## Fiber optical parametric chirped-pulse amplification in the femtosecond regime

Optics Express, Vol. 14, Issue 7, pp. 2783-2790 (2006)

http://dx.doi.org/10.1364/OE.14.002783

Acrobat PDF (127 KB)

### Abstract

We study parametric amplification in optical fibers for chirped-pulse femtosecond laser systems. Compared to conventional OPCPA operating in bulk crystals, the fiber geometry offers a greater interaction length and spatial confinement, an increased flexibility in the choice of wavelengths for signal and pump beams, and the robustness of fiber setups. As opposed to rare-earth doped fibers, parametric amplifiers potentially provide wideband amplification in arbitrary regions of the spectrum. Numerical simulations are undertaken as a proof of principle for a picosecond 1064 nm pump and femtosecond 1025 nm signal. Guidelines for phase matching engineering are given, and limitations in spectral bandwidth and achievable pulse energy are discussed.

© 2006 Optical Society of America

## 1. Introduction

1. N. Ishii, L. Turi, V. S. Yakovlev, T. Fuji, F. Krausz, A. Baltuska, R. Butkus, G. Veitas, V. Smilgevicius, R. Danielus, and A. Piskarskas, “Multimillijoule chirped parametric amplification of few-cycle pulses,” Opt. Lett. **30**, 567–569 (2005). [CrossRef] [PubMed]

*μ*m [2

2. J. V. Rudd, R. J. Law, T. S. Luk, and S. M. Cameron, “High-power optical parametric chirped-pulse amplifier system with a 1.55 *μ*m signal and a 1.064 *μ*m pump,” Opt. Lett. **30**, 1974–1976 (2005). [CrossRef] [PubMed]

3. I. Jovanovic, C. G. Brown, C. A. Ebbers, C. P. J. Barty, N. Forget, and C. Le Blanc, “Generation of high-contrast millijoule pulses by optical parametric chirped-pulse amplification in periodically poled *KTiOPO*_{4},” Opt. Lett. **30**, 1036–1038 (2005). [CrossRef] [PubMed]

4. J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. **8**, 506–520 (2002). [CrossRef]

5. A. Durecu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, ”Impact of pump phase modulation on system performance of fibre-optical parametric amplifiers,” Electron. Lett. **41**, 350–352 (2005). [CrossRef]

6. G. K. L. Wong, A. Y. H. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, ”Continuous-wave tunable optical parametric generation in a photonic-crystal fiber,” J. Opt. Soc. Am. B **22**, 2505–2511 (2005). [CrossRef]

## 2. Simulations

*β*

_{2}

*z*= 0.3 ps

^{2}and third-order dispersion of

*β*

_{3}

*z*= 3 × 10

^{-4}ps

^{3}. The amplifying fiber zero-dispersion wavelength is 1040 nm (

*β*

_{2}= -3.0 × 10

^{-3}ps

^{2}.m

^{-1}at 1064 nm), with a dispersion slope of 0.2 ps/nm

^{2}/km (

*β*

_{3}= 7.5 × 10

^{-5}ps

^{3}.m

^{-1}at 1064 nm), and an effective area of 18

*μ*m

^{2}, resulting in a nonlinear parameter

*γ*= 9.8 W

^{-1}.km

^{-1}. These specifications correspond to the commercially available fiber Crystal Fibre NL-4.8-1040. Since it is difficult to evaluate from the supplier data, the derivative of the dispersion slope with respect to wavelength is taken equal to zero in the first simulation. It is then optimized for bandwidth in section 3. The propagation is modeled using an extended version of the nonlinear Schrodinger equation including Raman, self steepening, and dispersion effects up to fourth order:

*u*is the electric field envelope,

*ω*

_{0}is the central angular frequency, and

*R*(

*t*) = (1 -

*f*)

_{R}*δ*(

*t*) +

*f*(

_{R}h_{R}*t*), where

*f*= 0.18, is the normalized nonlinear response function. A commonly used analytic approximation was made for the shape of

_{R}*h*(

_{R}*t*) [7]. The time, frequency and space sampling was checked to ensure accurate simulation results.

4. J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. **8**, 506–520 (2002). [CrossRef]

*β*

_{2}[8

8. M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. **21**, 573–575 (1996). [CrossRef] [PubMed]

## 3. Energy and bandwidth limitations

*ϕ*=

_{p}*γP*, where

_{p}z*γ*is the nonlinear coefficient of the fiber,

*P*is the peak pump power, and

_{p}*z*is the propagation distance. The value of the gain

*G*varies over the band-width of the amplifier, between a quadratic gain region in the vicinity of the pump wavelength and an exponential gain at the phase-matching wavelength. The dominant energy limitation comes from self-phase modulation on the signal that prevents proper recompression. Let us fix a maximum nonlinear phase value of

*ϕ*on the signal. Empirically, we found that

_{s}*ϕ*< 0.4 ensures no degradation on the output pulses. This nonlinear phase shift can be evaluated as

_{s}*P*(

_{s}*z*) is the peak signal power along the amplifier, and

*P*depends on the type of gain :

_{eq}*P*=

_{eq}*P*(0)(

_{s}*G*- 1)/ln(

*G*) for exponential gain and

*P*=

_{eq}*P*(0)

_{s}*G*/3 for quadratic gain. Replacing these expressions in the inequality that defines the maximum nonlinear phase shift, and defining the pulsewidth ratio between the stretched signal and pump

*R*, we obtain a limit on the signal to pump energy ratio at the input of the fiber

_{sp}*E*/

_{s}*E*. In the exponential gain region, we find

_{p}*GE*/

_{S}*E*. In our example, it evaluates to 3.8%, in good agreement with numerical simulations that give an output pulse energy of 1.5 nJ. The relation between the pulsewidth ratio and energy efficiency clearly appears in these inequalities, leading to a tradeoff between energy efficiency and bandwidth. In our example, setting all parameters constant except for pump pulsewidth, the maximum energy efficiency was found to be 15%, corresponding to 10 ps pump pulses. In this case, slight gain narrowing led to a recompressed pulse duration of 230 fs. Further decrease of the pump pulse duration led to significant gain narrowing and longer recompressed pulses at the output.

_{P}*γ*, while increasing the pump power or the length to compensate for the loss of efficiency in the interaction. However, for the type of fiber considered here, where guiding relies on total internal reflection between the silica core and the cladding essentially made of air, increasing the mode area translates into a modification of the dispersion properties. This in turn modifies the phase matching condition of the interaction, affecting the amplifier performance. Ultimately, for very large mode areas, the dispersion is essentially defined by the silica material, fixing the operation wavelength at 1.3

*μ*m. A possible way to overcome this problem could be to use fibers where guiding is based on a photonic bandgap, such as Bragg fibers [9

9. S. Fvrier, R. Jamier, J.-M. Blondy, S. L. Semjonov, M. E. Likhachev, M. M. Bubnov, E. M. Dianov, V. F. Khopin, M. Y. Salganskii, and A. N. Guryanov, ”Low Loss Large Mode Area Bragg Fibre,” 31th European Conference on Optical Communication, Post Deadline paper PD Th4.4.3, Glasgow, United-Kingdom, 25–29 September 2005.

10. J. Marcou, F. Brchet, and Ph. Roy, ”Design of weakly guiding Bragg fibres for chromatic dispersion shifting towards short wavelengths,” Journal of Optics A: Pure and Applied Optics **3**, S144–S153 (2001). [CrossRef]

*ϕ*, it is preferable to increase the pump power because increasing the length leads to a reduced bandwidth of the amplifier. Depending on the repetition rate and peak power of the pump pulses, issues such as optical surface damage and thermal effects in fibers must be addressed when scaling the pump power. For instance, end-caps might be used to avoid surface damage at the facets of the fiber. Increasing the signal stretching ratio provides a convenient way to increase output pulse energy while keeping self-phase modulation at a tolerable level. Although we use a stretching ratio of 20 to facilitate the numerical simulations, values of the order of 10000 are commonplace in experimental CPA systems. We therefore expect that >

_{p}*μ*J pulse energies are attainable using large-mode area fibers and longer stretched signal and pump pulses.

8. M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. **21**, 573–575 (1996). [CrossRef] [PubMed]

*β*

_{4}= 7×10

^{-55}s

^{2}.m

^{-1}at 1064 nm, pump pulses are 40 ps long with a peak power of 2 kW, and the fiber length is reduced to 30 cm. These parameters result in a flat CW gain region extending from 940 to 1010 nm using a 3 dB cutoff criterion, as shown in fig. 3. The input signal pulses are 70-fs FWHM long, centered at 980 nm, with a peak power of 50 W, and are stretched with the same dispersion values as in the first simulation. Figure 4 shows the input and output spectra and waveform for this configuration. The gain in energy is 27 dB, producing 1.7 nJ ouput pulses. Four-wave mixing generates some spectral content on the short-wavelength side of the signal, which prevents from using a signal wavelength closer to the pump. The amplified spectrum exhibits a slight gain narrowing effect, with the FWHM spectral width being reduced from 34 nm down to 27 nm, consistent with a recompressed pulsewidth of 85 fs.

## 4. Conclusion

11. C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. **8**, 538–547 (2002). [CrossRef]

## References and links

1. | N. Ishii, L. Turi, V. S. Yakovlev, T. Fuji, F. Krausz, A. Baltuska, R. Butkus, G. Veitas, V. Smilgevicius, R. Danielus, and A. Piskarskas, “Multimillijoule chirped parametric amplification of few-cycle pulses,” Opt. Lett. |

2. | J. V. Rudd, R. J. Law, T. S. Luk, and S. M. Cameron, “High-power optical parametric chirped-pulse amplifier system with a 1.55 |

3. | I. Jovanovic, C. G. Brown, C. A. Ebbers, C. P. J. Barty, N. Forget, and C. Le Blanc, “Generation of high-contrast millijoule pulses by optical parametric chirped-pulse amplification in periodically poled |

4. | J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, “Fiber-based optical parametric amplifiers and their applications,” IEEE J. Sel. Top. Quantum Electron. |

5. | A. Durecu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, and H. Maillotte, ”Impact of pump phase modulation on system performance of fibre-optical parametric amplifiers,” Electron. Lett. |

6. | G. K. L. Wong, A. Y. H. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, ”Continuous-wave tunable optical parametric generation in a photonic-crystal fiber,” J. Opt. Soc. Am. B |

7. | G. P. Agrawal, ”Nonlinear fiber optics,” second edition, p. 49 and p. 428 (Academic Press, 1995). |

8. | M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett. |

9. | S. Fvrier, R. Jamier, J.-M. Blondy, S. L. Semjonov, M. E. Likhachev, M. M. Bubnov, E. M. Dianov, V. F. Khopin, M. Y. Salganskii, and A. N. Guryanov, ”Low Loss Large Mode Area Bragg Fibre,” 31th European Conference on Optical Communication, Post Deadline paper PD Th4.4.3, Glasgow, United-Kingdom, 25–29 September 2005. |

10. | J. Marcou, F. Brchet, and Ph. Roy, ”Design of weakly guiding Bragg fibres for chromatic dispersion shifting towards short wavelengths,” Journal of Optics A: Pure and Applied Optics |

11. | C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, “Parametric amplifiers driven by two pump waves,” IEEE J. Sel. Top. Quantum Electron. |

**OCIS Codes**

(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

(320.7140) Ultrafast optics : Ultrafast processes in fibers

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: January 27, 2006

Revised Manuscript: March 22, 2006

Manuscript Accepted: March 25, 2006

Published: April 3, 2006

**Citation**

Marc Hanna, Frédéric Druon, and Patrick Georges, "Fiber optical parametric chirped-pulse amplification in the femtosecond regime," Opt. Express **14**, 2783-2790 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-7-2783

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### References

- N. Ishii, L. Turi, V. S. Yakovlev, T. Fuji, F. Krausz, A. Baltuska, R. Butkus, G. Veitas, V. Smilgevicius, R. Danielus, and A. Piskarskas, "Multimillijoule chirped parametric amplification of few-cycle pulses," Opt. Lett. 30,567-569 (2005). [CrossRef] [PubMed]
- J. V. Rudd, R. J. Law, T. S. Luk, and S. M. Cameron, "High-power optical parametric chirped-pulse amplifier system with a 1.55 μm signal and a 1.064 μm pump," Opt. Lett. 30,1974-1976 (2005). [CrossRef] [PubMed]
- I. Jovanovic, C. G. Brown, C. A. Ebbers, C. P. J. Barty, N. Forget, and C. Le Blanc, "Generation of high-contrast millijoule pulses by optical parametric chirped-pulse amplification in periodically poled KTiOPO4," Opt. Lett. 30,1036-1038 (2005). [CrossRef] [PubMed]
- J. Hansryd, P. A. Andrekson, M. Westlund, J. Lie, and P.-O. Hedekvist, "Fiber-based optical parametric amplifiers and their applications," IEEE J. Sel. Top. Quantum Electron. 8,506-520 (2002). [CrossRef]
- A. Durecu-Legrand, A. Mussot, C. Simonneau, D. Bayart, T. Sylvestre, E. Lantz, H. Maillotte, "Impact of pump phase modulation on system performance of fibre-optical parametric amplifiers," Electron. Lett. 41,350-352 (2005). [CrossRef]
- G. K. L. Wong, A. Y. H. Chen, S. G. Murdoch, R. Leonhardt, J. D. Harvey, N. Y. Joly, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Continuous-wave tunable optical parametric generation in a photonic-crystal fiber," J. Opt. Soc. Am. B 22,2505-2511 (2005). [CrossRef]
- G. P. Agrawal, "Nonlinear fiber optics, " second edition, p. 49 and p. 428 (Academic Press, 1995).
- M. E. Marhic, N. Kagi, T.-K. Chiang, and L. G. Kazovsky, "Broadband fiber optical parametric amplifiers," Opt. Lett. 21,573-575 (1996). [CrossRef] [PubMed]
- S. Fvrier, R. Jamier, J.-M. Blondy, S. L. Semjonov, M. E. Likhachev, M. M. Bubnov, E. M. Dianov, V. F. Khopin, M. Y. Salganskii, A. N. Guryanov, "Low Loss Large Mode Area Bragg Fibre," 31th European Conference on Optical Communication, Post Deadline paper PD Th4.4.3, Glasgow, United-Kingdom, 25-29 September 2005.
- J. Marcou, F. Brchet, Ph. Roy, "Design of weakly guiding Bragg fibres for chromatic dispersion shifting towards short wavelengths," Journal of Optics A: Pure and Applied Optics 3,S144-S153 (2001). [CrossRef]
- C. J. McKinstrie, S. Radic, and A. R. Chraplyvy, "Parametric amplifiers driven by two pump waves," IEEE J. Sel. Top. Quantum Electron. 8,538-547 (2002). [CrossRef]

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