## 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

The optical parametric amplification (OPA) is one of the optical nonlinear effects in which the signal and idler waves are amplified through the process of four wave mixing (FWM) [1]. Especially, the one-pump fiber optical fiber parametric amplification (FOPA) is a well known to be a means of realizing wideband amplification [2]. FOPA characteristics are highly dependent on the pump wavelength and dispersion characteristics of the fibers, that is, whether the pump wave is in normal dispersion region (NDR) or anomalous dispersion region (ADR) [3]. When the pump wave is in NDR, the gain spectra present two isolated and narrow gain peaks which are symmetric and far from the pump wavelength. A number of papers on FOPA have been reported so far, whereas the pump wavelength has been set around zero-dispersion wavelength (ZDW) of the nonlinear fiber, mostly silica-based dispersion-shifted fibers (DSF) or highly nonlinear fibers (HNLF), in order to exploit the broad bandwidth of FOPA.

On the other hand, Bismuth-Oxide-based highly nonlinear fiber (Bi-HNLF) is well known to have ultrahigh nonlinearity, around 1,000-times higher than the silica-based fibers[4][5]. It is also known that the threshold power of stimulated Brillouin scattering (SBS) *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.

Bi-HNLF has been applied to wavelength converters or demultiplexers based on FWM [6]. In these applications, the drawbacks of Bi-HNLF have been avoided by use of a short-piece of Bi-HNLF, around 1 meter. However, there has been no report of FOPA in Bi-HNLF, since Bi-HNLF has been believed not to be suitable for FOPA due to its large dispsersions. In this paper, we report one-pump FOPA in short Bi-HNLF 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.

## 2. Theory

As the starting point of the FOPA concerning a single pump, a signal, and an idler, having angular frequencies *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

where Δ*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].

Assuming the three waves remain in the same state of linear polarization along the entire fiber and the fiber has no attenuation, the parametric amplification factor *G _{p}* is given by

where *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

Hence, the substantial gain is obtained when Δ*β* satisfies

The Eq. (3) implies that the edge of the parametric gain is obtained when Δ*β*=0 or Δ*β*=-4*γ*
*P*
_{0} and the maximum gain is obtained when Δ*β*=-2*γ*
*P*
_{0}.

According to the above discussion, we can calculate the wavelength and the bandwidth of the parametric gain. Here, we assume that *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.

The wavelength of the gain peak *λ _{peak}* can be calculated by substituting Δ

*β*=-2γ

*P*

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

where Δ*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:

The Eq. (6) means that the FOPA gain bandwidth becomes narrower as the wavelength difference Δ*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.

We calculated the theoretical gain spectra at different pump wavelength and showed in Fig. 2 by using the Eq. (2), assuming the same conditions with the experiment in the next section. Here we neglect Raman scattering, spatial variation of the fiber dispersion, and fiber attenuation. The simulated gain spectra is shown in Table 1 for different pump wavelengths. The maximum gain is predicted to exceed 100dB, and the gain bandwidth is extremely narrow, narrower than 0.1nm. It is also observed that the gain wavelength shifts in proportion to the shift of pump wavelength.

## 3. Experiment

The experimental configuration is shown in Fig. 3, where the gain medium is Bi-HNLF, whose optical parameters are listed in Table 1. The source of the pump lightwave is the tunable laser 1 (TLS1). The pump lightwave is modulated with a pulse train having 8ns pulsewidth and 1/256 duty cycle by using a Mach-Zehnder Intensity Modulator (MZ-IM) to provide the peak pump power as high as 7W of peak power. The electric pulse signal is generated by an arbitrary waveform generator (AWG). A polarization controller 1 (PC1) is inserted due to the polarization dependency of MZ-IM. The modulated pump lightwave is then amplified by an Erbium doped fiber amplifier 1 (EDFA1) in order to compensate the attenuation of MZ-IM. It is further amplified by an EDFA2 with a maximum average output power of about 30dBm, and filtered by a wavelength tunable bandpass filter 1 (TBF1) and TBF2. The two TBFs are used to filter out the high-intensity ASE from EDFA2. The source of the signal lightwave is another TLS2. The signal light is attenuated by a variable optical attenuator (VOA). The pump and signal light-waves are combined by a 90/10 optical coupler and injected into the 2-m long Bi-HNLF, where FOPA is realized. Owing to the polarization dependency of FOPA, PC2 and PC3 are inserted. An isolator (ISO) is used to prevent reflections. Due to the very high peak power of the pump lightwave, the VOA is inserted just before the optical spectrum analyzer (OSA).

The experimental ASE spectra at each pump wavelength are shown in Fig. 4. The very narrow ASE spectrum is obtained and it shifts in proportion to the shift of the pump wavelength, as expected. This experimental ASE spectra show the good agreement with the theoretical calculation shown in Fig. 2. Also the Raman gain spectrum is observed at the longer (~35nm) wavelength side of the pump wavelength.

Figure 5 shows the measurement of FOPA in Bi-HNLF. The signal lightwave is amplified by 34dB. Since the pump is a pulse train with duty cycle of 1/256 whereas the signal is continuous wave (CW), the instantaneous parametric gain is estimated to reach 58dB. The idler lightwave is also amplified to the same level of the amplified signal lightwave, which also confirms the presence of FOPA.

The shift of ASE spectra at different pump wavelength is shown in Fig. 6. The bandwidth of the ASE spectra is about 0.75 nm. Figure 7 (a) shows the maximum gain as a function of the average pump power. This means that the parametric gain exponentially increases as the pump power increases and is not almost dependent on pump wavelength. The difference of the peak value of the parametric gain is originated from the polarization dependency. Furthermore, Fig. 7 (b) shows the 3 dB bandwidth of the ASE spectrum as a function of the average pump power. This means that the bandwidth increase linearly in proportion to the increase of the pump power as predicted from the Eq. (6).

## 4. Discussion

The shape of the experimental ASE spectra of FOPA in Bi-HNLF is much different from those of conventional HNLF or DSF. Figure 8 shows the results of the theoretical calculation using the parameters summarized in Table 1. We also assume that the ZDW *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 _{p}* is negligible owing to the large value of

*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

In this paper, we reported one-pump FOPA in short Bi-HNLF, for the first time to the best of our knowledge. 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.

## Acknowledgments

The authors would like to thank Dr. N. Sugimoto, Dr.T. Nagashima, Dr. T. Hasegawa and Dr. S. Ohara of Asahi Glass Co. for supplying the Bi-HNLF used in the experiment.

## References and links

**1. **G. P. Agrawal, *Nonlinear Fiber Optics* (Academic Press, 1989).

**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]

**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,” *IEEE J. Quantum Electron.* **10**, 5 (2004).

**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 , **3**, 467–468 (2005).

**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. **24**, 22–28 (2006).

**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]