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

Narrowband and tunable opticalparametric amplification in

Bismuth-Oxide-based highly nonlinearfiber

Kyota SekiDepartment of Electronic Engineering, Institute of Industrial Science, The University of

Tokyo, Japan

[email protected]

Shinji YamashitaDepartment of Electronic Engineering, Graduate School of Engineering, The University of

Tokyo, Japan

[email protected]

Abstract: The one-pump optical fiber parametric amplification (FOPA)has been well known to be a means for realizing wideband amplificationwhen the group-delay dispersion (β2) is small at the pump wavelength. Inthis paper, we report one-pump FOPA in short Bismuth-Oxide-based highlynonlinear fiber (Bi-HNLF) that has large normal dispersion at 1550nm,both theoretically and experimentally, for the first time tothe best of ourknowledge. We found that, due to the largeβ4 along with largeβ2, FOPA inthe Bi-HNLF is very narrowband, and its gain peak wavelengthis tunablein proportional to the pump wavelength. We achieved the gainbandwidth asnarrow as 0.75nm and gain peak as high as 58dB in the experiment using a2m-long Bi-HNLF.

© 2008 Optical Society of America

OCIS codes:(190:4975) Parametric processes; (190:2290) Fiber materials.

References and links1. 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).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 nonlinearfiber with a high SBS threshold and its application to four-wave-mixing wavelength conversion using a purecontinuous-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 fibre-based 80 Gbit/s wavelength conversion and demultiplexing using cross-phase modulation and filtering scheme,”IEEE Electron. Lett.41, 22 (2005).

#97663 - $15.00 USD Received 19 Jun 2008; revised 14 Aug 2008; accepted 15 Aug 2008; published 22 Aug 2008

(C) 2008 OSA 1 September 2008 / Vol. 16, No. 18 / OPTICS EXPRESS 13871

1. Introduction

The optical parametric amplification (OPA) is one of the optical nonlinear effects in whichthe 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 tobe a means of realizing wideband amplification [2]. FOPA characteristics are highly dependenton the pump wavelength and dispersion characteristics of the fibers, that is, whether the pumpwave is in normal dispersion region (NDR) or anomalous dispersion region (ADR) [3]. Whenthe pump wave is in NDR, the gain spectra present two isolatedand narrow gain peaks whichare symmetric and far from the pump wavelength. A number of papers on FOPA have beenreported 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 highlynonlinear 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 tohave ultrahigh nonlinearity, around 1,000-times higher than the silica-based fibers[4][5]. It isalso known that the threshold power of stimulated Brillouinscattering (SBS)PSBS is also higherthan the silica-based fibers. Hence, Bi-HNLF can lead to muchmore compact photonic devices.Drawbacks of Bi-HNLF are its large normal material dispersion (D ∼ −280ps/km/nm) andlarge attenuation (∼ 1000dB/km) around the wavelength region of 1550nm. Bi-HNLF is alsopredicted to have large higher-order dispersions, such asβ3 andβ4, because the variation ofdispersion is large at the wavelength far from ZDW. The optical parameters of Bi-HNLF aresummarized in Table 1 as compared to silica-based DSF and HNLF.

Table 1. Optical parameters of various types of nonlinear fibers [3].

DSF HNLF Bi-HNLFNonlinear coefficient [1/W/km] 2.3 18 ∼ 1350

Attenuation [dB/km] 0.2 0.5 ∼ 1000Dispersion [ps/km/nm] ∼ 0.1 0.6 −280

β2 [s2/3] −5.1×10−27 3.0×10−26 3.6×10−25

β3 [s3/3] 1.1×10−40 4.9×10−41 4.1×10−38

β4 [s4/3] −5.0×10−55 −5.8×10−56 −1.1×10−50

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 ofBi-HNLF, around 1 meter. However, there has been no report ofFOPA 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 theoreticallyand experimentally, for the firsttime to the best of our knowledge. We found that, due to the largeβ4 along with largeβ2, FOPAin the Bi-HNLF is very narrowband, and its gain peak wavelength is tunable in proportional tothe pump wavelength. We achieved the gain bandwidth as narrow as 0.75nm and gain peak ashigh 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, havingangular frequenciesωp, ωs, andωi which satisfy 2ωp = ωs +ωi, we have to consider the phasemismatching∆β which is approximately given by

∆β = βs +βi −2βp ≃ β2(∆ω)2 +β4

12(∆ω)4, (1)



where∆ω = ωs −ωp andβp, βs, andβi are the propagation constant of a pump, a signal, andan idler.βm is them-th derivative ofβ (ω), which is determined by the fiber properties [3].

Assuming the three waves remain in the same state of linear polarization along the entirefiber and the fiber has no attenuation, the parametric amplification factorGp is given by

Gp = 1+

[

γP0

gsinh(gL)

]2

, (2)

whereP0 is pump power,L is fiber length,γ is the nonlinear coefficient of the fiber, andg is theparametric gain, which is given by

g =

√

−∆β(

∆β4

+ γP0

)

. (3)

Hence, the substantial gain is obtained when∆β satisfies

−4γP0 < ∆β < 0. (4)

The Eq. (3) implies that the edge of the parametric gain is obtained when∆β = 0 or ∆β =−4γP0 and the maximum gain is obtained when∆β = −2γP0.

According to the above discussion, we can calculate the wavelength and the bandwidth of theparametric gain. Here, we assume thatβ2 = β3(ωp −ω0) andβ4 is a negative constant. Figure1 shows the relation between∆β and∆ω. This means that the FOPA characteristics are highlydependent on whether the pump wavelength is in NDR or ADR. In both cases, the gain spectrabecome 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 pumpwavelength.

O

04 Pγ−

Pump in ADR Pump in NDR

Gain Region

β∆

ω∆

Fig. 1. Phase mismatching∆β as a function of∆ω

The wavelength of the gain peakλpeak can be calculated by substituting∆β = −2γP0 to Eq.(3) and given by

λpeak ≃ λp ±λ 2

p

2πc

√

√

√

√

−β3(ωp −ω0)−√

β 23 (ωp −ω0)2−2β4γP0/3

β4/6= λp ±∆λ , (5)



where∆λ is the separation between the pump and the gain peak wavelengths. The variable termof the Eq. (5) is only the pump wavelength. The Eq. (5) indicates that the FOPA gain spectrumis symmetric with respect to the pump wavelength. In addition, when the pump wavelength isin NDR, the bandwidth of the parametric gainδλ can be calculated as follows:

δλ ≃λ 2

0

2πc

∣

∣∆ω|∆β=−4γP0−∆ω|∆β=0

∣

∣ ≃32

(

λ0

πc

)4 ∣

∣

∣

∣

γP0

β4(∆λ )3

∣

∣

∣

∣

(6)

The Eq. (6) means that the FOPA gain bandwidth becomes narrower as the wavelength dif-ference∆λ becomes larger, orβ4 becomes larger. These equations indicate thatβ4, the 4-thderivative of the propagation constantβ , plays an important role in determining the FOPAspectra. Owing to extremely largeβ4 in Bi-HNLF, the FOPA spectrum in Bi-HNLF is muchdifferent from that in the conventional silica-based DSF orHNLF.

0

20

40

60

80

100

120

140

1500 1520 1540 1560 1580 1600 1620

Gai

n [d

B]

λ [nm]

λp = 1555 [nm]λp = 1556 [nm]λp = 1557 [nm]λp = 1558 [nm]λp = 1559 [nm]λp = 1560 [nm]λp = 1561 [nm]λp = 1562 [nm]λp = 1563 [nm]

Fig. 2. Theoretical gain spectra at different pump wavelength in Bi-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 maximumgain is predicted to exceed 100dB, and the gain bandwidth is extremely narrow, narrower than0.1nm. It is also observed that the gain wavelength shifts in proportion to the shift of pumpwavelength.

3. Experiment

The experimental configuration is shown in Fig. 3, where the gain medium is Bi-HNLF, whoseoptical 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 1/256duty cycle by using a Mach-Zehnder Intensity Modulator (MZ-IM) to provide the peak pumppower as high as 7W of peak power. The electric pulse signal isgenerated by an arbitrarywaveform generator (AWG). A polarization controller 1 (PC1)is inserted due to the polariza-tion dependency of MZ-IM. The modulated pump lightwave is then amplified by an Erbiumdoped fiber amplifier 1 (EDFA1) in order to compensate the attenuation of MZ-IM. It is further



TLS1

TLS2

PC2

PC3

PC1

MZ-IM

90

EDFA1

VOATBFEDFA2 TBF

10

ISO

Bi-HNLF

VOA

OSA

2040 ns 2040 ns

8 ns8 ns8 ns

t

Signal

Pump

AWG

Fig. 3. Experimental Setup

amplified by an EDFA2 with a maximum average output power of about 30dBm, and filtered bya wavelength tunable bandpass filter 1 (TBF1) and TBF2. The two TBFs are used to filter outthe high-intensity ASE from EDFA2. The source of the signal lightwave is another TLS2. Thesignal 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, whereFOPA 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 pumplightwave, the VOA is inserted just before the optical spectrum analyzer (OSA).

-70

-60

-50

-40

-30

-20

-10

0

10

1500 1520 1540 1560 1580 1600 1620

Po

we

r[d

Bm

]

λs [nm]

λp = 1555[nm]λp = 1556[nm]λp = 1557[nm]λp = 1558[nm]λp = 1559[nm]λp = 1560[nm]λp = 1561[nm]λp = 1562[nm]λp = 1563[nm]

Pump

Parametric Gain

Parametric Gain

Raman Gain

Fig. 4. Experimental ASE spectra at different pump wavelength in Bi-HNLF.

The experimental ASE spectra at each pump wavelength are shown in Fig. 4. The very nar-row 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 cal-culation 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 signallightwave is amplified by34dB. Since the pump is a pulse train with duty cycle of 1/256 whereas the signal is continuouswave (CW), the instantaneous parametric gain is estimated toreach 58dB. The idler lightwaveis also amplified to the same level of the amplified signal lightwave, which also confirms thepresence of FOPA.

The shift of ASE spectra at different pump wavelength is shown in Fig. 6. The bandwidth ofthe ASE spectra is about 0.75 nm. Figure 7 (a) shows the maximum gain as a function of theaverage pump power. This means that the parametric gain exponentially increases as the pumppower increases and is not almost dependent on pump wavelength. The difference of the peak



-80

-60

-40

-20

0

1500 1520 1540 1560 1580 1600 1620

Po

we

r[d

Bm

]

λs [nm]

Signal and PumpPumpSignal

Pump

Signal IdlerAbout34[dB] Gain

Fig. 5. Measurement of optical parametric amplification.

-70

-60

-50

-40

-30

-20

1508 1510 1512 1514 1516 1518

Pow

er[d

Bm

]

λs [nm]

λp = 1555[nm]λp = 1556[nm]λp = 1557[nm]λp = 1558[nm]λp = 1559[nm]λp = 1560[nm]

Fig. 6. The shift of ASE spectra as the pump wavelength is changed.

0

5

10

15

20

25

30

35

40

200 250 300 350 400 450 500 550 600

aver

age

Gai

n[dB

]

average P0 [mW]

λp = 1557[nm]λp = 1560[nm]λp = 1561[nm]λp = 1562[nm]

(a) Maximum gain as a function of the averagepump power.

0.5

0.55

0.6

0.65

0.7

0.75

200 250 300 350 400 450 500

Ban

dwid

th [n

m]

average P0 [mW]

(b) 3 dB bandwidth as a function of the averagepump power.

Fig. 7. Average pump power dependency of the maximum gain and 3 dB bandwidth

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 functionof the average pump power.This means that the bandwidth increase linearly in proportion to the increase of the pump poweras predicted from the Eq. (6).



4. Discussion

0

10

20

30

40

50

1300 1350 1400 1450 1500 1550 1600

Gai

n [d

B]

λ [nm]

λp = 1526.9 [nm]λp = 1530.4 [nm]λp = 1533.4 [nm]λp = 1536.6 [nm]λp = 1538.0 [nm]λp = 1539.0 [nm]λp = 1540.0 [nm]λp = 1541.0 [nm]λp = 1542.0 [nm]

(a) DSF.

0

10

20

30

40

50

60

70

80

90

1300 1350 1400 1450 1500 1550 1600

Gai

n [d

B]

λ [nm]

λp = 1553 [nm]λp = 1554 [nm]λp = 1555 [nm]λp = 1556 [nm]λp = 1557 [nm]λp = 1558 [nm]

(b) HNLF .

Fig. 8. Theoretical gain spectra at different pump wavelength in DSF and HNLF.

The shape of the experimental ASE spectra of FOPA in Bi-HNLF is much different fromthose of conventional HNLF or DSF. Figure 8 shows the resultsof the theoretical calculationusing the parameters summarized in Table 1. We also assume that the ZDWλ0 = 1556nm,fiber lengthL = 30m, and peak powerP0 = 20W for HNLF, andλ0 = 1542.3nm, fiber lengthL = 200m, and peak powerP0 = 12W for DSF. Bi-HNLF has large normal dispersion,i.e. theZDW in Bi-HNLF is far from 1550nm. In this case, the variationof ωp is negligible owing tothe large value ofωp−ω0 in Eq. (5). This means that the value of∆λ in Eq. (5) can be regardedas a constant. Furthermore, the absolute value ofβ4 in Bi-HNLF is predicted to be extremelylarge as compared to the standard silica-based DSF or HNLF, therefore the bandwidth of FOPAin Bi-HNLF narrows according to Eq. (6). Discrepancies between the simulation (Fig. 2) andthe experiment (Fig. 4) might be because we neglected large fiber attenuation, splicing loss, andspatial 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 ourknowledge. Due to the largeβ4 along with largeβ2, FOPA in the Bi-HNLF is very narrowband,and its gain peak wavelength is tunable in proportional to the pump wavelength. We achievedthe gain bandwidth as narrow as 0.75nm and gain peak as high as 58dB in the experiment usinga 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.



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