## Narrowband and tunable optical parametric amplification in Bismuth-Oxide-based highly nonlinear fiber

Optics Express, Vol. 16, Issue 18, pp. 13871-13877 (2008)

http://dx.doi.org/10.1364/OE.16.013871

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### Abstract

The one-pump optical fiber parametric amplification (FOPA) has been well known to be a means for realizing wideband amplification when the group-delay dispersion (*β*_{2}) is small at the pump wavelength. In this paper, we report one-pump FOPA in short Bismuth-Oxide-based highly nonlinear fiber (Bi-HNLF) that has large normal dispersion at 1550nm, both theoretically and experimentally, for the first time to the best of our knowledge. We found that, due to the large *β*_{4} along with large *β*_{2}, FOPA in the Bi-HNLF is very narrowband, and its gain peak wavelength is tunable in proportional to the pump wavelength. We achieved the gain bandwidth as narrow as 0.75nm and gain peak as high as 58dB in the experiment using a 2m-long Bi-HNLF.

© 2008 Optical Society of America

## 1. Introduction

2. 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]

*P*

_{SBS}is also higher than the silica-based fibers. Hence, Bi-HNLF can lead to much more compact photonic devices. Drawbacks of Bi-HNLF are its large normal material dispersion (

*D*~-280ps/km/nm) and large attenuation (~1000dB/km) around the wavelength region of 1550nm. Bi-HNLF is also predicted to have large higher-order dispersions, such as β

_{3}and β

_{4}, because the variation of dispersion is large at the wavelength far from ZDW. The optical parameters of Bi-HNLF are summarized in Table 1 as compared to silica-based DSF and HNLF.

6. J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Bismuth oxide nonlinear fibrebased 80 Gbit/s wavelength conversion and demultiplexing using cross-phase modulation and filtering scheme,” IEEE Electron. Lett. **41**, 22 (2005). [CrossRef]

_{4}along with large β

_{2}, FOPA in the Bi-HNLF is very narrowband, and its gain peak wavelength is tunable in proportional to the pump wavelength. We achieved the gain bandwidth as narrow as 0.75nm and gain peak as high as 58dB in the experiment using a 2m-long Bi-HNLF.

## 2. Theory

*ω*,

_{p}*ω*, and

_{s}*ω*which satisfy 2

_{i}*ω*=

_{p}*ω*+

_{s}*ω*, we have to consider the phase mismatching Δ

_{i}*β*which is approximately given by

*ω*=

*ω*-

_{s}*ω*and

_{p}*β*,

_{p}*β*, and

_{s}*β*are the propagation constant of a pump, a signal, and an idler.

_{i}*β*is the

_{m}*m*-th derivative of

*β*(

*ω*), which is determined by the fiber properties [3].

*G*is given by

_{p}*P*

_{0}is pump power,

*L*is fiber length,

*γ*is the nonlinear coefficient of the fiber, and

*g*is the parametric gain, which is given by

*β*satisfies

*β*=0 or Δ

*β*=-4

*γ*

*P*

_{0}and the maximum gain is obtained when Δ

*β*=-2

*γ*

*P*

_{0}.

*β*

_{2}=

*β*

_{3}(

*ω*-

_{p}*ω*

_{0}) and

*β*

_{4}is a negative constant. Figure 1 shows the relation between Δ

*β*and Δ

*ω*. This means that the FOPA characteristics are highly dependent on whether the pump wavelength is in NDR or ADR. In both cases, the gain spectra become symmetric with respect to the pump wavelength. Notably, when the pump is in NDR, the gain spectra symmetrically split into two isolated and narrow gain peaks far from the pump wavelength.

*λ*can be calculated by substituting Δ

_{peak}*β*=-2γ

*P*

_{0}to Eq. (3) and given by

*λ*is the separation between the pump and the gain peak wavelengths. The variable term of the Eq. (5) is only the pump wavelength. The Eq. (5) indicates that the FOPA gain spectrum is symmetric with respect to the pump wavelength. In addition, when the pump wavelength is in NDR, the bandwidth of the parametric gain

*δλ*can be calculated as follows:

*λ*becomes larger, or

*β*

_{4}becomes larger. These equations indicate that

*β*

_{4}, the 4-th derivative of the propagation constant

*β*, plays an important role in determining the FOPA spectra. Owing to extremely large

*β*

_{4}in Bi-HNLF, the FOPA spectrum in Bi-HNLF is much different from that in the conventional silica-based DSF or HNLF.

## 3. Experiment

## 4. Discussion

*λ*

_{0}=1556nm, fiber length

*L*=30m, and peak power

*P*

_{0}=20W for HNLF, and

*λ*

_{0}=1542.3nm, fiber length

*L*=200m, and peak power

*P*

_{0}=12W for DSF. Bi-HNLF has large normal dispersion,

*i.e.*the ZDW in Bi-HNLF is far from 1550nm. In this case, the variation of

*ω*is negligible owing to the large value of

_{p}*ω*-

_{p}*ω*

_{0}in Eq. (5). This means that the value of Δ

*λ*in Eq. (5) can be regarded as a constant. Furthermore, the absolute value of

*β*

_{4}in Bi-HNLF is predicted to be extremely large as compared to the standard silica-based DSF or HNLF, therefore the bandwidth of FOPA in Bi-HNLF narrows according to Eq. (6). Discrepancies between the simulation (Fig. 2) and the experiment (Fig. 4) might be because we neglected large fiber attenuation, splicing loss, and spatial variation of the fiber dispersion.

## 5. Conclusion

*β*

_{4}along with large

*β*

_{2}, FOPA in the Bi-HNLF is very narrowband, and its gain peak wavelength is tunable in proportional to the pump wavelength. We achieved the gain bandwidth as narrow as 0.75nm and gain peak as high as 58dB in the experiment using a 2m-long Bi-HNLF.

## Acknowledgments

## References and links

1. | G. P. Agrawal, |

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

3. | M. E. Marhic, K. K-Y. Wong, and L. G. Kazovsky, “Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers,” |

4. | J. H. Lee, T. Tanemura, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Comparison of Kerr Nonlinearlity Figure-of-Merit Including Stimulated Brillouin Scattering for Bismuth Oxide- and Silica-based Nonlinear Fibers,” ECOC’05 , |

5. | J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Bismuth-Oxide-based nonlinear fiber with a high SBS threshold and its application to four-wave-mixing wavelength conversion using a pure continuous-wave pump,” IEEE Photon J. Lightwave Technol. |

6. | J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Bismuth oxide nonlinear fibrebased 80 Gbit/s wavelength conversion and demultiplexing using cross-phase modulation and filtering scheme,” IEEE Electron. Lett. |

**OCIS Codes**

(160.2290) Materials : Fiber materials

(190.4975) Nonlinear optics : Parametric processes

**ToC Category:**

Nonlinear Optics

**History**

Original Manuscript: June 19, 2008

Revised Manuscript: August 14, 2008

Manuscript Accepted: August 15, 2008

Published: August 22, 2008

**Citation**

Kyota Seki and Shinji Yamashita, "Narrowband and tunable optical parametric amplification in Bismuth-Oxide-based highly nonlinear fiber," Opt. Express **16**, 13871-13877 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-18-13871

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### References

- G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1989).
- 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]
- M. E. Marhic, K. K-Y. Wong, and L. G. Kazovsky, "Wide-band tuning of the gain spectra of one-pump fiber optical parametric amplifiers," IEEE J. Quantum Electron. 10, 5 (2004).
- J. H. Lee, T. Tanemura, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, "Comparison of Kerr Nonlinearlity Figure-of-Merit Including Stimulated Brillouin Scattering for Bismuth Oxide- and Silicabased Nonlinear Fibers," ECOC�?? 05, 467-468 (2005).
- J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, "Bismuth-Oxide-based nonlinear fiber with a high SBS threshold and its application to four-wave-mixing wavelength conversion using a pure continuous-wave pump," J. Lightwave Technol. 24, 22-28 (2006).
- J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, "Bismuth oxide nonlinear fibrebased 80 Gbit/s wavelength conversion and demultiplexing using cross-phase modulation and filtering scheme," IEEE Electron. Lett. 41, 22 (2005). [CrossRef]

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