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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 23 — Nov. 18, 2013
  • pp: 28403–28413
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Efficient one-third harmonic generation in highly Germania-doped fibers enhanced by pump attenuation

Tianye Huang, Xuguang Shao, Zhifang Wu, Timothy Lee, Yunxu Sun, Huy Quoc Lam, Jing Zhang, Gilberto Brambilla, and Shum Ping  »View Author Affiliations


Optics Express, Vol. 21, Issue 23, pp. 28403-28413 (2013)
http://dx.doi.org/10.1364/OE.21.028403


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Abstract

We provide a comprehensive study on one-third harmonic generation (OTHG) in highly Germania-doped fiber (HGDF) by analyzing the phase matching conditions for the step index-profile and optimizing the design parameters. For stimulated OTHG in HGDF, the process can be enhanced by fiber attenuation at the pump wavelength which dynamically compensates the accumulated phase-mismatch along the fiber. With 500 W pump and 35 W seed power, simulation results show that a 31% conversion efficiency, which is 4 times higher than the lossless OTHG process, can be achieved in 34 m of HGDF with 90 mol. % GeO2 doping in the core.

© 2013 Optical Society of America

1. Introduction

Highly Germania-doped fiber (HGDF) consisting of a Germania-Silica core within a Silica cladding has attracted extensive interest in the past years [9

9. H. Takahashi and I. Sugimoto, “A germanium-oxide glass optical fiber prepared by a VAD method,” J. Lightwave Technol. 2(5), 613–616 (1984). [CrossRef]

13

13. E. A. Anashkina, A. V. Andrianov, M. Yu. Koptev, V. M. Mashinsky, S. V. Muravyev, and A. V. Kim, “Generating tunable optical pulses over the ultrabroad range of 1.6-2.5 μm in GeO2-doped silica fibers with an Er:fiber laser source,” Opt. Express 20(24), 27102–27107 (2012). [CrossRef] [PubMed]

]. Also, HGDF is a good candidate for OTHG because of its capability to achieve inter-modal phase matching and low attenuation characteristics around 0.5 µm and 1.5 µm. However, to date, the role of doping concentration in HGDFs for OTHG has yet to be addressed in detail.

In this paper, a comprehensive study of the stimulated OTHG process in HGDFs is performed. The phase matching parameters in step-index fiber are designed. Different modes are discussed in terms of overlap integrals and the most suitable one is then chosen for inter-modal phase matching. The performances of different HGDFs are simulated and evaluated along with the possibility for pump attenuation in playing a contributing role towards efficient OTHG.

2. Phase matching in HGDFs

OTHG and THG share the same phase matching conditions, which have previously been discussed for glass microfibers [1

1. V. Grubsky and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express 13(18), 6798–6806 (2005). [CrossRef] [PubMed]

, 2

2. T. Lee, Y. Jung, C. A. Codemard, M. Ding, N. G. R. Broderick, and G. Brambilla, “Broadband third harmonic generation in tapered silica fibres,” Opt. Express 20(8), 8503–8511 (2012). [CrossRef] [PubMed]

]. The main disadvantage is that the interactive length is limited to several centimeters because of the difficulty in fabricating long microfibers whilst maintaining the small diameter required for phase matching. High-delta micro-structured fibers were also employed to realize phase matching [14

14. A. Efimov, A. J. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell, “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express 11(20), 2567–2576 (2003). [CrossRef] [PubMed]

]. More recently, Tarnowski et al. proposed an approach to compensate for the phase mismatch for THG by using quasi-phase matching technique based on the grating written in the fiber [15

15. K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, “Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings,” IEEE J. Quantum Electron. 47(5), 622–629 (2011). [CrossRef]

]. However, the fabrication processes of these fibers are quite complicated. On the other hand, high numerical aperture (NA) fibers offer an attractive choice to achieve phase matching because the big fibers can be straightforwardly fabricated to much longer interactive lengths [6

6. M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A 84(3), 033823 (2011). [CrossRef]

, 16

16. K. Bencheikh, S. Richard, G. Mélin, G. Krabshuis, F. Gooijer, and J. A. Levenson, “Phase-matched third-harmonic generation in highly germanium-doped fiber,” Opt. Lett. 37(3), 289–291 (2012). [CrossRef] [PubMed]

]. Here we demonstrate a detailed analysis for phase matching conditions in HGDFs.

3. Analysis and simulation results

dP1dz=α1P12J3γ0P132P312sinψ
(4)
dP3dz=α3P3+2J3γ0P132P312sinψ
(5)
dψdz=Δβ+γ0[(6J23J1)P1+(3J56J2)P3+J3(P132P3123P112P312)cosψ]
(6)

As shown in Eqs. (4) and (5), the power flow direction is determined by the sign of sin ψ, if sin ψ > 0, it is THG process, otherwise OTHG. If sin ψ < 0 is satisfied at the input of the interactive media and the right hand side of Eq. (6) is kept approximately to be 0, power can be transferred from the pump (P3) to signal (P1) continuously. However, as P1 increases and P3 decreases, Eq. (6) becomes none zero and ψ deviates from sin ψ < 0 because of the fiber loss and different Kerr coefficients (6J2-3J1 and 3J5-6J2), hence changing the varying rate and direction of the power flow. Additionally, according to Eq. (4), it is easy to note that the varying rate of P1 can be quite low with a small seed light (P1) at the input of the interactive media because the varying rate is proportional to P11.5. With small P1, simply increasing the pump power contributes little to the conversion rate improvement. This feature is totally different with THG, whose power changing rate can be increased by strong pump, as shown in Eq. (5). Therefore, in order to obtain efficient OTHG, a potential method is to stimulate the process with powerful seed. The theoretical analysis for lossless OTHG proposed in [8

8. S. Afshar V, M. A. Lohe, T. Lee, T. M. Monro, and N. G. R. Broderick, “Efficient third and one-third harmonic generation in nonlinear waveguides,” Opt. Lett. 38(3), 329–331 (2013). [CrossRef] [PubMed]

] points out that the maximum conversion efficiency is dominated by the total input power and waveguide structure. In the above mentioned HGDF, according to our calculation, the relationship of overlap integrals cannot fulfill the special requirements mentioned in [8

8. S. Afshar V, M. A. Lohe, T. Lee, T. M. Monro, and N. G. R. Broderick, “Efficient third and one-third harmonic generation in nonlinear waveguides,” Opt. Lett. 38(3), 329–331 (2013). [CrossRef] [PubMed]

] for efficient OTHG process. However, because of the existence of loss which can be quite different at pump and signal wavelengths, the conversion mechanics are slightly different. Since the losses of pure silica and GeO2 at 0.532 µm are about 11 dB/km and 300 dB/km and 0.2 dB/km and 0.6 dB/km at 1.596 µm [20

20. E. M. Dianov and V. M. Mashinsky, “Germania-based core optical fibers,” J. Lightwave Technol. 23(11), 3500–3508 (2005). [CrossRef]

], we use a linear relation to approximate the HGDF loss at different doping concentration, the attenuation coefficient at longer wavelength is much smaller which raises the possibility for dynamically compensating for the phase mismatch during propagation along fiber.

In order to investigate the parametric process in the above mentioned HGDF, we return to Eq. (6) which shows that ψ is determined by four terms including a linear Δβ term (regarded as constant along a longitudinally invariant fiber). We also define the Kerr coefficients K1 = 6J2-3J1, and K3 = 3J5-6J2, whose values as a function of doping concentration are demonstrated in Fig. 4
Fig. 4 K1 and K3 as a function of doping concentration
. Their behavior can be divided into three regimes:

(1) 0 < J3 << K3 < K1 (90 mol. % and 100 mol. % doping)

Since K1 and K3 are much larger than J3, the last term of Eq. (6) can be neglected and the equation approximated as:
dψdz=Δβ+γ0(K1P1+K3P3)
(7)
In this case, if sin ψ < 0 is fulfilled at the input of the fiber, power can transfer from P3 to P1 due to OTHG process. Given this is a lossless process, the increasing rate of K1P1 must be faster than the decreasing rate of K3P3 because K1 > K3, and therefore after propagating along a short distance of fiber, the power will transfer from P1 to P3 again then oscillating between the two waves. However, the condition will be different considering large pump loss. Combining the effect of power attenuation caused by parametric processes (i.e. the transfer of power to the other wavelength) and fiber loss, the increment of K1P1 can be comparable with the decrement of K3P3 so that ψ changes slowly and P1 can build up continuously over a long fiber length. When ψ changes to make sin ψ > 0, the THG process starts and power begins to transfer from P1 to P3, reducing K1P1 and increasing K3P3. Similarly, the changing rate of K1P1 is faster than K3P3, meanwhile a large α3 prevents the increasing of K3P3. These two terms cannot balance with each other, and therefore ψ changes fast and it is difficult to maintain sin ψ > 0. ψ will vary such that sin ψ falls below 0 after a short propagation length and return to OTHG process again, as a result P1 can accumulate. In this case, OTHG can benefit from the large loss at pump wavelength.

(2) 0 < J3K3 << K1 (40 mol. % and 50 mol. % doping)

This case is similar to the first one, but the balance between phase terms is more difficult because of the small values of K3 and J3. If the pump loss is too small, the K1P1 term will dominate the phase varying rate and make the process close to the lossless one. Even if, the loss is large enough to compensate phase changing at the input of fiber, OTHG cannot benefit from pump attenuation for long distances since the pump power decays exponentially along the fiber. After a certain distance, the balance can be break.

(3) K3 < 0 < J3 << K1 (30 mol. %, 60 mol. %, 70 mol. % and 80 mol. % doping)

In the OTHG process, both K1P1 and K3P3 increase while the changing direction of the J3 term (the last term in Eq. (6)) is determined by the sign of cos ψ which can be positive or negative during OTHG process. Nevertheless, J3 is too small compared with K1, so K1P1 and K3P3 lead to a fast phase variation. While the OTHG buildup region is restricted to – π < ψ < 0, ψ cannot stay in this favorable region for a long propagating length. Therefore, it is difficult to realize efficient OTHG.

As we mentioned above, with doping concentrations of 30 mol. %, 60 mol. %, 70 mol. % and 80 mol. %, pump loss is no longer favorable for OTHG. The performances of these four doping concentration are demonstrated in Figs. 8(a)
Fig. 8 Contour map of conversion efficiency in (a) 30 mol. %, (b) 60 mol. %, (c) 70 mol. %, and (d) 80 mol. % doping fiber plotted against propagation constant mismatch and fiber length
8(d), respectively. From the efficiency contour maps, it is apparent that η cannot go up higher after reaching their first efficiency peak which limits conversion to < 5%.

4. Conclusion

In summary, we have designed step-index HGDFs for phase-matched OTHG and analyzed the performances for different fibers. Parameters such as effective indices, core diameters, and overlap integrals for HGDFs with different doping concentrations were investigated. In specially designed HGDF with core GeO2 doping levels of 90 mol. %, the pump loss is no longer a disadvantage and can be used to compensate the accumulated phase-mismatch dynamically along the fiber for efficient OTHG. According to our simulation, 31% conversion efficiency which is nearly 4 times higher than the equivalent lossless process is achievable over 34 m of fiber with a doping concentration of 90 mol. % in the core. The results demonstrate that HGDFs can potentially be applied for efficient OTHG which is significant in the area of triple photons generation and parametric amplification.

Acknowledgments

This work was supported by the Singapore A*STAR SERC Grant: “Advanced Optics in Engineering” Program (Grant No. 1223600001). G. Brambilla gratefully acknowledges the Royal Society (London) for his University Research Fellowship.

References and links

1.

V. Grubsky and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express 13(18), 6798–6806 (2005). [CrossRef] [PubMed]

2.

T. Lee, Y. Jung, C. A. Codemard, M. Ding, N. G. R. Broderick, and G. Brambilla, “Broadband third harmonic generation in tapered silica fibres,” Opt. Express 20(8), 8503–8511 (2012). [CrossRef] [PubMed]

3.

A. Coillet and P. Grelu, “Third-harmonic generation in optical microfibers: from silica experiments to highly nonlinear glass prospects,” Opt. Commun. 285(16), 3493–3497 (2012). [CrossRef]

4.

W. Gao, K. Ogawa, X. Xue, M. Liao, D. Deng, T. Cheng, T. Suzuki, and Y. Ohishi, “Third-harmonic generation in an elliptical-core ZBLAN fluoride fiber,” Opt. Lett. 38(14), 2566–2568 (2013). [CrossRef] [PubMed]

5.

F. Gravier and B. Boulanger, “Triple-photon generation: comparison between theory and experiment,” J. Opt. Soc. Am. B 25(1), 98–102 (2008). [CrossRef]

6.

M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A 84(3), 033823 (2011). [CrossRef]

7.

S. Richard, K. Bencheikh, B. Boulanger, and J. A. Levenson, “Semiclassical model of triple photons generation in optical fibers,” Opt. Lett. 36(15), 3000–3002 (2011). [CrossRef] [PubMed]

8.

S. Afshar V, M. A. Lohe, T. Lee, T. M. Monro, and N. G. R. Broderick, “Efficient third and one-third harmonic generation in nonlinear waveguides,” Opt. Lett. 38(3), 329–331 (2013). [CrossRef] [PubMed]

9.

H. Takahashi and I. Sugimoto, “A germanium-oxide glass optical fiber prepared by a VAD method,” J. Lightwave Technol. 2(5), 613–616 (1984). [CrossRef]

10.

S. Sakaguchi and S. Todoroki, “Optical properties of GeO2 glass and optical fibers,” Appl. Opt. 36(27), 6809–6814 (1997). [CrossRef] [PubMed]

11.

K. Kravtsov, Y. K. Huang, and P. R. Prucnal, “All-optical 160 Gbits/s time-domain demultiplexer based on the heavily GeO2-doped silica-based nonlinear fiber,” Opt. Lett. 34(4), 491–493 (2009). [CrossRef] [PubMed]

12.

V. Kamynin, A. S. Kurkov, and V. M. Mashinsky, “Supercontinuum generation up to 2.7 µm in the germanate-glass-core and silica-glass-cladding fiber,” Laser Phys. Lett. 9(3), 219–222 (2012). [CrossRef]

13.

E. A. Anashkina, A. V. Andrianov, M. Yu. Koptev, V. M. Mashinsky, S. V. Muravyev, and A. V. Kim, “Generating tunable optical pulses over the ultrabroad range of 1.6-2.5 μm in GeO2-doped silica fibers with an Er:fiber laser source,” Opt. Express 20(24), 27102–27107 (2012). [CrossRef] [PubMed]

14.

A. Efimov, A. J. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell, “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express 11(20), 2567–2576 (2003). [CrossRef] [PubMed]

15.

K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, “Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings,” IEEE J. Quantum Electron. 47(5), 622–629 (2011). [CrossRef]

16.

K. Bencheikh, S. Richard, G. Mélin, G. Krabshuis, F. Gooijer, and J. A. Levenson, “Phase-matched third-harmonic generation in highly germanium-doped fiber,” Opt. Lett. 37(3), 289–291 (2012). [CrossRef] [PubMed]

17.

J. W. Fleming, “Dispersion in GeO2-SiO2 glasses,” Appl. Opt. 23(24), 4486–4493 (1984). [CrossRef] [PubMed]

18.

A. Snyder and J. Love, Optical Waveguide Theory, 1st ed. (Springer, 1983).

19.

A. Wada, S. Okude, T. Sakai, and R. Yamauchi, “GeO2 concentration dependence of nonlinear refractive index coefficients of silica-based optical fibers,” Electron. Commun. Jpn. Part Commun. 79(11), 12–19 (1996). [CrossRef]

20.

E. M. Dianov and V. M. Mashinsky, “Germania-based core optical fibers,” J. Lightwave Technol. 23(11), 3500–3508 (2005). [CrossRef]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(070.4340) Fourier optics and signal processing : Nonlinear optical signal processing
(190.2620) Nonlinear optics : Harmonic generation and mixing

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: October 2, 2013
Revised Manuscript: November 2, 2013
Manuscript Accepted: November 4, 2013
Published: November 11, 2013

Citation
Tianye Huang, Xuguang Shao, Zhifang Wu, Timothy Lee, Yunxu Sun, Huy Quoc Lam, Jing Zhang, Gilberto Brambilla, and Shum Ping, "Efficient one-third harmonic generation in highly Germania-doped fibers enhanced by pump attenuation," Opt. Express 21, 28403-28413 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-23-28403


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References

  1. V. Grubsky and A. Savchenko, “Glass micro-fibers for efficient third harmonic generation,” Opt. Express13(18), 6798–6806 (2005). [CrossRef] [PubMed]
  2. T. Lee, Y. Jung, C. A. Codemard, M. Ding, N. G. R. Broderick, and G. Brambilla, “Broadband third harmonic generation in tapered silica fibres,” Opt. Express20(8), 8503–8511 (2012). [CrossRef] [PubMed]
  3. A. Coillet and P. Grelu, “Third-harmonic generation in optical microfibers: from silica experiments to highly nonlinear glass prospects,” Opt. Commun.285(16), 3493–3497 (2012). [CrossRef]
  4. W. Gao, K. Ogawa, X. Xue, M. Liao, D. Deng, T. Cheng, T. Suzuki, and Y. Ohishi, “Third-harmonic generation in an elliptical-core ZBLAN fluoride fiber,” Opt. Lett.38(14), 2566–2568 (2013). [CrossRef] [PubMed]
  5. F. Gravier and B. Boulanger, “Triple-photon generation: comparison between theory and experiment,” J. Opt. Soc. Am. B25(1), 98–102 (2008). [CrossRef]
  6. M. Corona, K. Garay-Palmett, and A. B. U’Ren, “Third-order spontaneous parametric down-conversion in thin optical fibers as a photon-triplet source,” Phys. Rev. A84(3), 033823 (2011). [CrossRef]
  7. S. Richard, K. Bencheikh, B. Boulanger, and J. A. Levenson, “Semiclassical model of triple photons generation in optical fibers,” Opt. Lett.36(15), 3000–3002 (2011). [CrossRef] [PubMed]
  8. S. Afshar V, M. A. Lohe, T. Lee, T. M. Monro, and N. G. R. Broderick, “Efficient third and one-third harmonic generation in nonlinear waveguides,” Opt. Lett.38(3), 329–331 (2013). [CrossRef] [PubMed]
  9. H. Takahashi and I. Sugimoto, “A germanium-oxide glass optical fiber prepared by a VAD method,” J. Lightwave Technol.2(5), 613–616 (1984). [CrossRef]
  10. S. Sakaguchi and S. Todoroki, “Optical properties of GeO2 glass and optical fibers,” Appl. Opt.36(27), 6809–6814 (1997). [CrossRef] [PubMed]
  11. K. Kravtsov, Y. K. Huang, and P. R. Prucnal, “All-optical 160 Gbits/s time-domain demultiplexer based on the heavily GeO2-doped silica-based nonlinear fiber,” Opt. Lett.34(4), 491–493 (2009). [CrossRef] [PubMed]
  12. V. Kamynin, A. S. Kurkov, and V. M. Mashinsky, “Supercontinuum generation up to 2.7 µm in the germanate-glass-core and silica-glass-cladding fiber,” Laser Phys. Lett.9(3), 219–222 (2012). [CrossRef]
  13. E. A. Anashkina, A. V. Andrianov, M. Yu. Koptev, V. M. Mashinsky, S. V. Muravyev, and A. V. Kim, “Generating tunable optical pulses over the ultrabroad range of 1.6-2.5 μm in GeO2-doped silica fibers with an Er:fiber laser source,” Opt. Express20(24), 27102–27107 (2012). [CrossRef] [PubMed]
  14. A. Efimov, A. J. Taylor, F. Omenetto, J. Knight, W. Wadsworth, and P. Russell, “Phase-matched third harmonic generation in microstructured fibers,” Opt. Express11(20), 2567–2576 (2003). [CrossRef] [PubMed]
  15. K. Tarnowski, B. Kibler, C. Finot, and W. Urbanczyk, “Quasi-phase-matched third harmonic generation in optical fibers using refractive-index gratings,” IEEE J. Quantum Electron.47(5), 622–629 (2011). [CrossRef]
  16. K. Bencheikh, S. Richard, G. Mélin, G. Krabshuis, F. Gooijer, and J. A. Levenson, “Phase-matched third-harmonic generation in highly germanium-doped fiber,” Opt. Lett.37(3), 289–291 (2012). [CrossRef] [PubMed]
  17. J. W. Fleming, “Dispersion in GeO2-SiO2 glasses,” Appl. Opt.23(24), 4486–4493 (1984). [CrossRef] [PubMed]
  18. A. Snyder and J. Love, Optical Waveguide Theory, 1st ed. (Springer, 1983).
  19. A. Wada, S. Okude, T. Sakai, and R. Yamauchi, “GeO2 concentration dependence of nonlinear refractive index coefficients of silica-based optical fibers,” Electron. Commun. Jpn. Part Commun.79(11), 12–19 (1996). [CrossRef]
  20. E. M. Dianov and V. M. Mashinsky, “Germania-based core optical fibers,” J. Lightwave Technol.23(11), 3500–3508 (2005). [CrossRef]

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