Numerical investigation of mid-infrared supercontinuum generation up to 5 μm in single mode fluoride fiber

doi:10.1364/OE.19.010041

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Numerical investigation of mid-infrared supercontinuum generation up to 5 μm in single mode fluoride fiber

Lai Liu, Guanshi Qin, Qijun Tian, Dan Zhao, and Weiping Qin »View Author Affiliations

Optics Express, Vol. 19, Issue 11, pp. 10041-10048 (2011)
http://dx.doi.org/10.1364/OE.19.010041

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▸ Article Outline
– Abstract
1. Introduction
2. Methods for numerical simulation
3. SC generation in fluoride fibers
4. Conclusion
– References and links

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Abstract

We numerically investigate mid-infrared supercontinuum generation in single mode fluoride fiber pumped by 1.56 μm picosecond fiber lasers. To get high energy conversion efficiency in mid-infrared region, the ratio of power generated in 2.5 ~5 μm range to the total input power for supercontinuum generation is optimized by varying the pulse width, peak power and fiber length. The long wavelength edge of the supercontinuum spectrum can be extended to 4.8 μm in a 100 cm long fluoride fiber pumped by a 1.56 μm fiber laser with a pulse width of 4 ps and a peak power of 100 kW, and the corresponding ratio of power generated in 2.5 ~5 μm range to the total input power is about 44.6%. The spectral broadening is mainly caused by self-phase modulation, stimulated Raman scattering and four-wave mixing. The simulated results show that high average power supercontinuum light source in 2.5 ~5 μm range could be obtained in fluoride fibers pumped by 1.56 μm picosecond fiber lasers.

1. Introduction

Mid-infrared light source has been used in numerous fields such as monitoring plasma etching process, combustion flow monitoring, chemical sensors, astronomy, military, biomedical surgery [1

M. G. Allen, “Diode laser absorption sensors for gas-dynamic and combustion flows,” Meas. Sci. Technol. 9(4), 545–562 (1998).

]. Supercontinuum (SC) generation in optical fibers, as one of the most promising approaches to obtain broadband mid-infrared light source, has been widely investigated [2

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).

]. To generate mid-infrared SC light source, recently, much attention has been paid to non-silica fibers (e.g., Bi₂O₃-based, tellurite [3

P. Domachuk, N. A. Wolchover, M. Cronin-Golomb, A. Wang, A. K. George, C. M. B. Cordeiro, J. C. Knight, and F. G. Omenetto, “Over 4000 nm bandwidth of mid-IR supercontinuum generation in sub-centimeter segments of highly nonlinear tellurite PCFs,” Opt. Express 16(10), 7161–7168 (2008). [PubMed]

–6

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(6), 061106 (2010).

], chalcogenide [7

D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33(7), 660–662 (2008). [PubMed]

–10

J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Computational study of 3-5 μm source created by using supercontinuum generation in As₂S₃ chalcogenide fibers with a pump at 2 μm,” Opt. Lett. 35(17), 2907–2909 (2010). [PubMed]

], and fluoride fibers [11

C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to the midinfrared by pumping ZBLAN fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. 18(1), 91–93 (2006).

–14

G. Qin, X. Yan, C. Kito, M. Liao, C. Chaudhari, T. Suzuki, and Y. Ohishi, “Ultrabroadband supercontinuum generation from ultraviolet to 6.28μm in a fluoride fiber,” Appl. Phys. Lett. 95(16), 161103 (2009).

]) with low transmission loss at the mid-infrared region for generating mid-infrared SC light. A SC spectrum with a bandwidth exceeding 4000 nm has been generated in 9 mm long tellurite microstructured fiber pumped by a 1550 nm femtosecond laser [3

]. Broadband SC light expanding from 0.6 to 2.8 μm was demonstrated in short length zero-dispersion wavelength decreasing tellurite microstructured fibers by one of the authors [5

G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Zero-dispersion-wavelength-decreasing tellurite microstructured fiber for wide and flattened supercontinuum generation,” Opt. Lett. 35(2), 136–138 (2010). [PubMed]

]. In case of chalcogenide fibers, Shaw et al. demonstrated experimentally the SC generation from 2 to 3.4 μm in As₂S₃ fibers [8

J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Chalcogenide glass–fiber-based mid-IR sources and applications,” IEEE J. Sel. Top. Quantum Electron. 15(1), 114–119 (2009).

]. Hu et al. showed through numerical simulations that a relatively flat SC spectrum with a width of 4000 nm could be generated using four-wave mixing combining with self-phase modulation and the soliton self-frequency shift in a 0.1 m long As₂Se₃ microstructured fiber, more than 25% of input power could be shifted into the region between 3 and 5 μm in a 0.5 m long As₂S₃ microstructured fiber pumped by a 2 μm laser with a peak power of 1 kW and a pulse width of 500 fs [9

J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the bandwidth of supercontinuum generation in As₂Se₃ chalcogenide fibers,” Opt. Express 18(7), 6722–6739 (2010). [PubMed]

,10

For fluoride fibers, in 2006, Hagen et al. reported SC generation extended to 3.4μm in 91 cm long fluoride fibers [11

], for the first time. Several months later, Xia et al. reported an ultra-broadband SC generation from 0.8 to 4.5 μm in fluoride fibers by nanosecond diode pumping [12

C. Xia, M. Kumar, O. P. Kulkarni, M. N. Islam, F. L. Terry Jr, M. J. Freeman, M. Poulain, and G. Mazé, “Mid-infrared supercontimuum generation to 4.5 μm in ZBLAN fluoride fibers by nanosecond diode pumping,” Opt. Lett. 31(17), 2553–2555 (2006). [PubMed]

]. In 2009, Islam et al. demonstrated high average power (~10.5 W) SC generation expanding from 0.8 to 3.5 μm [13

C. Xia, Z. Xu, M. N. Islam, F. L. Terry Jr, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 W time-averaged power mid-IR supercontinuum generation extending beyond 4 μm with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15(2), 422–434 (2009).

]. Very recently, ultra-broadband SC generation from ultraviolet to 6.28 μm in a centimeter-long fluoride fiber was reported by one of the authors [14

]. These experimental results show that fluoride fiber is a promising candidate for generating mid-infrared SC light source. Although many efforts have been devoted to extending the spectral range or to increasing average power of mid-infrared SC light in fluoride fibers, the ratio of power generated in the mid-infrared region (2.5 ~5 μm) to the total input power, a key issue for mid-infrared applications, was rarely investigated. For example, according to our calculation, the ratio of power generated in 2.5 ~5 μm range to the total input power for SC generation in fluoride fibers pumped by ns lasers was 14.2% [12

,13

], which was quite lower for real applications. The power conversion ratio can be improved by extending the long wavelength edge of the output SC spectrum to 5μm efficiently and increasing the power generated in 2.5 ~5 μm range. It should be noted that, for the case pumped by ns lasers, if the effects of the transmission loss of fluoride fibers were not considered, high average power SC with high conversion ratio in 2.5 ~5 μm range would be obtained by increasing the fluoride fiber length (e.g. tens of meters) owing to efficient nonlinear interaction in longer fibers. However, the real SC spectrum from the longer fluoride fiber would be limited in spectra range by the transmission loss of the fluoride fiber [5

,12

,13

], as shown in Fig. 1(b) . Therefore, high average power SC with high conversion ratio in 2.5 ~5 μm range would not be obtained by solely increasing the fluoride fiber length owing to the effects of the transmission loss for the case pumped by ns lasers [12

,13

], but in short length (e.g. several tens of centimeters) fluoride fibers pumped by shorter pulsed lasers [14

]. That is the reason why the reported power conversion ratio of SC generation in fluoride fibers pumped by ns lasers is just up to 14.2% [12

,13

]. We have considered that the ratio of power generated in 2.5 ~5 μm range to the total input power for SC generation in fluoride fibers could be improved by optimizing the parameters of pump lasers (e.g. by using picosecond or femtosecond lasers as pump sources) and fluoride fibers.

Fig. 1 (a) Calculated dispersion data of the fundamental propagating mode in the fluoride fiber we used. (b) The transmission loss of fluoride fiber we used.

For real applications, it is desired to generate SC light source in the mid-infrared region of 2.5~5 μm with high average power and high power conversion ratio in mid-infrared region. For this purpose, it is necessary to increase the peak power of the pump laser (e.g. picosecond or femtosecond laser). However, this might damage the fluoride fiber if the peak power is too high (the damage threshold reported for this material pumped by a 1.56 μm picosecond laser was about 300 GW/cm² [13

,15

B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996).

]). To avoid the damage, one possible way for generating high average power mid-infrared SC light is to increase the pulse width moderately [6

], e.g. using a pulse width of several picoseconds.

In this paper, we investigated SC generation in fluoride fibers pumped by 1.56μm picosecond fiber lasers through numerical simulations, which aimed to improve energy conversion efficiency in mid-infrared region.

2. Methods for numerical simulation

By solving the Maxwell Equations we can get the generalized nonlinear Schrödinger equation (GNLSE) which accurately describes the ultrashort pulse (>30 fs) propagation in fibers. The commonly used NLSE is given in the form below [2

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).

,16

G. P. Agrawal, Nonlinear Fiber Optics , 4th ed. (Academic. Press, 2009).

]

\frac{\partial A}{\partial z} = - \frac{α}{2} A - (\sum_{k \geq 2} β_{n} \frac{i^{n - 1}}{n!} \frac{\partial^{n}}{\partial T^{n}}) A + i γ (A {| A |}^{2} + \frac{i}{ω_{0}} \frac{\partial}{\partial T} ({| A |}^{2} A) - f_{R} A \frac{\partial {| A |}^{2}}{\partial T} \int_{- \infty}^{\infty} t h (t) d t),

where a frame of reference moving with the pulse at the group velocity

ν_{g}

(the so-called retarded frame) is used by making the transformation

T = t - z / v_{g} = t - β_{1 z},

where α is the transmission loss of the fluoride fiber. The terms

β_{n}

is group velocity dispersion (GVD) for n = 2 and high order dispersion for n>2. In our calculation n is up to 8. The term including

A {| A |}^{2}

is self-phase modulation (SPM) in which the frequency shift is proportional to the intensity of the incident pulse. The term including the product of

ω_{0}^{- 1}

and the first derivative of

P_{N L}

is responsible for self-steepening and shock wave formation. The last term originates from the delayed Raman response, and is responsible for Raman scattering. The Raman gain spectrum is given by

g_{R} (Δ ω) = \frac{ω_{0}}{c n_{0}} f_{R} χ^{(3)} Im [{\tilde{h}}_{R} (Δ ω)],

where

Δ ω = ω - ω_{0}

and Im stands for the imaginary part. The real part of

\tilde{h} (Δ ω)

can be obtained from the imaginary part by using the Kramers-Kronig relations. The Fourier transformation of

\tilde{h} (Δ ω)

can provide the Raman response function

h_{R} (t)

. An approximate analytic form of the Raman response function is given by

h_{R} (t) = \frac{τ_{1}^{2} + τ_{2}^{2}}{τ_{1} τ_{2}^{2}} \exp (- \frac{t}{τ_{2}}) \sin (\frac{t}{τ_{1}}) .

For fluoride fibers, the derived values from the Raman gain spectrum of fluoride glasses are

τ_{1}

= 9 fs,

τ_{2}

= 134 fs, and

f_{R}

= 0.1929 [16

G. P. Agrawal, Nonlinear Fiber Optics , 4th ed. (Academic. Press, 2009).

–18

Y. Durteste, M. Monerie, and P. Lamouler, “Raman amplification in fluoride glass fiber,” Electron. Lett. 21(17), 723–724 (1985).

The initial incident pulse we choose has a hyperbolic-secant field profile, which is common for passively mode-locked fiber lasers.

A (0, T) = \sqrt{P_{0}} \sec h (\frac{T}{T_{0}}),

where P ₀ is the peak power and T ₀ is the input pulse width. The relation between T _FWHM (FWHM refers to full width at half maximum) and T ₀ is given below

T_{F W H M} = 1.763 T_{0} .

All the pulse width mentioned in this paper is FWHM of the pulse.

Noise is also included in our calculation, the average power for the random noise is 10⁻⁹ W.

The Split-step Fourier Method is used to solve the NLSE. To make sure of the accuracy of numerical results, 2¹⁴ time and frequency discretization points and a longitudinal step size <5 μm were used in our simulations. The 4th-order Runge-Kutta algorithm was used in our calculations [19

J. Hult, “A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25(12), 3770–3775 (2007).

3. SC generation in fluoride fibers

3.1 Features of fluoride fiber

The step-index fluoride fiber we used has a core diameter of 9 μm, a numerical aperture (NA) of 0.2, and a zero dispersion wavelength of 1.65 μm. Figure 1(a) shows the calculated dispersion data of the fundamental propagation mode in the fluoride fiber. The calculated nonlinear coefficient at 1.56 μm is 1.3385 km⁻¹W⁻¹, by using a nonlinear refractive index of 2.1×10⁻²⁰ m² W⁻¹. Figure 1(b) shows the transmission loss of fluoride fiber we used. Since the fiber loss increases greatly for the long wavelength region (>4 μm) [20

D. Tran, G. Sigel, and B. Bendow, “Heavy metal fluoride glasses and fibers: a review,” J. Lightwave Technol. 2(5), 566–586 (1984).

], the effects of the transmission loss of fluoride fiber shown by Fig. 1(b) on the calculated output SC spectra were considered in the simulations. Therefore, loss effects must be considered when the fiber length reaches dozens of centimeters for mid-infrared SC generation.

3.2 Simulated results

In the simulations, the pumping wavelength was set as 1.56 μm, a typical operating wavelength of Er³⁺ - doped fiber lasers. Although the pumping wavelength was located at the normal dispersion region in this case, broadband SC light source could still be obtained in optical fibers with small absolute values of dispersion [6

], which is our case. The curves in Fig. 2 show the simulated normalized output pulse profiles from a 70 cm long fluoride fiber pumped by a 1.56 μm fiber laser with a pulse width of 4 ps and a peak power of (a) 10 kW, (b) 20 kW, (c) 30 kW, (d) 40 kW, (e) 100 kW, and (f) 200kW. A temporal window of 62 ps was used in the simulations. It is seen that such a temporal window is wide enough to preclude the occurrence of spurious interferences between the leading and the trailing edge of the output pulse even when the pump peak power is increased to 200 kW. The pulse splitting occurs with increasing the pump peak power, which is mainly caused by self-phase modulation (SPM) and stimulated Raman scattering effects.

Fig. 2 Simulated output pulse profiles from a 70 cm long fluoride fiber pumped by a 1.56 μm fiber laser with a pulse width of 4 ps and a peak power of (a) 10 kW, (b) 20 kW, (c) 30 kW, (d) 40 kW, (e) 100 kW, and (f) 200kW.

The blue curves in Fig. 3 show the corresponding simulated SC spectra output from a 70 cm long fluoride fiber pumped by a 1.56 μm fiber laser with a pulse width of 4 ps and a peak power of (a) 10 kW, (b) 20 kW, (c) 30 kW, (d) 40 kW, (e) 100 kW, and (f) 200kW by considering the transmission loss. The red curves in Fig. 3 show the simulated data without considering the transmission loss. A spectral window of 0.9 ~5 μm was used in the simulations. This is because that the transmission loss of fluoride fiber we used becomes very large (>9 dB/m) when the wavelength is larger than 5 μm, as shown in Fig. 1(b). It means that we cannot get efficient SC generation in spectral range of >5μm in a several-meter-long fluoride fiber owing to the effects of the transmission loss, as with our case. It is seen that, SC light expanding from 0.9 to 5μm would be generated in the 70-cm-long fluoride fiber pumped by a 1.56 μm fiber laser with a pulse width of 4 ps and a peak power of 200 kW.

Fig. 3 Simulated SC spectra output from a 70 cm long fluoride fiber pumped by a 1.56 μm fiber laser with a pulse width of 4 ps and a peak power of (a) 10 kW, (b) 20 kW, (c) 30 kW, (d) 40 kW, (e) 100 kW, and (f) 200kW by considering the transmission loss of fluoride fiber. The red curves in Fig. 3 shows the simulated data without considering the transmission loss of fluoride fiber.

Figure 4(a) shows the simulated temporal evolution in the 70-cm-long fluoride fiber when pumped at 1.56 μm with a pulse width of 4 ps and a peak power of 200 kW. It is seen that the pulse splitting occurs at the position of ~30 cm inside the fiber, and spurious interferences between the leading and the trailing edge of the output pulse is not observed. This shows that such a temporal window (~62 ps) is wide enough for our simulations. Figure 4 (b) shows the simulated spectral evolution of SC generation in the 70-cm-long fluoride fiber when pumped at 1.56 μm with a pulse width of 4 ps and a peak power of 200 kW. It is seen that the initial spectral broadening along the fiber is mainly caused by SPM and stimulated Raman scattering. Further spectral broadening along the fiber is caused by SPM, stimulated Raman scattering, and four-wave mixing. This is because that the pumping wavelength (~1.56 μm) is located at the normal dispersion region and the real fiber length (~70 cm) is much shorter than the dispersion length (1072.5 m) [2

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).

]. Therefore, the spectral broadening in fluoride fibers is primarily caused by SPM, Raman scattering and four-wave mixing. In addition, as we can see from Fig. 4(b), most (corresponding to the red color region) of the generated SC spectrum are located in the spectral window of 0.9 ~5 μm we used in the simulations, which also shows that such a spectral window (0.9 ~5 μm) is wide enough for our simulations.

Fig. 4 Simulated (a) temporal and (b) spectral evolution of SC generation in a 70-cm-long fluoride fiber when pumped at 1.56 μm with a pulse width of 4 ps and a peak power of 200 kW .

As aforementioned, the ratio of power generated in 2.5 ~5 μm range to the total input power for supercontinuum generation is very important for real applications. Figure 5 shows the dependence of the ratio of power generated in the mid-infrared region (>2.5 μm) on the pump peak power for SC generation in a 70-cm-long fluoride fiber pumped by a 1.56 μm fiber laser with a pulse width of 4 ps. By increasing the pump peak power from 10 to 200 kW, the ratio of power generated in the mid-infrared region (>2.5 μm) increases from 8.9 × 10⁻¹¹% to 32.4% owing to the enlargement of the long wavelength edge of SC spectrum. Here, it should be noted that, the calculated power conversion ratio is defined as the ratio of power generated in the mid-infrared region (2.5 ~5 μm) to the total input power by considering the effects of the transmission loss of fluoride fiber. As aforementioned, the transmission loss of fluoride fiber we used becomes very large (>9 dB/m) when the wavelength is larger than 5 μm, as shown in Fig. 1(b). It means that we cannot get efficient SC generation in spectral range of >5μm in a several-meter-long fluoride fiber owing to the effects of the transmission loss, as with our case. In addition, as we can see from Fig. 4(b), most (corresponding to the red color region) of the generated SC spectrum are located in the spectral window of 0.9 ~5 μm we used in the simulations of SC generation from the 70-cm-long fluoride fiber when pumped at 1.56 μm with a pulse width of 4 ps and a peak power of 200 kW, which also shows that such a spectral window (0.9 ~5 μm) is wide enough for our simulations. Therefore, the selection of a spectral window of 0.9 ~5 μm in the simulations nearly has no effects on the calculation of the power conversion ratio.

Fig. 5 Dependence of the ratio of power generated in the mid-infrared region (>2.5 μm) on the pump peak power for SC generation in the 70-cm-long fluoride fiber pumped by a 1.56 μm fiber with a pulse width of 4ps.

To further improve the ratio of power generated in the mid-infrared region (>2.5 μm), we investigated the dependence of the ratio of power generated in the mid-infrared region (>2.5 μm) on the fiber length and the pump pulse width, as shown in Fig. 6 . When the pump peak power is set as 100 kW and the fiber length is longer than 80 cm, the ratio can reach to more than 30% for the pump pulse width varying from 2 to 5 ps owing to the enlargement of the long wavelength edge of SC spectrum. Especially, the power conversion ratio can reach to 44.6% in a 100 cm fluoride fiber pumped by a 1.56 μm laser with a pulse width of 3 ps or 4 ps and a peak power of 100 kW. Such a ratio (~44.6%) is much higher than that (~14.2%) of the case pumped by ns lasers [12

,13

]. This is because that the spectral broadening in optical fibers pumped by ps lasers is more efficient than that pumped by ns lasers owing to the short pulse width of picosecond laser as well as its large spectral bandwidth [2

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).

]. As aforementioned, the real SC spectrum from the longer fluoride fiber would be limited in spectra range by the transmission loss of the fluoride fiber [5

,12

,13

], as shown in Fig. 1(b). Therefore, high average power SC with high conversion ratio in 2.5 ~5 μm range would not be obtained by solely increasing the fluoride fiber length owing to the effects of the transmission loss for the case pumped by ns lasers [12

,13

], but in short length (e.g. several tens of centimeters) fluoride fibers pumped by shorter pulsed lasers. That is the reason why the reported power conversion ratio of SC generation in fluoride fibers pumped by ns lasers is just up to 14.2% [12

,13

Fig. 6 The dependence of the ratio of power generated in the mid-infrared region (>2.5 μm) on the fiber length and the pump pulse width.

4. Conclusion

In summary, we numerically investigated SC generation in single mode fluoride fiber pumped by 1.56μm picosecond fiber lasers in order to get high energy conversion efficiency in mid-infrared region. The ratio of power generated in 2.5 ~5 μm range to the total input power for supercontinuum generation is optimized by varying the pulse width, peak power and fiber length. The simulated results showed that high average power SC light source expanding from 1 to 5 μm with a 44.9% ratio of power generated in the mid-infrared region (>2.5 μm), could be generated from a 100 cm long single mode fluoride fiber with a zero-dispersion wavelength of ~1.65 μm by using a 1.56 μm picosecond fiber laser as the pump source.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (NSFC) (grants 60908001, 61077033, 51072065, and 60908031), the Program for New Century Excellent Talents in University (No: NCET-08-0243), the National High Technology Research and Development Program of China (863 Program:2009AA03Z309).

References and links

1.	M. G. Allen, “Diode laser absorption sensors for gas-dynamic and combustion flows,” Meas. Sci. Technol. 9(4), 545–562 (1998).
2.	J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
3.	P. Domachuk, N. A. Wolchover, M. Cronin-Golomb, A. Wang, A. K. George, C. M. B. Cordeiro, J. C. Knight, and F. G. Omenetto, “Over 4000 nm bandwidth of mid-IR supercontinuum generation in sub-centimeter segments of highly nonlinear tellurite PCFs,” Opt. Express 16(10), 7161–7168 (2008). [PubMed]
4.	X. Feng, W. H. Loh, J. C. Flanagan, A. Camerlingo, S. Dasgupta, P. Petropoulos, P. Horak, K. E. Frampton, N. M. White, J. H. Price, H. N. Rutt, and D. J. Richardson, “Single-mode tellurite glass holey fiber with extremely large mode area for infrared nonlinear applications,” Opt. Express 16(18), 13651–13656 (2008). [PubMed]
5.	G. Qin, X. Yan, C. Kito, M. Liao, T. Suzuki, A. Mori, and Y. Ohishi, “Zero-dispersion-wavelength-decreasing tellurite microstructured fiber for wide and flattened supercontinuum generation,” Opt. Lett. 35(2), 136–138 (2010). [PubMed]
6.	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(6), 061106 (2010).
7.	D. I. Yeom, E. C. Mägi, M. R. E. Lamont, M. A. F. Roelens, L. Fu, and B. J. Eggleton, “Low-threshold supercontinuum generation in highly nonlinear chalcogenide nanowires,” Opt. Lett. 33(7), 660–662 (2008). [PubMed]
8.	J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal, “Chalcogenide glass–fiber-based mid-IR sources and applications,” IEEE J. Sel. Top. Quantum Electron. 15(1), 114–119 (2009).
9.	J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Maximizing the bandwidth of supercontinuum generation in As₂Se₃ chalcogenide fibers,” Opt. Express 18(7), 6722–6739 (2010). [PubMed]
10.	J. Hu, C. R. Menyuk, L. B. Shaw, J. S. Sanghera, and I. D. Aggarwal, “Computational study of 3-5 μm source created by using supercontinuum generation in As₂S₃ chalcogenide fibers with a pump at 2 μm,” Opt. Lett. 35(17), 2907–2909 (2010). [PubMed]
11.	C. L. Hagen, J. W. Walewski, and S. T. Sanders, “Generation of a continuum extending to the midinfrared by pumping ZBLAN fiber with an ultrafast 1550-nm source,” IEEE Photon. Technol. Lett. 18(1), 91–93 (2006).
12.	C. Xia, M. Kumar, O. P. Kulkarni, M. N. Islam, F. L. Terry Jr, M. J. Freeman, M. Poulain, and G. Mazé, “Mid-infrared supercontimuum generation to 4.5 μm in ZBLAN fluoride fibers by nanosecond diode pumping,” Opt. Lett. 31(17), 2553–2555 (2006). [PubMed]
13.	C. Xia, Z. Xu, M. N. Islam, F. L. Terry Jr, M. J. Freeman, A. Zakel, and J. Mauricio, “10.5 W time-averaged power mid-IR supercontinuum generation extending beyond 4 μm with direct pulse pattern modulation,” IEEE J. Sel. Top. Quantum Electron. 15(2), 422–434 (2009).
14.	G. Qin, X. Yan, C. Kito, M. Liao, C. Chaudhari, T. Suzuki, and Y. Ohishi, “Ultrabroadband supercontinuum generation from ultraviolet to 6.28μm in a fluoride fiber,” Appl. Phys. Lett. 95(16), 161103 (2009).
15.	B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B 13(2), 459–468 (1996).
16.	G. P. Agrawal, Nonlinear Fiber Optics , 4th ed. (Academic. Press, 2009).
17.	D. Hollenbeck and C. D. Cantrell, “Multiple-vibrational-mode model for fiber-optic Raman gain spectrum and response function,” J. Opt. Soc. Am. B 19(12), 2886–2892 (2002).
18.	Y. Durteste, M. Monerie, and P. Lamouler, “Raman amplification in fluoride glass fiber,” Electron. Lett. 21(17), 723–724 (1985).
19.	J. Hult, “A fourth-order Runge–Kutta in the interaction picture method for simulating supercontinuum generation in optical fibers,” J. Lightwave Technol. 25(12), 3770–3775 (2007).
20.	D. Tran, G. Sigel, and B. Bendow, “Heavy metal fluoride glasses and fibers: a review,” J. Lightwave Technol. 2(5), 566–586 (1984).

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(320.6629) Ultrafast optics : Supercontinuum generation

ToC Category:
Ultrafast Optics

History
Original Manuscript: January 19, 2011
Revised Manuscript: April 14, 2011
Manuscript Accepted: April 29, 2011
Published: May 9, 2011

Citation
Lai Liu, Guanshi Qin, Qijun Tian, Dan Zhao, and Weiping Qin, "Numerical investigation of mid-infrared supercontinuum generation up to 5 μm in single mode fluoride fiber," Opt. Express 19, 10041-10048 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-11-10041

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