## Optical parametric gain and bandwidth in highly nonlinear tellurite hybrid microstructured optical fiber with four zero-dispersion wavelengths |

Optics Express, Vol. 21, Issue 17, pp. 20303-20312 (2013)

http://dx.doi.org/10.1364/OE.21.020303

Acrobat PDF (3136 KB)

### 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 TeO_{2}–Li_{2}O–WO_{3}–MoO_{3}–Nb_{2}O_{5} and TeO_{2}–ZnO–Na_{2}O–P_{2}O_{5} 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

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. 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]

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. 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]

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]

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]

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]

_{2}–Li

_{2}O–WO

_{3}–MoO

_{3}–Nb

_{2}O

_{5}(TLWMN) core and TeO

_{2}–ZnO–Na

_{2}O–P

_{2}O

_{5}(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

*ω*

_{1}=

*ω*

_{2}=

*ω*

_{p}. 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]

*A*,

_{p}*A*and

_{i}*A*are the field amplitudes of the pump, the idler and the signal, respectively. The nonlinear coefficient is calculated by γ =

_{s}*n*

_{2}

*ω*/c

*A*

_{eff}where

*n*

_{2}is the nonlinear refractive index,

*A*

_{eff}is the effective mode area and Δ

*β*is the linear phase-mismatch.

*P*is the pump power,

*ω*,

_{p}*ω*and

_{i}*ω*are the angular frequencies of the pump, the idler and the signal waves, respectively. The linear phase-mismatch Δ

_{s}*β*can be expressed bywhere

*n*(

_{eff}*ω*),

_{i}*n*(

_{eff}*ω*) and

_{s}*n*(

_{eff}*ω*) are the effective refractive indices at

_{p}*ω*,

_{i}*ω*and

_{s}*ω*, respectively. The frequency dependent effective refractive index

_{p}*n*(

_{eff}*ω*) 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) 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

_{i}^{−4}. Because the

*n*(

_{eff}*ω*) 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 n

_{i}_{eff}(λ) included both material and waveguide dispersions.

*β*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 Δ

*ω*= |

*ω*-

_{s}*ω*| in Eq. (7) [17

_{p}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]

*β*

_{2}and

*β*

_{4}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 (

*β*

_{6},

*β*

_{8}…) 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.

*G*) is given bywhere L is the fiber length,

_{s}*P*(0) and

_{s}*P*(

_{s}*L*) are the signal power at the input and output of the fiber and the parametric gain coefficient

*g*is in the form ofFor conventional silica fibers which have low nonlinear coefficient, the signal gain

*G*given by Eq. (8) is dominated by the characteristic of sinh

_{s}^{2}(

*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]

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. 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]

*g*, the linear phase-mismatch must satisfy the condition −4

*γP*<∆

*β*<0. In the special case of perfect phase matching when Eq. (5) is satisfied, the maximum signal gain occurs. At that time, ∆

*β*= − 2

*γP*and

*g*

_{max}=

*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]

*g*becomes imaginary. In practice, imaginary

*g*is obtained when

*g*and the optical signal gain

*G*are given by

_{s}*G*is governed by sin

_{s}^{2}(

*g*. When the product of

_{i}L)*g*reaches the value of π/2, the contribution of sin

_{i}L^{2}(

*g*is maximum. If the nonlinear coefficient

_{i}L)*γ*is sufficiently large, actual signal gain

*G*can be obtained even though

_{s}*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

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]

_{core}= 2.058 and n

_{cladding}= 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

^{−1}km

^{−1}which is 369 times larger than that of the silica HNLF [17

**19**(7), 977–981 (2001). [CrossRef]

## 4. Numerical analysis of FOPA performance

*G*in dB scale was simulated at different pump wavelength λ

_{s}_{p}, fiber length

*L*and pump power

*P.*The gain bandwidths are determined from the FOPA gain spectra.

*g*is imaginary, the signal gain map, the signal gain spectrum and linear phase-mismatch ∆

*β*were calculated. They are shown in Fig. 2 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

*G*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

_{s}*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.

*β*and the signal gain spectra at the pump wavelength λ = 1550 nm for different fiber length

*L*. As the linear phase mismatch given by Eq. (6) is independent with fiber length, the value of ∆

*β*was kept when

*L*varied from 10 to 90 cm. Contrary to ∆

*β*, the signal gain

*G*increased with

_{s}*L*except for the two ranges I and II marked in Figs. 3(a) and 3(b). When the signal is in the wavelength ranges I and II, it is noted that

*g*takes imaginary values because ∆

*β<− 4γP*and Eq. (10) is satisfied. Consequently, the signal gain

*G*is governed by sin

_{s}^{2}(

*g*as expressed in Eq. (12). It was found in the ranges I and II that an increase in the signal gain occured when the fiber length changed from 10 to 50 cm. Under these conditions, a broad gain bandwidth of 760 nm was obtained. However, the signal gain trends to drop off for longer fibers. When the fiber length

_{i}L)*L*reached 90 cm, the signal gain became zero in the ranges I and II and the total gain bandwidth was reduced. The total gain bandwidth got narrower and divided into 3 separate parts. The broadest central part was 473 nm from 1350 to 1823 nm. The results in Fig. 3(b) obviously show that highly nonlinear tellurite HMOF with short fiber length can generate actual signal gain in the wavelength regions where

*g*is imaginary, therefore, broader gain bandwidth can be achieved. Conversely, the use of long fiber causes a decrease in signal gain and makes the total gain bandwidth narrow. The signal gain generated even when

*g*is imaginary is attributed to the high nonlinear coefficient of tellurite HMOFs. This feature has never been demonstrated for silica fibers due to their low nonlinearity.

*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

*G*was obtained when Δ

_{s}*β*reached −2

*γP*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

**19**(7), 977–981 (2001). [CrossRef]

*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.

*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

^{−1}km

^{−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]

*G*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

_{s}*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

*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

^{−1}km

^{−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

## References and links

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

2. | R. Dabu, “Very broad gain bandwidth parametric amplification in nonlinear crystals at critical wavelength degeneracy,” Opt. Express |

3. | J. E. Sharping, M. Fiorentino, A. Coker, P. Kumar, and R. S. Windeler, “Four-wave mixing in microstructure fiber,” Opt. Lett. |

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 |

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 |

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. |

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. Express |

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. |

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. |

10. | G. P. Agrawal, “Nonlinear fiber optics: its history and recent progress,” J. Opt. Soc. Am. B |

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. |

12. | J. Hansryd and P. A. Andrekson, “Wavelength tunable 40 GHz pulse source based on fiber optical parametric amplifier,” Electron. Lett. |

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. |

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 |

15. | J. A. Levenson, I. Abram, Th. Rivera, and P. Grangier, “Reduction of quantum noise in optical parametric amplification,” J. Opt. Soc. Am. B |

16. | K. Inoue, “Four wave mixing in an optical fiber in the zero dispersion wavelength region,” J. Lightwave Technol. |

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. |

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. |

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. |

20. | R. H. Stolen, M. A. Bösch, and C. Lin, “Phase matching in birefringent fibers,” Opt. Lett. |

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 |

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 |

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. |

24. | A. X. Lin, A. Ryasnyanskiy, and J. Toulouse, “Tunable third-harmonic generation in a solid-core tellurite glass fiber,” Opt. Lett. |

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 |

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 |

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 |

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 |

29. | M. R. E. Lamont, B. T. Kuhlmey, and C. M. de Sterke, “Multi-order dispersion engineering for optimal four-wave mixing,” Opt. Express |

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 |

**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

- 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]
- R. Dabu, “Very broad gain bandwidth parametric amplification in nonlinear crystals at critical wavelength degeneracy,” Opt. Express18(11), 11689–11699 (2010). [CrossRef] [PubMed]
- 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]
- 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]
- 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]
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