## Asymmetric gain-saturated spectrum in fiber optical parametric amplifiers |

Optics Express, Vol. 20, Issue 14, pp. 15530-15539 (2012)

http://dx.doi.org/10.1364/OE.20.015530

Acrobat PDF (870 KB)

### Abstract

We demonstrate experimentally and numerically an unexpected spectral asymmetry in the saturated-gain spectrum of single-pump fiber optical parametric amplifiers. The interaction between higher-order four-wave mixing products and dispersive waves radiated as an effect of third-order dispersion influences the energy transfer to the signal, depending on its detuning with respect to the pump, and breaks the symmetry of the gain expected from phase-matching considerations in unsaturated amplifiers. The asymmetry feature of the saturated spectrum is shown to particularly depend on the dispersion characteristics of the amplifier and shows local maxima for specific dispersion values.

© 2012 OSA

## 1. Introduction

1. K. Inoue, “Optical level equalisation based on gain saturation in fibre optical parametric amplifier,” Electron. Lett. **36**(12), 1016–1018 (2000). [CrossRef]

3. A. Vedadi, A. M. Ariaei, M. M. Jadidi, and J. A. Salehi, “Theoretical study of high repetition rate short pulse generation with fiber optical parametric amplification,” J. Lightwave Technol. **30**(9), 1263–1268 (2012). [CrossRef]

2. C. Peucheret, M. Lorenzen, J. Seoane, D. Noordegraaf, C. V. Nielsen, L. Grüner-Nielsen, and K. Rottwitt, “Amplitude regeneration of RZ-DPSK signals in single-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. **21**(13), 872–874 (2009). [CrossRef]

4. K. Inoue and T. Mukai, “Experimental study of noise characteristics of a gain-saturated fiber optical parametric amplifier,” J. Lightwave Technol. **20**(6), 969–974 (2002). [CrossRef]

*β*, depends only on even-order dispersion as well as on the even powers of the pump-signal frequency separation [5]. Some spectral asymmetry may however be observed for wideband unsaturated FOPAs as a result of stimulated Raman scattering [6

6. A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, “Combined effect of Raman and parametric gain on single-pump parametric amplifiers,” Opt. Express **15**(13), 8104–8114 (2007). [CrossRef] [PubMed]

7. P. Kylemark, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Semi-analytical saturation theory of fiber optical parametric amplifiers,” J. Lightwave Technol. **24**(9), 3471–3479 (2006). [CrossRef]

8. K. Inoue and T. Mukai, “Signal wavelength dependence of gain saturation in a fiber optical parametric amplifier,” Opt. Lett. **26**(1), 10–12 (2001). [CrossRef] [PubMed]

## 2. Experimental observation

_{P}= 1557.5 nm that is phase modulated using a 10-Gb/s 2

^{7}-1 pseudorandom binary sequence (PRBS) to suppress stimulated Brillouin scattering, amplified by an erbium-doped fiber amplifier (EDFA) and filtered by a 1-nm bandwidth optical band pass filter (OBPF) to reduce the produced amplified spontaneous emission (ASE) noise.

_{0}= 1550.4 nm, nonlinear coefficient of 10.7 W

^{−1}⋅km

^{−1}, dispersion slope of 0.0185 ps/(nm

^{2}⋅km), and attenuation of 0.7 dB/km. The pump power at the HNLF input is 28.6 dBm. The gain spectra are measured using an optical spectrum analyzer (OSA).

_{S}) of −3 dBm (modest saturation) and −0.2 dBm (strong saturation) are shown in Fig. 2 . The experimental unsaturated gain spectrum is symmetric and has 25.4-dB gain at 1546 nm (anti-Stokes side) and 1570 nm (Stokes side). Clearly, one can see that the maximum gain drops differently at the two lobes of the spectrum when the gain enters saturation. The measured gain differences between the wavelengths corresponding to the maximum unsaturated gain are 1.9 dB and 3.5 dB when P

_{S}is −3 dBm and −0.2 dBm, respectively.

## 3. Interplay of HFPs and dispersive waves

*Δω*. The

_{PS}= |ω_{P}-ω_{S}|*n*

^{th}order HFP, noted

*n*HFP, is at angular frequency

*ω*(

_{n}= mω_{S}-*m-*1)

*ω*on the signal side when

_{P}*n*=

*m-*1 (for integer

*m*≥2), or on the idler side when

*n*=

*m*+ 1 (for integer

*m*≤-2). In the time domain, the total (pump, signal, idler and HFPs) power appears as oscillations that transform into a train of short pulses when the number and power of the HFPs increase. Therefore, as the amplifier enters the saturation regime and short pulses are formed, higher order dispersion, and more specifically TOD, affect considerably the dynamic of the propagating waves. Since the pump is located in the anomalous dispersion region of the fiber, the short pulses are perturbed in the presence of TOD and emit DWs to become stable as fundamental solitons [9

9. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A **51**(3), 2602–2607 (1995). [CrossRef] [PubMed]

10. A. K. Abeeluck and C. Headley, “Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation,” Opt. Lett. **30**(1), 61–63 (2005). [CrossRef] [PubMed]

11. M. Droques, B. Barviau, A. Kudlinski, M. Taki, A. Boucon, T. Sylvestre, and A. Mussot, “Symmetry-breaking dynamics of the modulational instability spectrum,” Opt. Lett. **36**(8), 1359–1361 (2011). [CrossRef] [PubMed]

*∆ω*such thatwhere

_{DW}*β*and

_{2}*β*are the second-order dispersion (SOD) and TOD, respectively,

_{3}*P*is the pump power and

_{P}*γ*is the nonlinear coefficient [12]. Energy transfer to shorter wavelengths as DWs disturbs the symmetric FWM efficiency between the two sides of the gain spectrum. If the condition

*∆ω*(

_{DW}=*n + 1*)

*∆ω*is satisfied, where

_{PS}*n*is an integer

*n*≥1 and

*∆ω*is the pump-signal angular frequency separation, the DWs will overlap at the anti-Stokes side with the signal (when λ

_{PS}_{S}< λ

_{P}) or idler (when λ

_{S}> λ

_{P}) for

*n*= 0, the first order HFP for

*n*= 1 (1HFP when λ

_{S}< λ

_{P}or −1HFP when λ

_{S}> λ

_{P}) and so on.

*n|*≥ 1 reduces the energy transfer to the wavelength at

*n*= 0 corresponding to the signal (idler) when λ

_{S}< λ

_{P}(λ

_{S}> λ

_{P}), hence reducing the gain or conversion efficiency at the anti-Stokes side.

_{P0}= λ

_{P}- λ

_{0}). As it can be seen, the wavelengths of the generated DWs overlap with the signal or the HFPs when ∆λ

_{P0}is between 3 and 10 nm. In the experiment reported in Sect. 2, ∆λ

_{P0}= 7.1 nm, for which it can be seen from Fig. 3(b) that the 1HFP almost overlaps with the DWs, which leads to energy transfer to the 1HFP, which in turn reduces the signal gain at the anti-stokes side of the spectrum.

_{S}= 1546 nm or −1HFP for λ

_{S}= 1570 nm) coinciding with the DWs on the anti-Stokes side. The steep power growth of the first order HFP on the anti-Stokes side is also clearly observed.

## 4. Numerical simulations

*ω*, depend on both SOD and TOD, their overlaps with the HFPs can be tuned by adjusting either the SOD or TOD of the fibre. Modification of the SOD can modify both the wavelength of the phase-matched signal and that of the DWs, while variations of TOD has an impact only on the wavelength of the DWs as the phase-matched signal wavelength depends only on SOD. Here we investigate the effect of both dispersion terms.

_{DW}### 4.1 Impact of SOD

*β*can be neglected, and in the unsaturated regime (i.e. the pump power dominates over the power of the signal and idler), is expressed aswhere Δ

_{3}*β*is the linear phase mismatch parameter. In what follows, the bandwidth of the FOPA is defined as the frequency separation between the two phase-matched signal wavelengths, i.e.

_{P0}. In order to evaluate the effect of amplifier bandwidth, or equivalently SOD, on the saturated gain, the signal gain and idler conversion efficiency spectra are simulated for three bandwidths obtained with three different values of ∆λ

_{P0}corresponding to emitted DWs overlapping with the phase-matched signal, 1HFP and 2HFP, respectively. Figure 6(a)-(c) show the saturated signal gain and idler conversion efficiency spectra and Fig. 6(d)-(f) show the output spectra for signals tuned to the maximum unsaturated gain on the short wavelength side of the spectrum. The signal input power is −0.2 dBm and all other parameters are the same as those in the experiment. The idler conversion efficiency spectra are mirror images of the signal spectra as they are plotted as a function of the signal-pump wavelength separation. The significant growth of the 1HFP and 2HFP are obvious in Fig. 6(b),(e) and Fig. 6(c),(f), respectively, when the HFPs are resonant with the emitted DWs. The saturated gain difference between the two sides of the spectrum is 0.2 dB, 5.1 dB and 4.4 dB for the broad, relatively narrow and narrow-band amplifiers in Fig. 6(a)-(c), respectively. A movie (Media 1) illustrating the temporal and spectral evolution of the total output power with ∆λ

_{P0}(or equivalently

*β*(

_{2}*ω*)) can be seen online. The simulations presented in the movie confirm well the growth of HFPs when they are close to DW wavelengths depicted by dashed blue line in the movie.

_{P}*P*(

_{I}*L*), and the signal output power,

*P*(

_{S}*L*)

*β*(

_{2}*ω*) for different saturation levels. In the small signal gain regime, the asymmetry factor is equal to one for all the amplifier bandwidths (corresponding to different values of

_{P}*β*(

_{2}*ω*) or equivalently ∆λ

_{P}_{P0}). The asymmetry factor becomes larger than one when the signal input power is increased to the saturation regime, indicating different energy transfers at the two sides of the spectrum.

_{P0}, or equivalently higher absolute values of

*β*(

_{2}*ω*).

_{P}### 4.2 Impact of TOD

*n =*0, its corresponding 1HFP for

*n =*1, and 2HFP for

*n =*2. The asymmetry factor is plotted as a function of dispersion slope for different signal input power levels in Fig. 8 . In this figure the SOD is fixed and equal to −0.169 ps

^{2}/km. This value corresponds to the dispersion at the pump wavelength of the experimental FOPA. Therefore all FOPAs obtained by varying the dispersion slope in Fig. 8 have the same unsaturated gain spectrum as in Fig. 5. The asymmetry factor is equal to one for unsaturated gain, which indicates that the signal and idler have the same output powers independently of the dispersion slope magnitude, as expected.

## 5. Discussion

## 6. Conclusion

## References and links

1. | K. Inoue, “Optical level equalisation based on gain saturation in fibre optical parametric amplifier,” Electron. Lett. |

2. | C. Peucheret, M. Lorenzen, J. Seoane, D. Noordegraaf, C. V. Nielsen, L. Grüner-Nielsen, and K. Rottwitt, “Amplitude regeneration of RZ-DPSK signals in single-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett. |

3. | A. Vedadi, A. M. Ariaei, M. M. Jadidi, and J. A. Salehi, “Theoretical study of high repetition rate short pulse generation with fiber optical parametric amplification,” J. Lightwave Technol. |

4. | K. Inoue and T. Mukai, “Experimental study of noise characteristics of a gain-saturated fiber optical parametric amplifier,” J. Lightwave Technol. |

5. | M. E. Marhic, |

6. | A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, “Combined effect of Raman and parametric gain on single-pump parametric amplifiers,” Opt. Express |

7. | P. Kylemark, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Semi-analytical saturation theory of fiber optical parametric amplifiers,” J. Lightwave Technol. |

8. | K. Inoue and T. Mukai, “Signal wavelength dependence of gain saturation in a fiber optical parametric amplifier,” Opt. Lett. |

9. | N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A |

10. | A. K. Abeeluck and C. Headley, “Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation,” Opt. Lett. |

11. | M. Droques, B. Barviau, A. Kudlinski, M. Taki, A. Boucon, T. Sylvestre, and A. Mussot, “Symmetry-breaking dynamics of the modulational instability spectrum,” Opt. Lett. |

12. | G. P. Agrawal, |

13. | K. Inoue and T. Mukai, “Spectral hole in the amplified spontaneous emission spectrum of a fiber optical parametric amplifier,” Opt. Lett. |

**OCIS Codes**

(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

(190.4410) Nonlinear optics : Nonlinear optics, parametric processes

(190.4970) Nonlinear optics : Parametric oscillators and amplifiers

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: May 1, 2012

Revised Manuscript: June 18, 2012

Manuscript Accepted: June 19, 2012

Published: June 26, 2012

**Citation**

Zohreh Lali-Dastjerdi, Karsten Rottwitt, Michael Galili, and Christophe Peucheret, "Asymmetric gain-saturated spectrum in fiber optical parametric amplifiers," Opt. Express **20**, 15530-15539 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-14-15530

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### References

- K. Inoue, “Optical level equalisation based on gain saturation in fibre optical parametric amplifier,” Electron. Lett.36(12), 1016–1018 (2000). [CrossRef]
- C. Peucheret, M. Lorenzen, J. Seoane, D. Noordegraaf, C. V. Nielsen, L. Grüner-Nielsen, and K. Rottwitt, “Amplitude regeneration of RZ-DPSK signals in single-pump fiber-optic parametric amplifiers,” IEEE Photon. Technol. Lett.21(13), 872–874 (2009). [CrossRef]
- A. Vedadi, A. M. Ariaei, M. M. Jadidi, and J. A. Salehi, “Theoretical study of high repetition rate short pulse generation with fiber optical parametric amplification,” J. Lightwave Technol.30(9), 1263–1268 (2012). [CrossRef]
- K. Inoue and T. Mukai, “Experimental study of noise characteristics of a gain-saturated fiber optical parametric amplifier,” J. Lightwave Technol.20(6), 969–974 (2002). [CrossRef]
- M. E. Marhic, Fiber optical parametric amplifiers, oscillators and related devices (Cambridge University Press, 2008), Chap. 5.
- A. S. Y. Hsieh, G. K. L. Wong, S. G. Murdoch, S. Coen, F. Vanholsbeeck, R. Leonhardt, and J. D. Harvey, “Combined effect of Raman and parametric gain on single-pump parametric amplifiers,” Opt. Express15(13), 8104–8114 (2007). [CrossRef] [PubMed]
- P. Kylemark, H. Sunnerud, M. Karlsson, and P. A. Andrekson, “Semi-analytical saturation theory of fiber optical parametric amplifiers,” J. Lightwave Technol.24(9), 3471–3479 (2006). [CrossRef]
- K. Inoue and T. Mukai, “Signal wavelength dependence of gain saturation in a fiber optical parametric amplifier,” Opt. Lett.26(1), 10–12 (2001). [CrossRef] [PubMed]
- N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51(3), 2602–2607 (1995). [CrossRef] [PubMed]
- A. K. Abeeluck and C. Headley, “Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation,” Opt. Lett.30(1), 61–63 (2005). [CrossRef] [PubMed]
- M. Droques, B. Barviau, A. Kudlinski, M. Taki, A. Boucon, T. Sylvestre, and A. Mussot, “Symmetry-breaking dynamics of the modulational instability spectrum,” Opt. Lett.36(8), 1359–1361 (2011). [CrossRef] [PubMed]
- G. P. Agrawal, Nonlinear Fiber Optics 3rd ed. (Academic Press, 2006), Chap. 2 and 12.
- K. Inoue and T. Mukai, “Spectral hole in the amplified spontaneous emission spectrum of a fiber optical parametric amplifier,” Opt. Lett.26(12), 869–871 (2001). [CrossRef] [PubMed]

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