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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 20303–20312
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Optical parametric gain and bandwidth in highly nonlinear tellurite hybrid microstructured optical fiber with four zero-dispersion wavelengths

Tong Hoang Tuan, Tonglei Cheng, Koji Asano, Zhongchao Duan, Weiqing Gao, Dinghuan Deng, Takenobu Suzuki, and Yasutake Ohishi  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 20303-20312 (2013)
http://dx.doi.org/10.1364/OE.21.020303


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Abstract

The parametric amplification gain and bandwidth in highly nonlinear tellurite hybrid microstructured optical fiber (HMOF) are simulated based on four wave mixing process. The fiber core and cladding materials are made of TeO2–Li2O–WO3–MoO3–Nb2O5 and TeO2–ZnO–Na2O–P2O5 glass, respectively. The fiber has four zero-dispersion wavelengths and the chromatic dispersion is flattened near the zero-dispersion wavelengths. A broad gain bandwidth as wide as 1200 nm from 1290 to 2490 nm can be realized in the near infrared window by using a tellurite HMOF as short as 25 cm.

© 2013 OSA

1. Introduction

In recent decades, the field of nonlinear fiber optics has grown rapidly and attracted much attention due to the revolutionary developments of laser and optical fiber properties. One of the well-studied nonlinear effects in optical fibers is four wave mixing (FWM) which allows selective energy conversion from the pump wavelength to the red-shifted Stokes and the blue-shifted anti-Stokes wavelengths [1

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

4

4. B. Fang, O. Cohen, J. B. Moreno, and V. O. Lorenz, “State engineering of photon pairs produced through dual-pump spontaneous four-wave mixing,” Opt. Express 21(3), 2707–2717 (2013). [CrossRef] [PubMed]

]. The nonlinear phenomenon of FWM can be exploited for various interesting applications such as signal amplification, wavelength conversion, phase conjugation, optical regenerators and optical demultiplexers [5

5. G. M. Lloyd, I. G. Hughes, R. Bratfalean, and P. Ewart, “Broadband degenerate four-wave mixing of OH for flame thermometry,” Appl. Phys. B 67(1), 107–113 (1998). [CrossRef]

10

10. G. P. Agrawal, “Nonlinear fiber optics: its history and recent progress,” J. Opt. Soc. Am. B 28(12), A1–A10 (2011). [CrossRef]

]. Among them, fiber-based optical parametric amplifier (FOPA) is known as one of the most potential applications. Wideband and flattened gain profiles contrary to the Erbium-doped fiber amplifier (EDFA) could be provided by FOPA since the parametric gain process does not rely on energy transitions between energy states [11

11. 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(3), 506–520 (2002). [CrossRef]

]. This optical amplifier potentially offers high signal gain, wide gain bandwidth and low noise at arbitrary pump and signal wavelengths. FOPAs are very useful not only for high-speed and long-haul transmission system, but also for wavelength conversion, ultrafast all-optical signal processing, pulse regeneration, optical time-devision demultiplexing, optical sampling, quantum noise and correlation [12

12. J. Hansryd and P. A. Andrekson, “Wavelength tunable 40 GHz pulse source based on fiber optical parametric amplifier,” Electron. Lett. 37(9), 584–585 (2001). [CrossRef]

15

15. J. A. Levenson, I. Abram, Th. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993). [CrossRef]

].

Most FOPAs have been based on silica dispersion-shifted fibers. However, the low nonlinearity of silica fibers requires the fiber length of several kilometers to obtain practical FOPA gain [16

16. K. Inoue, “Four wave mixing in an optical fiber in the zero dispersion wavelength region,” J. Lightwave Technol. 10(11), 1553–1561 (1992). [CrossRef]

]. The important issue is that the deviation of zero-dispersion wavelength (ZDW) in such practical long fibers strongly affects FWM behaviors and makes the efficiency decrease. As a result, the efficient performance of FWM process demands high nonlinearity, low dispersion and short fiber length. In last decade, several reports on silica highly nonlinear fibers (HNLFs) [17

17. M. C. Ho, K. Uesaka, M. Marhic, Y. Akasaka, and L. G. Kazosky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain,” J. Lightwave Technol. 19(7), 977–981 (2001). [CrossRef]

] and photonic crystal fibers [18

18. K. K. Chow, C. Shu, C. Lin, and A. Bjarklev, “Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber,” IEEE Photon. Technol. Lett. 17(3), 624–626 (2005). [CrossRef]

] have shown improved FOPA performances by using just several ten meters of fiber. Furthermore, FWM-based wavelength conversion has been obtained by highly nonlinear bismuth-oxide fiber which is less than 1 meter [19

19. J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Four-wave-mixing-based wavelength conversion of 40-Gb/s nonreturn-to-zero signal using 40-cm bismuth oxide nonlinear optical fiber,” IEEE Photon. Technol. Lett. 17(7), 1474–1476 (2005). [CrossRef]

]. The efficiency of FWM depends on phase-matching condition which depends on chromatic dispersion profile of the optical fibers [20

20. R. H. Stolen, M. A. Bösch, and C. Lin, “Phase matching in birefringent fibers,” Opt. Lett. 6(5), 213–215 (1981). [CrossRef] [PubMed]

, 21

21. E. A. Zlobina, S. I. Kablukov, and S. A. Babin, “Phase matching for parametric generation in polarization maintaining photonic crystal fiber pumped by tunable Yb-doped fiber laser,” J. Opt. Soc. Am. B 29(8), 1959–1976 (2012). [CrossRef]

]. Although novel glass materials with extremely high nonlinearity such as bismuth-oxide, tellurite-oxide and chalcogenide glasses could reduce the interaction length, their large material dispersions and the difficulties in tailoring zero-dispersions for those fibers are the serious technical issue to be overcome.

Tellurite glasses with highly nonlinear refractive indices and wide transmission ranges have unique characterstics for various applications in optical telecommunications, laser amplifiers, nonlinear fiber optics, etc [22

22. M. Liao, X. Yan, W. Gao, Z. Duan, G. Qin, T. Suzuki, and Y. Ohishi, “Five-order SRSs and supercontinuum generation from a tapered tellurite microstructured fiber with longitudinally varying dispersion,” Opt. Express 19(16), 15389–15396 (2011). [CrossRef] [PubMed]

24

24. A. X. Lin, A. Ryasnyanskiy, and J. Toulouse, “Tunable third-harmonic generation in a solid-core tellurite glass fiber,” Opt. Lett. 36(17), 3437–3439 (2011). [CrossRef] [PubMed]

]. The chromatic dispersion profile of tellurite fibers could be tailored and the ZDWs could be shifted to telecommunication window by using microstructured optical fibers (MOFs) [25

25. M. Liao, X. Yan, G. Qin, C. Chaudhari, T. Suzuki, and Y. Ohishi, “A highly non-linear tellurite microstructure fiber with multi-ring holes for supercontinuum generation,” Opt. Express 17(18), 15481–15490 (2009). [CrossRef] [PubMed]

, 26

26. M. Liao, C. Chaudhari, G. Qin, X. Yan, T. Suzuki, and Y. Ohishi, “Tellurite microstructure fibers with small hexagonal core for supercontinuum generation,” Opt. Express 17(14), 12174–12182 (2009). [CrossRef] [PubMed]

]. By increasing the refractive index difference (∆n) between the core and cladding materials, highly nonlinear tellurite hybrid microstructured optical fibers (HMOFs) can provide the possibility of engineering near-zero flattened chromatic dispersion profiles with high freedom. This important property of tellurite HMOFs is promising for many potential applications including FOPA. Lately, it has been demonstrated that the tellurite HMOFs can be successfully fabricated [27

27. Z. Duan, M. Liao, X. Yan, C. Kito, T. Suzuki, and Y. Ohishi, “Tellurite composite microstructured optical fibers with tailored chromatic dispersion for nonlinear applications,” Appl. Phys. Express 4(72502), 1–3 (2011).

, 28

28. T. H. Tuan, K. Asano, Z. Duan, M. Liao, T. Suzuki, and Y. Ohishi, “Novel tellurite-phosphate composite microstructured optical fibers for highly nonlinear applications,” Phys. Status Solidi C 9(12), 2598–2601 (2012). [CrossRef]

]. However, the performance of FOPA by using tellurite HMOFs have not been investigated.

In this paper, we present the performance of optical parametric amplification which is simulated based on four wave mixing process in a highly nonlinear tellurite HMOF with TeO2–Li2O–WO3–MoO3–Nb2O5 (TLWMN) core and TeO2–ZnO–Na2O–P2O5 (TZNP) cladding glasses. The tellurite HMOF has four ZDWs and a very near-zero flattened chromatic dispersion profile from 1.3 to 2.3 μm. The linear phase-mismatch, the optical signal gain and the bandwidth are calculated with changes in fiber length and pump power. Our results show that highly nonlinear tellurite HMOFs with short fiber length are attractive for broadband FOPA.

2. Basic theoretical analyses

The FWM in optical fibers is a third-order nonlinear parametric process governed by a phase-matching condition. In this work, we are mainly interested in the degenerate FWM which involves the single pump frequency ω1 = ω2 = ωp. The theory of degenerate FWM has been well established and the pump, signal and idler wave evolution can be expressed by Eqs. (1), (2) and (3) if the transmission loss is low enough to be negligible [11

11. 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(3), 506–520 (2002). [CrossRef]

].
Apz=iγ[(|Ap|2+2(|Ai|2+|As|2))Ap+2AiAsA*pexp(iΔβz)]
(1)
Asz=iγ[(|As|2+2(|Ap|2+|Ai|2))As+A2pA*iexp(iΔβz)]
(2)
Aiz=iγ[(|Ai|2+2(|Ap|2+|As|2))Ai+A2pA*sexp(iΔβz)]
(3)
where Ap, Ai and As are the field amplitudes of the pump, the idler and the signal, respectively. The nonlinear coefficient is calculated by γ = n2ω/cAeff where n2 is the nonlinear refractive index, Aeff is the effective mode area and Δβ is the linear phase-mismatch.

In degenerate FWM, the photons from the pump frequency are annihilated and simultaneously new photons at the idler and signal frequencies are created to conserve the net energy and momentum during the parametric interaction.
2ωp=ωi+ωs
(4)
The phase-matching condition for this process is given by
κ=Δβ+2γP=0
(5)
where P is the pump power, ωp, ωi and ωs are the angular frequencies of the pump, the idler and the signal waves, respectively. The linear phase-mismatch Δβ can be expressed by
Δβ=βi+βs2βp=neff(ωi)ωic+neff(ωs)ωsc2neff(ωp)ωpc
(6)
where neff(ωi), neff(ωs) and neff(ωp) are the effective refractive indices at ωi, ωs and ωp, respectively. The frequency dependent effective refractive index neff(ωi) was a solution of the matrix eigenvalue problem originated from the Maxwell’s equations. It is accurately solved by employing the Lumerical Mode solution software, in company with the input of the fiber cross-section parameters as depicted in Fig. 1(a)
Fig. 1 (a) The structure of the highly nonlinear tellurite HMOF. The core diameter D = 0.894 μm, the air hole diameter d = 2.26 μm and the pitch Λ = 1.997 μm. (b) The chromatic dispersion of the highly nonlinear tellurite HMOF with four ZDWs at 1422, 1678, 1849 and 2195 nm.
and the refractive indices of the core and cladding materials. In practice, the refractive indices were experimentally obtained using the minimum-deviation method with the accuracy of ± 10−4. Because the neff(ωi) was obtained from the Maxwell’s equations that were built for a specific cross-section of the tellurite HMOF, it included not only the contributions of the material properties but also the waveguide properties. Therefore, the linear phase-mismatch and chromatic dispersion calculated from neff(λ) included both material and waveguide dispersions.

Commonly, the value of linear phase-mismatch Δβ is calculated by introducing the Taylor series expansion and the approximation up to the second term is usually taken. The gain bandwidth is determined from Δω = |ωs -ωp | in Eq. (7) [17

17. M. C. Ho, K. Uesaka, M. Marhic, Y. Akasaka, and L. G. Kazosky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain,” J. Lightwave Technol. 19(7), 977–981 (2001). [CrossRef]

]
Δββ2(Δω)2+112β4(Δω)4
(7)
However, when the values of β2 and β4 become very small, Eq. (7) is not precise enough to estimate the effect of the linear phase mismatch on OPA performance because the contributions of higher order dispersion parameters (β6, β8…) are not taken into account. In this work, because the linear phase-mismatch was fully calculated, the results for phase matching condition and signal gain of optical parametric amplification which are based on the linear phase-mismatch became more accurate.

When a strong pump and a weak incident signal waves were input, it is considered that the pump remains undepleted during the parametric gain process. The coupled amplitude equations Eqs. (1)-(3) are solved to give the evolution of the pump, the signal and the idler power along the fiber length. The optical signal gain (Gs) is given by
Gs=Ps(L)Ps(0)=1+(γPg)2sinh2(gL)
(8)
where L is the fiber length, Ps(0) and Ps(L) are the signal power at the input and output of the fiber and the parametric gain coefficient g is in the form of
g=(γP)2(κ2)2=(γP)2(γP+Δβ2)2
(9)
For conventional silica fibers which have low nonlinear coefficient, the signal gain Gs given by Eq. (8) is dominated by the characteristic of sinh2(gL). In particular, the actual signal gain only occurs when g remains real [29

29. M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, “Multi-order dispersion engineering for optimal four-wave mixing,” Opt. Express 16(10), 7551–7563 (2008). [CrossRef] [PubMed]

] and the fiber is long enough (from tens of meters to several kilometers) [1

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

, 16

16. K. Inoue, “Four wave mixing in an optical fiber in the zero dispersion wavelength region,” J. Lightwave Technol. 10(11), 1553–1561 (1992). [CrossRef]

, 17

17. M. C. Ho, K. Uesaka, M. Marhic, Y. Akasaka, and L. G. Kazosky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain,” J. Lightwave Technol. 19(7), 977–981 (2001). [CrossRef]

]. In order to obtain real value of g, the linear phase-mismatch must satisfy the condition −4γP<∆β<0. In the special case of perfect phase matching when Eq. (5) is satisfied, the maximum signal gain occurs. At that time, ∆β = − 2γP and gmax = γP. Moreover, it is noted from Eq. (8) for a fixed value of signal gain, it is possible to decrease the pump power P and the fiber length L. The benefit of using short fiber is to decrease the deviation of ZDW along the fiber and to increase the amplifier bandwidth [11

11. 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(3), 506–520 (2002). [CrossRef]

].

On the other hand, for tellurite HMOFs with extremely high nonlinearity, practical signal gain can also occur even if g becomes imaginary. In practice, imaginary g is obtained when

(γP)2(κ2)2<0
(10)

Under this condition, the parametric gain coefficient g and the optical signal gain Gs are given by

g=i(κ2)2(γP)2=igi
(11)
Gs=1+(γPgi)2sin2(giL)
(12)

From Eq. (12), it is noted that the optical signal gain Gs is governed by sin2(giL). When the product of giL reaches the value of π/2, the contribution of sin2(giL) is maximum. If the nonlinear coefficient γ is sufficiently large, actual signal gain Gs can be obtained even though g remains imaginary. Therefore, tellurite HMOFs with highly nonlinearity could have enhanced gain bandwidth of FOPA compared with that of silica fibers.

3. Highly nonlinear tellurite HMOF and chromatic dispersion engineering

Recently, nonsilica glasses such as tellurite and chalcogenide glasses are well-known as highly nonlinear materials but their material dispersions are very large and the zero dispersion wavelength is far from the telecom window. For tellurite glass, it was reported that the zero dispersion wavelength was shifted to near the telecom window using microstructured optical fibers [25

25. M. Liao, X. Yan, G. Qin, C. Chaudhari, T. Suzuki, and Y. Ohishi, “A highly non-linear tellurite microstructure fiber with multi-ring holes for supercontinuum generation,” Opt. Express 17(18), 15481–15490 (2009). [CrossRef] [PubMed]

, 26

26. M. Liao, C. Chaudhari, G. Qin, X. Yan, T. Suzuki, and Y. Ohishi, “Tellurite microstructure fibers with small hexagonal core for supercontinuum generation,” Opt. Express 17(14), 12174–12182 (2009). [CrossRef] [PubMed]

]. In addition, the chromatic dispersion of tellurite optical fibers could be tailored with high freedom by employing the refractive index difference between core and cladding materials (Δn = 0.11) [27

27. Z. Duan, M. Liao, X. Yan, C. Kito, T. Suzuki, and Y. Ohishi, “Tellurite composite microstructured optical fibers with tailored chromatic dispersion for nonlinear applications,” Appl. Phys. Express 4(72502), 1–3 (2011).

]. However, their chromatic dispersions were still not small enough in the telecom window. In this work, an improvement in tailoring the chromatic dispersion profile of tellurite optical fibers is demonstrated by using small core diameter, simple microstructure of air hole and high refractive index difference. Figure 1(a) shows the structure of the proposed novel highly nonlinear tellurite HMOF with a ring of six air holes in the cladding region. The core diameter is D = 0.894 μm and the air hole diameter is d = 2.26 μm. The distance between the center of two adjacent air holes, the pitch (Λ), is 1.997 μm. The fiber core and cladding are made of TLWMN and TZNP glass, respectively. At 1550 nm, their refractive indices are ncore = 2.058 and ncladding = 1.568. These refractive indices make the refractive index difference ∆n = 0.49. As shown in Fig. 1(b), the combination of large ∆n and air holes makes a near-zero flattened chromatic dispersion profile from 1.3 to 2.3 μm with four ZDWs at 1422, 1678, 1849 and 2195 nm. At 1550 nm, the calculated nonlinear coefficient of the tellurite HMOF is very large γ = 6642 W−1km−1 which is 369 times larger than that of the silica HNLF [17

17. M. C. Ho, K. Uesaka, M. Marhic, Y. Akasaka, and L. G. Kazosky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain,” J. Lightwave Technol. 19(7), 977–981 (2001). [CrossRef]

]. Those characteristics of the proposed tellurite HMOF are attractive for broadband wavelength conversion and FOPA.

4. Numerical analysis of FOPA performance

Using the calculated nonlinear coefficient and linear phase-mismatch, the optical signal gain Gs in dB scale was simulated at different pump wavelength λp, fiber length L and pump power P. The gain bandwidths are determined from the FOPA gain spectra.

In order to explain the effect of the fiber length when parametric gain coefficient g is imaginary, the signal gain map, the signal gain spectrum and linear phase-mismatch ∆β were calculated. They are shown in Fig. 2
Fig. 2 (a), (c), (e) Optical signal gain maps and (b), (d), (f) optical signal gain spectra and linear phase-mismatch at pump wavelength λ = 1550 nm. The pump power P = 1 W and the fiber length changed from 30 to 50 cm.
for different fiber length L = 30, 40, 50 cm and pump power P = 1 W. The figures on the left hand side, Figs. 2(a), 2(c) and (2e), indicate the signal gain maps in which the colors express the magnitude of the signal gain. Because the signal gain Gs depends on the fiber length as given in Eq. (8), it is shown in Figs. 2(b), 2(d) and (2f) that the signal gain increases when fiber length L increases from 30 to 50 cm. For L = 50 cm, the signal gain is larger than 5 dB over a broad gain bandwidth of 760 nm which is defined as the wavelength interval between the wavelengths where the signal gain becomes zero. In addition, the gain bandwidth kept 760 nm for L = 30, 40 and 50 cm.

The effects of pump power on the FOPA performance of our proposed highly nonlinear tellurite HMOF are shown in Figs. 4
Fig. 4 (a), (c), (e) Optical signal gain maps and (b), (d), (f) optical signal gain spectra and linear phase-mismatch at pump wavelength λ = 1550 nm for different pump power P = 1, 2 and 3 W. The fiber length is 25 cm.
and 5
Fig. 5 The signal gain spectra at pump wavelength λ = 1700 nm, L = 25 cm and pump power changes from 1 to 4W. These spectra are obtained from Fig. 4(a), 4(c) and 4(e).
. Figures 4(a), 4(c) and 4(e) show the signal gain maps of 25-cm tellurite HMOFs for different pump power P. The pump and signal wavelength varied from 1000 to 3000 nm. Figures 4(b), 4(d) and 4(f) show the signal gain spectra and the linear phase-mismatch of 25-cm tellurite HMOFs for different pump power P when the pump wavelength is fixed at 1550 nm. As can be seen in Figs. 4(b), 4(d) and 4(f), the signal gain increases with the pump power. The highest gain value was about 9 dB for P = 1 W while they were 22 and 36 dB for P = 2 W and P = 3 W, respectively. The maximum value of signal gain Gs was obtained when Δβ reached −2γP because the phase-matching condition given by Eq. (5) is satisfied. On the other hand, the signal gain bandwidth was about 760 nm which is much broader than the 200-nm bandwidth of the silica HNLF as reported in [17

17. M. C. Ho, K. Uesaka, M. Marhic, Y. Akasaka, and L. G. Kazosky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain,” J. Lightwave Technol. 19(7), 977–981 (2001). [CrossRef]

].

In Figs. 4(a), 4(c) and 4(e), the magnitude of the signal gain is expressed by the color scale of the signal gain maps. The dark blue color indicates the regions where signal gain are nearly zero. When the pump wavelength is 1700 nm and the pump power is 1W, the signal wavelength regions from 1300 to 1400 nm and 2160 to 2420 nm are shown in dark blue color. However, as the pump power changed from 1 to 3 W, the width of those dark blue regions reduced and even disappeared for the pump power P = 3 W. Correspondingly, the gain bandwidth at the pump wavelength of 1700 nm was improved. This feature is clearly interpreted in Fig. 5 where the signal gain spectra of 25-cm tellurite HMOF are shown for the pump wavelength λ = 1700 nm and the pump power P changes from 1 to 4 W. For P = 1 W, there was no signal gain in the wavelength ranges from 1300 to 1400 nm and from 2160 to 2420 nm. A gain bandwidth of 760 nm was acquired in the central wavelength range, located from 1400 to 2160 nm, with the gain intensity from 5 to 9 dB. The gain bandwidth expanded to 950 nm for P = 2W and connected to the two adjacent ranges on the left and right hand side for P>3 W. The total gain bandwidth was thus as broad as 1200 nm for P = 3 W and P = 4 W. As P = 4 W, the gain intensity was higher than 14 dB and could be as large as 50 dB. Additionally, relatively uniform gain was obtained over the ranges from 1300 to 1400 nm, 1550 to 1850 nm and 2200 to 2400 nm. It is interesting to realize from Fig. 5 that such a gain bandwidth as broad as 1200 nm (from 1290 to 2490 nm) with high signal gain can be achieved by using our tellurite HMOF as short as 25 cm for the pump power of 4 W. The use of short fiber length is good for dispersion fluctuation control while the low pump power is favorable to suppress the noise from Raman and stimulated Brillouin scattering effects which are important issues for the performance of FOPA.

In order to illustrate the advantages of high nonlinear coefficient when parametric gain coefficient g is imaginary, the signal gain of the proposed tellurite HMOF was compared with the result that differs only in the value of nonlinear coefficient γ. From this point of view, the tellurite HMOF was supposed to have lower value of γ while other parameters were invariable to observe how the signal gain varied under this condition. The value of γ was supposed to be as low as the value for the lead-silicate HNLF (640 W−1km−1 at λ = 1550 nm) which was shown in [30

30. P. Petropoulos, H. Ebendorff-Heidepriem, V. Finazzi, R. C. Moore, K. Frampton, D. J. Richardson, and T. M. Monro, “Highly nonlinear and anomalously dispersive lead silicate glass holey fibers,” Opt. Express 11(26), 3568–3573 (2003). [CrossRef] [PubMed]

] and the calculated signal gain was shown in Fig. 6
Fig. 6 The optical signal gain spectrum under the condition that γ is equal to 640 W−1km−1 at the pump wavelength λ = 1550 nm, L = 50 cm and P = 1 W.
. The fiber length was 50 cm and the pump power was also 1 W. As a result, the maximum optical signal gain Gs was 0.43 dB and the gain bandwidth was about 240 nm. Those values are much smaller than the values of the highly nonlinear tellurite HMOF mentioned in Fig. 2(f). The results in Fig. 6 indicated that the signal gain significantly decreased and was not generated in the wavelength ranges where g was imaginary even when a short fiber length of 50 cm was used. This clearly confirms the importance of both high nonlinear coefficient and short fiber length in the proposed tellurite HMOF.

5. Conclusion

The performance of FOPA has been simulated for the highly nonlinear tellurite HMOF which has four ZDWs and near-zero flattened dispersion profile from 1.3 to 2.3 μm. The linear phase-mismatch, optical signal gain and gain bandwidth are calculated precisely by using a full propagation constant which includes the contribution of all high-order dispersion parameters. In contrast with silica fibers, the signal gain can be generated in the wavelength regions where ∆β<− 4γP and the parametric gain coefficient g is imaginary. By using highly nonlinear tellurite HMOFs with short fiber length L<90 cm, the gain bandwidth as broad as 760 nm is obtained. The increase in pump power from 1 to 4 W not only increases the signal gain intensity but also broadens the gain bandwidth of FOPA. At 1700-nm pump wavelength, the gain intensity which is higher than 14 dB and could be as large as 50 dB over a very broad gain bandwidth of 1200 nm (from 1290 to 2490 nm) are obtained when the fiber length is as short as 25 cm and the pump power is 4 W. Those properties of FOPA could be obtained by using tellurite HMOFs with very high nonlinearity of 6642 W−1km−1 as designed in this work. To our best knowledge, it is the first time to demonstrate that highly nonlinear tellurite HMOFs are attractive candidates for high performance FOPA.

Acknowledgment

This work is supported by MEXT, the Support Program for Forming Strategic Research Infrastructure (2011-2015).

References and links

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S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave-mixing,” IEEE Photon. Technol. Lett. 14(10), 1406–1408 (2002). [CrossRef]

9.

P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett. 103(4), 043602 (2009). [CrossRef] [PubMed]

10.

G. P. Agrawal, “Nonlinear fiber optics: its history and recent progress,” J. Opt. Soc. Am. B 28(12), A1–A10 (2011). [CrossRef]

11.

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(3), 506–520 (2002). [CrossRef]

12.

J. Hansryd and P. A. Andrekson, “Wavelength tunable 40 GHz pulse source based on fiber optical parametric amplifier,” Electron. Lett. 37(9), 584–585 (2001). [CrossRef]

13.

J. Hansryd and P. A. Andrekson, “O-TDM demultiplexer with 40 dB gain based on a fiber optical parametric amplifier,” IEEE Photon. Technol. Lett. 13(7), 732–734 (2001). [CrossRef]

14.

J. Li, J. Hansryd, P.-O. Hedekvist, P. A. Andrekson, and S. N. Knudsen, “300 Gbit/s eye-diagram measurement by optical sampling using fiber based parametric amplification,”in Proceedings of the Optical Fiber Communication (OFC) Conf. and Exhibit 4, (2001).

15.

J. A. Levenson, I. Abram, Th. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B 10(11), 2233–2238 (1993). [CrossRef]

16.

K. Inoue, “Four wave mixing in an optical fiber in the zero dispersion wavelength region,” J. Lightwave Technol. 10(11), 1553–1561 (1992). [CrossRef]

17.

M. C. Ho, K. Uesaka, M. Marhic, Y. Akasaka, and L. G. Kazosky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain,” J. Lightwave Technol. 19(7), 977–981 (2001). [CrossRef]

18.

K. K. Chow, C. Shu, C. Lin, and A. Bjarklev, “Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber,” IEEE Photon. Technol. Lett. 17(3), 624–626 (2005). [CrossRef]

19.

J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Four-wave-mixing-based wavelength conversion of 40-Gb/s nonreturn-to-zero signal using 40-cm bismuth oxide nonlinear optical fiber,” IEEE Photon. Technol. Lett. 17(7), 1474–1476 (2005). [CrossRef]

20.

R. H. Stolen, M. A. Bösch, and C. Lin, “Phase matching in birefringent fibers,” Opt. Lett. 6(5), 213–215 (1981). [CrossRef] [PubMed]

21.

E. A. Zlobina, S. I. Kablukov, and S. A. Babin, “Phase matching for parametric generation in polarization maintaining photonic crystal fiber pumped by tunable Yb-doped fiber laser,” J. Opt. Soc. Am. B 29(8), 1959–1976 (2012). [CrossRef]

22.

M. Liao, X. Yan, W. Gao, Z. Duan, G. Qin, T. Suzuki, and Y. Ohishi, “Five-order SRSs and supercontinuum generation from a tapered tellurite microstructured fiber with longitudinally varying dispersion,” Opt. Express 19(16), 15389–15396 (2011). [CrossRef] [PubMed]

23.

D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, “Thulium pumped high power supercontinuum in loss-determined optimum lengths of tellurite photonic crystal fiber,” Appl. Phys. Lett. 97(061106), 1–3 (2010).

24.

A. X. Lin, A. Ryasnyanskiy, and J. Toulouse, “Tunable third-harmonic generation in a solid-core tellurite glass fiber,” Opt. Lett. 36(17), 3437–3439 (2011). [CrossRef] [PubMed]

25.

M. Liao, X. Yan, G. Qin, C. Chaudhari, T. Suzuki, and Y. Ohishi, “A highly non-linear tellurite microstructure fiber with multi-ring holes for supercontinuum generation,” Opt. Express 17(18), 15481–15490 (2009). [CrossRef] [PubMed]

26.

M. Liao, C. Chaudhari, G. Qin, X. Yan, T. Suzuki, and Y. Ohishi, “Tellurite microstructure fibers with small hexagonal core for supercontinuum generation,” Opt. Express 17(14), 12174–12182 (2009). [CrossRef] [PubMed]

27.

Z. Duan, M. Liao, X. Yan, C. Kito, T. Suzuki, and Y. Ohishi, “Tellurite composite microstructured optical fibers with tailored chromatic dispersion for nonlinear applications,” Appl. Phys. Express 4(72502), 1–3 (2011).

28.

T. H. Tuan, K. Asano, Z. Duan, M. Liao, T. Suzuki, and Y. Ohishi, “Novel tellurite-phosphate composite microstructured optical fibers for highly nonlinear applications,” Phys. Status Solidi C 9(12), 2598–2601 (2012). [CrossRef]

29.

M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, “Multi-order dispersion engineering for optimal four-wave mixing,” Opt. Express 16(10), 7551–7563 (2008). [CrossRef] [PubMed]

30.

P. Petropoulos, H. Ebendorff-Heidepriem, V. Finazzi, R. C. Moore, K. Frampton, D. J. Richardson, and T. M. Monro, “Highly nonlinear and anomalously dispersive lead silicate glass holey fibers,” Opt. Express 11(26), 3568–3573 (2003). [CrossRef] [PubMed]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(060.4005) Fiber optics and optical communications : Microstructured fibers

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 11, 2013
Revised Manuscript: July 27, 2013
Manuscript Accepted: August 2, 2013
Published: August 22, 2013

Citation
Tong Hoang Tuan, Tonglei Cheng, Koji Asano, Zhongchao Duan, Weiqing Gao, Dinghuan Deng, Takenobu Suzuki, and Yasutake Ohishi, "Optical parametric gain and bandwidth in highly nonlinear tellurite hybrid microstructured optical fiber with four zero-dispersion wavelengths," Opt. Express 21, 20303-20312 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-20303


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References

  1. M. E. Marhic, N. Kagi, T. K. Chiang, and L. G. Kazovsky, “Broadband fiber optical parametric amplifiers,” Opt. Lett.21(8), 573–575 (1996). [CrossRef] [PubMed]
  2. R. Dabu, “Very broad gain bandwidth parametric amplification in nonlinear crystals at critical wavelength degeneracy,” Opt. Express18(11), 11689–11699 (2010). [CrossRef] [PubMed]
  3. J. E. Sharping, M. Fiorentino, A. Coker, P. Kumar, and R. S. Windeler, “Four-wave mixing in microstructure fiber,” Opt. Lett.26(14), 1048–1050 (2001). [CrossRef] [PubMed]
  4. B. Fang, O. Cohen, J. B. Moreno, and V. O. Lorenz, “State engineering of photon pairs produced through dual-pump spontaneous four-wave mixing,” Opt. Express21(3), 2707–2717 (2013). [CrossRef] [PubMed]
  5. G. M. Lloyd, I. G. Hughes, R. Bratfalean, and P. Ewart, “Broadband degenerate four-wave mixing of OH for flame thermometry,” Appl. Phys. B67(1), 107–113 (1998). [CrossRef]
  6. A. L. Zhang and M. S. Demokan, “Broadband wavelength converter based on four-wave mixing in a highly nonlinear photonic crystal fiber,” Opt. Lett.30(18), 2375–2377 (2005). [CrossRef] [PubMed]
  7. C. S. Brès, S. Zlatanovic, A. O. J. Wiberg, and S. Radic, “Continuous-wave four-wave mixing in cm-long Chalcogenide microstructured fiber,” Opt. Express19(26), B621–B627 (2011). [CrossRef] [PubMed]
  8. S. Radic, C. J. McKinstrie, A. R. Chraplyvy, G. Raybon, J. C. Centanni, C. G. Jorgensen, K. Brar, and C. Headley, “Continuous-wave parametric gain synthesis using nondegenerate pump four-wave-mixing,” IEEE Photon. Technol. Lett.14(10), 1406–1408 (2002). [CrossRef]
  9. P. Londero, V. Venkataraman, A. R. Bhagwat, A. D. Slepkov, and A. L. Gaeta, “Ultralow-power four-wave mixing with Rb in a hollow-core photonic band-gap fiber,” Phys. Rev. Lett.103(4), 043602 (2009). [CrossRef] [PubMed]
  10. G. P. Agrawal, “Nonlinear fiber optics: its history and recent progress,” J. Opt. Soc. Am. B28(12), A1–A10 (2011). [CrossRef]
  11. 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(3), 506–520 (2002). [CrossRef]
  12. J. Hansryd and P. A. Andrekson, “Wavelength tunable 40 GHz pulse source based on fiber optical parametric amplifier,” Electron. Lett.37(9), 584–585 (2001). [CrossRef]
  13. J. Hansryd and P. A. Andrekson, “O-TDM demultiplexer with 40 dB gain based on a fiber optical parametric amplifier,” IEEE Photon. Technol. Lett.13(7), 732–734 (2001). [CrossRef]
  14. J. Li, J. Hansryd, P.-O. Hedekvist, P. A. Andrekson, and S. N. Knudsen, “300 Gbit/s eye-diagram measurement by optical sampling using fiber based parametric amplification,”in Proceedings of the Optical Fiber Communication (OFC) Conf. and Exhibit 4, (2001).
  15. J. A. Levenson, I. Abram, Th. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B10(11), 2233–2238 (1993). [CrossRef]
  16. K. Inoue, “Four wave mixing in an optical fiber in the zero dispersion wavelength region,” J. Lightwave Technol.10(11), 1553–1561 (1992). [CrossRef]
  17. M. C. Ho, K. Uesaka, M. Marhic, Y. Akasaka, and L. G. Kazosky, “200-nm-bandwidth fiber optical amplifier combining parametric and Raman gain,” J. Lightwave Technol.19(7), 977–981 (2001). [CrossRef]
  18. K. K. Chow, C. Shu, C. Lin, and A. Bjarklev, “Polarization-insensitive widely tunable wavelength converter based on four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber,” IEEE Photon. Technol. Lett.17(3), 624–626 (2005). [CrossRef]
  19. J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, and K. Kikuchi, “Four-wave-mixing-based wavelength conversion of 40-Gb/s nonreturn-to-zero signal using 40-cm bismuth oxide nonlinear optical fiber,” IEEE Photon. Technol. Lett.17(7), 1474–1476 (2005). [CrossRef]
  20. R. H. Stolen, M. A. Bösch, and C. Lin, “Phase matching in birefringent fibers,” Opt. Lett.6(5), 213–215 (1981). [CrossRef] [PubMed]
  21. E. A. Zlobina, S. I. Kablukov, and S. A. Babin, “Phase matching for parametric generation in polarization maintaining photonic crystal fiber pumped by tunable Yb-doped fiber laser,” J. Opt. Soc. Am. B29(8), 1959–1976 (2012). [CrossRef]
  22. M. Liao, X. Yan, W. Gao, Z. Duan, G. Qin, T. Suzuki, and Y. Ohishi, “Five-order SRSs and supercontinuum generation from a tapered tellurite microstructured fiber with longitudinally varying dispersion,” Opt. Express19(16), 15389–15396 (2011). [CrossRef] [PubMed]
  23. D. Buccoliero, H. Steffensen, O. Bang, H. Ebendorff-Heidepriem, and T. M. Monro, “Thulium pumped high power supercontinuum in loss-determined optimum lengths of tellurite photonic crystal fiber,” Appl. Phys. Lett.97(061106), 1–3 (2010).
  24. A. X. Lin, A. Ryasnyanskiy, and J. Toulouse, “Tunable third-harmonic generation in a solid-core tellurite glass fiber,” Opt. Lett.36(17), 3437–3439 (2011). [CrossRef] [PubMed]
  25. M. Liao, X. Yan, G. Qin, C. Chaudhari, T. Suzuki, and Y. Ohishi, “A highly non-linear tellurite microstructure fiber with multi-ring holes for supercontinuum generation,” Opt. Express17(18), 15481–15490 (2009). [CrossRef] [PubMed]
  26. M. Liao, C. Chaudhari, G. Qin, X. Yan, T. Suzuki, and Y. Ohishi, “Tellurite microstructure fibers with small hexagonal core for supercontinuum generation,” Opt. Express17(14), 12174–12182 (2009). [CrossRef] [PubMed]
  27. Z. Duan, M. Liao, X. Yan, C. Kito, T. Suzuki, and Y. Ohishi, “Tellurite composite microstructured optical fibers with tailored chromatic dispersion for nonlinear applications,” Appl. Phys. Express4(72502), 1–3 (2011).
  28. T. H. Tuan, K. Asano, Z. Duan, M. Liao, T. Suzuki, and Y. Ohishi, “Novel tellurite-phosphate composite microstructured optical fibers for highly nonlinear applications,” Phys. Status Solidi C9(12), 2598–2601 (2012). [CrossRef]
  29. M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, “Multi-order dispersion engineering for optimal four-wave mixing,” Opt. Express16(10), 7551–7563 (2008). [CrossRef] [PubMed]
  30. P. Petropoulos, H. Ebendorff-Heidepriem, V. Finazzi, R. C. Moore, K. Frampton, D. J. Richardson, and T. M. Monro, “Highly nonlinear and anomalously dispersive lead silicate glass holey fibers,” Opt. Express11(26), 3568–3573 (2003). [CrossRef] [PubMed]

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