidth,” Quantum Electron. 39(5), 393 (2009).
[Crossref]

Jaskorzynska, B.

Katw, W.L.

W.L. Katw, “Phase-Sensitive Amplification of Pulses in Nonlinear Optical Fibers”, in book Computational Wave Propagation, T. Hagstrom, B. Engquist, and G.A. Kriegsmann, eds. (Springer-VerlagNew York, 1996).

Kim, A.

Kimmel, M.

Konyashchenko, A.

Koposova, E. V.

S. N. Vlasov, E. V. Koposova, and G. I. Freidman, “Interaction of frequency-modulated light beams in multistage parametric amplifiers at the maximum gain bandwidth,” Quantum Electron. 39(5), 393 (2009).
[Crossref]

Kutay, M. A.

H. M. Ozaktas, M. A. Kutay, and Z. Zalevsky, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, Chichester, 2001).

Lebedev, S.

Limpert, J.

Link, S.

Liu, X.

Lutsenko, A.

Ma, J.

Malyutin, A. A.

I. Epatko, A. A. Malyutin, R. V. Serov, D. Solov’ev, and A. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28(8), 697 (1998).
[Crossref]

Meyerov, I.

Morice, O.

O. Morice, “Miró: complete modeling and software for pulse amplification and propagation in high-power laser systems,” Opt. Engineering 42(6), 1530–1541 (2003).
[Crossref]

Mourou, G.

Nilsson, J.

Ozaktas, H. M.

H. M. Ozaktas, M. A. Kutay, and Z. Zalevsky, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, Chichester, 2001).

Qian, L.

Schimpf, D.

Seise, E.

Sergeev, A.

Serov, R. V.

I. Epatko, A. A. Malyutin, R. V. Serov, D. Solov’ev, and A. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28(8), 697 (1998).
[Crossref]

Shreenath, A. P.

Smith, A. V.

Smith, J. O.

J. O. Smith, Mathematics of the Discrete Fourier Transform (DFT) (W3K Publishing, 2007).

Solov’ev, D.

I. Epatko, A. A. Malyutin, R. V. Serov, D. Solov’ev, and A. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28(8), 697 (1998).
[Crossref]

Tenyakov, S. Y.

Trebino, R.

Tunnermann, A.

Vanin, E.

Vlasov, S. N.

S. N. Vlasov, E. V. Koposova, and G. I. Freidman, “Interaction of frequency-modulated light beams in multistage parametric amplifiers at the maximum gain bandwidth,” Quantum Electron. 39(5), 393 (2009).
[Crossref]

Wang, J.

Wang, Y.

Xie, G.

Yuan, P.

Zalevsky, Z.

H. M. Ozaktas, M. A. Kutay, and Z. Zalevsky, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, Chichester, 2001).

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

Opt. Engineering (1)

O. Morice, “Miró: complete modeling and software for pulse amplification and propagation in high-power laser systems,” Opt. Engineering 42(6), 1530–1541 (2003).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Quantum Electron. (2)

I. Epatko, A. A. Malyutin, R. V. Serov, D. Solov’ev, and A. Chulkin, “New algorithm for numerical simulation of the propagation of laser radiation,” Quantum Electron. 28(8), 697 (1998).
[Crossref]

S. N. Vlasov, E. V. Koposova, and G. I. Freidman, “Interaction of frequency-modulated light beams in multistage parametric amplifiers at the maximum gain bandwidth,” Quantum Electron. 39(5), 393 (2009).
[Crossref]

Other (4)

G. P. Agarwal, Nonlinear Fiber Optics (Fourth Edition) (Academic, San Diego, 2006).

J. O. Smith, Mathematics of the Discrete Fourier Transform (DFT) (W3K Publishing, 2007).

H. M. Ozaktas, M. A. Kutay, and Z. Zalevsky, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, Chichester, 2001).

W.L. Katw, “Phase-Sensitive Amplification of Pulses in Nonlinear Optical Fibers”, in book Computational Wave Propagation, T. Hagstrom, B. Engquist, and G.A. Kriegsmann, eds. (Springer-VerlagNew York, 1996).

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Figures (3)

Fig. 1
Fig. 1

Folding effect of FFT: (a) chirped pulse spectral intensity (solid line) and spectral phase (dashed line), (b) inverse Fourier transforms computed by standard FFT with grid sizes 256 (green line), 512 (dotted red line), 1024 (blue solid line with crosses), and by our modified transform with grid size 256 (filled gray curve). Temporal grid sizes are shown by dashed vertical lines.

Fig. 2
Fig. 2

The calculated CPA output: a) the Spectrum (gray shaded curve, basic algorithm; red dashed line, advanced algorithm) and spectral phase (black line with crosses, basic; green dashed line, advanced); b) The temporal profile (gray shaded curve, basic; red line, advanced); c) The temporal profile of output pulse with pre- and post-pulses (red dotted line, basic; black line, advanced).

Fig. 3
Fig. 3

The calculated OPCPA output: a) the Spectrum (gray shaded curve, basic algorithm; red dashed line, advanced algorithm) and spectral phase (black line with crosses, basic; green dashed line, advanced); b) The temporal profile (gray shaded curve, basic; red line, advanced); c) The temporal profile of output pulse with pre- and post-pulses (red dotted line, basic; black line, advanced).

Equations (10)

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F ^ [ A ] ( ω ) = 1 2 π A ( t ) exp ( i ω t ) d t .
B ( T ) = 1 2 π A ( t ) exp ( i α ω 2 2 + i ω t i ω T ) d t d ω .
exp ( i α ω 2 2 + i ω ( t T ) ) d ω = 2 α exp ( i ( t T ) 2 2 α ) exp ( i q 2 ) d q = 2 i π α exp ( i ( t T ) 2 2 α ) .
B ( T ) = i 2 π α exp ( i T 2 2 α ) A ( t ) exp ( i t 2 2 α + i t T α ) d t ,
B ( T ) = i α exp ( i T 2 2 α ) F ^ [ F ^ 1 [ B ω exp ( i α ω 2 2 ) ] ( t ) exp ( i t 2 2 α ) ] ( T α ) .
B ω ( ω ) = α i exp ( i α ω 2 2 ) F ^ [ F ^ 1 [ B ( α Ω ) exp ( i α Ω 2 2 ) ] ( t ) exp ( i t 2 2 α ) ] ( ω ) .
B ( T ) i α exp ( i T 2 α ) B ω ( T α ) .
A z = i β 2 2 2 A t 2 + β 3 6 3 A t 3 + g 2 A + i γ | A | 2 A ,
( z + 1 v s , i t + i β 2 s , i 2 2 t 2 ) A s , i = i ω s , i d e f f n s , i c A p A i , s e i Δ k z
( z + 1 v p t + i β 2 p 2 2 t 2 ) A p = i ω p d e f f n p c A s A i e i Δ k z

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