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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 19 — Sep. 15, 2008
  • pp: 14792–14800
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Broadband supercontinuum generation covering UV to mid-IR region by using three pumping sources in single crystal sapphire fiber

Jae Hun Kim, Meng-Ku Chen, Chia-En Yang, Jon Lee, Kebin Shi, Zhiwen Liu, Stuart (Shizhuo) Yin, Karl Reichard, Paul Ruffin, Eugene Edwards, Christina Brantley, and Claire Luo  »View Author Affiliations


Optics Express, Vol. 16, Issue 19, pp. 14792-14800 (2008)
http://dx.doi.org/10.1364/OE.16.014792


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Abstract

In this paper, we demonstrate that the the bandwidth of the supercontinuum spectrum generated in a large mode area sapphire fiber can be enhanced by employing triple pumping sources. Three pumping sources with wavelengths of 784nm, 1290nm, and 2000nm are launched into a single crystal sapphire fiber that is 5cm in length and has a core diameter of 115μm. The nonlinear interactions due to self-phase modulation and four-wave mixing form a broadband supercontinuum that covers the UV, visible, near-IR and lower mid-IR regions. Furthermore, we explore the possibility of generating a broadband supercontinuum expanding from the UV to far-IR region by increasing the number of pumping sources with wavelengths in the mid- and far-IR.

© 2008 Optical Society of America

1. Introduction

Supercontinuum generation (SCG) refers to the creation of a broadband light source due to the nonlinear interactions of laser pulses inside an optical medium. Many applications in spectroscopy [1

1. S. T. Sanders, “Wavelength-agile fiber laser using group-velocity dispersion of pulsed super-continua and application to broadband absorption spectroscopy,” Appl. Phys. B-Lasers Opt. 75, 799–802 (2002). [CrossRef]

], confocal microscopy [2

2. K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express 12, 2096–2101 (2004). [CrossRef] [PubMed]

, 3

3. K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263, 156–162 (2006). [CrossRef]

], optical communication [4

4. T. Morioka, K. Mori, and M. Saruwatari, “More than 100-wavelength-channel picosecond optical pulse generation from single laser source using supercontinuum in optical fibres,” Electron. Lett. 29, 862–864 (1993). [CrossRef]

], medical imaging [5

5. A. A. Ivanov, M. V. Alfimov, A. B. Fedotov, A. A. Podshivalov, D. Chorvat, and A. M. Zheltikov, “An all-solid-state sub-40-fs self-starting Cr4+: Forsterite laser with holey-fiber beam delivery and chirp control for coherence-domain and nonlinear-optical biomedical applications,” Laser Phys. 11, 158–163 (2001).

], optical coherence tomography [6

6. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001). [CrossRef]

], and remote sensing [7

7. D. M. Brown, K. Shi, Z. Liu, and R. Philbrick, “Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents,” Opt. Express 16, 8457–8471 (2008). [CrossRef] [PubMed]

] require a broadband light source and may benefit from SCG.

Recently, the importance of a broadband light source covering the UV through mid-IR has increased. In spectroscopy, many chemicals have distinct peaks in UV, visible, near-, mid-, and far-IR. However, the spectra of many chemicals can only be differentiated by a small number of peaks in a certain range. Thus, the scanning range needs to be as wide as possible to distinguish these small differences. Remote sensing applications would also benefit from a broadband light source. The system described in Reference [8

8. P. Weibring, H. Edner, and S. Svanberg, “Versatile mobile lidar system for environmental monitoring,” Appl. Opt. 42, 3583–3594 (2003). [CrossRef] [PubMed]

] utilizes both UV and mid-IR optical sources generated by an optical parametric oscillator (OPO) to perform remote-sensing for environmental conditions such as air pollution and water vapor, and for terrestrial monitoring. Even though conventional sources such as OPOs, tunable solid-state lasers, and quantum cascaded lasers (QCLs) can cover a wide spectral range by continuously tuning the wavelength [9

9. I. T. Sorokina and K. L. Vodopyanov, Solid-state mid-infrared laser sources (Springer-Verlag, Berlin Heidelberg, 2003). [CrossRef]

], they cannot cover the entire range simultaneously because of the time delay during wavelength switching. Very wide range SCG from the UV to mid-IR (up to 4.5µm) in air has been previously reported [10

10. J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J.-P. Wolf, Y.-B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, “Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere,” Opt. Lett. 25, 1397–1399 (2000). [CrossRef]

]. However, this result was obtained in air by employing input pulses with an extremely high peak power density level on the order of a terawatt. Recently, broadband supercontinua from optical fibers covering more than an octave span have been demonstrated with relatively small intensity input pulses by many researchers [11

11. V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultraband supercontinuum generation,” Opt. Express 10, 1520–1525 (2002).

13

13. F. G. Omenetto, N. A. Wolchover, M. R. Wehner, M. Ross, A. Efimov, A. J. Taylor, V. V. R. K. Kumar, A. K. George, J. C. Knight, N. Y. Joly, and P. St. J. Russel, “Spectrally smooth supercontinuum from 350nm to 3µm in sub-centimeter lengths of soft-glass photonic crystal fibers,” Opt. Express 14, 4928–4934 (2006). [CrossRef] [PubMed]

]. Reference [13

13. F. G. Omenetto, N. A. Wolchover, M. R. Wehner, M. Ross, A. Efimov, A. J. Taylor, V. V. R. K. Kumar, A. K. George, J. C. Knight, N. Y. Joly, and P. St. J. Russel, “Spectrally smooth supercontinuum from 350nm to 3µm in sub-centimeter lengths of soft-glass photonic crystal fibers,” Opt. Express 14, 4928–4934 (2006). [CrossRef] [PubMed]

] shows that a SF-6 photonic crystal fiber (PCF) with a very small mode area (2.6µm diameter) and a nonlinear refractive index of 2.2×10-19m2/W can generate a spectrum that spans from 350nm to 3000nm. We previously reported supercontinua in a sapphire fiber with spectral spans from 450nm to 1350nm and from 1200nm to 2800nm [14

14. S. Yin, J. H. Kim, C. Zhan, J. W. An, J. Lee, P. Ruffin, E. Edwards, C. Brantley, and C. Luo, “Supercontinuum generation in single crystal sapphire fibers,” Opt. Commun. 281, 1113–1117 (2008). [CrossRef]

, 15

15. J. H. Kim, M.-K. Chen, C.-E. Yang, J. Lee, S. Yin, P. Ruffin, E. Edwards, C. Brantley, and C. Luo, “Broadband IR supercontinuum generation using single crystal sapphire fibers,” Opt. Express 16, 4085–4093 (2008). [CrossRef] [PubMed]

]. The fibers used in these papers were multimode and had a core diameter of 115µm. Sapphire fibers are well suited for SCG because they exhibit a high damage threshold (up to1.3kJ/cm2) and a nonlinear refractive index similar to silica fibers (3 × 10-20m2/W) [16

16. A. Major, F. Yoshino, I. Nikolakakos, J. Aitchison, and P. Smith, “Dispersion of the nonlinear refractive index in sapphire,” Opt. Lett. 29, 602–604 (2004). [CrossRef] [PubMed]

18

18. R. Nubling and J. Harrington, “Optical properties of single-crystal sapphire fibers,” Appl. Opt. 36, 5934–5940 (1997). [CrossRef] [PubMed]

]. They also have good transparency up to 5µm [17

17. R. W. Waynant, S. Oshry, and M. Fink, “Infrared measurements of sapphire fibers for medical applications,” Appl. Opt. 32, 390–392 (1993). [CrossRef] [PubMed]

,18

18. R. Nubling and J. Harrington, “Optical properties of single-crystal sapphire fibers,” Appl. Opt. 36, 5934–5940 (1997). [CrossRef] [PubMed]

]. Additionally, sapphire fiber is fabricated using a technique based on laser heated pedestal growth (LHPG) [18

18. R. Nubling and J. Harrington, “Optical properties of single-crystal sapphire fibers,” Appl. Opt. 36, 5934–5940 (1997). [CrossRef] [PubMed]

20

20. G. Merberg and J. Harrington, “Optical and mechanical properties of single-crystal sapphire optical fibers,” Appl. Opt. 32, 3201–3209 (1993). [CrossRef] [PubMed]

], which is a matured technology. However, the nonlinear coefficient of a sapphire fiber (γ = 1.171 × 10-5/m·W at 1.55µm) is 14,000 times smaller than PCF fiber (γ = 0.1680/m·W at 1.55µm) due to its large mode area. Although the large mode area of the sapphire fiber significantly reduces its nonlinear coefficient, SCG in fibers with a larger mode area has generated a great deal of interest for the following reasons [21

21. G. Genty, T. Ritari, and H. Ludvigsen, “Supercontinuum generation in large mode-area microstructured fibers,” Opt. Express 13, 8625–8633 (2005). [CrossRef] [PubMed]

23

23. T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000). [CrossRef]

]: the coupling efficiency is very high, and the chance of surface damage decreases since the input light does not have to be as tightly focused as in the case of PCF fiber [18

18. R. Nubling and J. Harrington, “Optical properties of single-crystal sapphire fibers,” Appl. Opt. 36, 5934–5940 (1997). [CrossRef] [PubMed]

]. To maintain the advantages of a large mode area sapphire fiber (i.e. high coupling efficiency, high damage threshold, and good IR transparency) while improving the supercontinuum bandwidth, we adopt a multiple pumping source scheme.

Previously, SCG using dual-wavelength pumping has been reported [24

24. G. Genty, M. Lehtonen, and H. Ludvigsen, “Route to broadband blue-light generation in microstructured optical fibers,” Opt. Lett. 30, 756–758 (2005). [CrossRef] [PubMed]

28

28. E. Räikkönen, S. C. Buchter, and M. Kaivola, “Generation of monochromatic visible light in microstructured optical fiber by nondegenerate four-wave mixing,” Appl. Phys. B 91, 461–465 (2008). [CrossRef]

]. Dual-wavelength pumping broadens the spectrum via cross-phase modulation (XPM) [24

24. G. Genty, M. Lehtonen, and H. Ludvigsen, “Route to broadband blue-light generation in microstructured optical fibers,” Opt. Lett. 30, 756–758 (2005). [CrossRef] [PubMed]

26

26. E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen, and S. C. Buchter, “Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers,” Opt. Express 14, 7914–7923 (2006). [CrossRef] [PubMed]

], generates peaks at sidebands due to XPM-induced instability [27

27. E. E. Serebryannikov, S. O. Konorov, A. A. Ivanov, M. V. Alfimov, M. Scalora, and A. M. Zheltikov, “Cross-phase-modulation-induced instability in photonic-crystal fibers,” Phys. Rev. E 72, 027601-1–027601-3 (2005). [CrossRef]

], and causes nondegenerate four-wave mixing (FWM) [28

28. E. Räikkönen, S. C. Buchter, and M. Kaivola, “Generation of monochromatic visible light in microstructured optical fiber by nondegenerate four-wave mixing,” Appl. Phys. B 91, 461–465 (2008). [CrossRef]

]. But, the broadened spectrum created by dual-wavelength pumping in many papers has a discontinuity between the supercontinua generated by each pump wavelength [24

24. G. Genty, M. Lehtonen, and H. Ludvigsen, “Route to broadband blue-light generation in microstructured optical fibers,” Opt. Lett. 30, 756–758 (2005). [CrossRef] [PubMed]

,26

26. E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen, and S. C. Buchter, “Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers,” Opt. Express 14, 7914–7923 (2006). [CrossRef] [PubMed]

28

28. E. Räikkönen, S. C. Buchter, and M. Kaivola, “Generation of monochromatic visible light in microstructured optical fiber by nondegenerate four-wave mixing,” Appl. Phys. B 91, 461–465 (2008). [CrossRef]

]. Even though these spectra are overlapped in several papers, the total reported span is much less than two octaves [25

25. T. Schreiber, T. V. Andersen, D. Schimpf, J. Limbert, and A. Tünnermann, “Supercontinuum generation by femtosecond single and dual wavelength pumping in photonic crystal fibers with two zero dispersion wavelengths,” Opt. Express 13, 9556–9569 (2005). [CrossRef] [PubMed]

].

In this paper, we employ triple pumping sources to generate supercontinuum in a single crystal sapphire fiber. Our supercontinuum covers a very broad spectrum from the UV to the lower end of the mid-IR without spectra discontinuity. By using triple pumping sources, we can generate a very broad spectrum despite using a large mode area. Also, an even broader spectrum may be generated by increasing the number of pumping sources in the longer IR wavelengths.

2. Technical approach

We followed the procedure in [29

29. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express 12, 124–135 (2003). [CrossRef]

, 30

30. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989). [CrossRef]

] to derive the nonlinear Schödinger equation (NLSE) for the propagation of three pumping sources in an optical fiber. The generalized NLSE describing single pulse propagation in an optical fiber can be expressed as [29

29. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express 12, 124–135 (2003). [CrossRef]

, 30

30. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989). [CrossRef]

]:

Az+α2AΣn2in+1n!βnnATn=+iγ(1+iω0T)A·+R(T')A(z,TT')2dT',
(1)

where R (T) represents the instantaneous and the delayed material response [29

29. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express 12, 124–135 (2003). [CrossRef]

] while α is the fiber loss, and βn is the nth propagation constant.

The nonlinear part of Eq. (1) can be expressed in terms of new variable V as [29

29. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express 12, 124–135 (2003). [CrossRef]

, 30

30. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989). [CrossRef]

]:

Vz=iγV·R(T)*(V02+V2)γ1ω0T(V·R(T)*V2),
(2)
whereV(z,T)=A(z,T)exp[iγ(R(T)*A02)(zz0)].
(3)

In that case, the multiple pumping sources propagating in an optical fiber can be expressed as [31

31. N. K. Das, Y. Yamayoshi, and H. Kawaguchi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by the finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184–1192 (2000). [CrossRef]

]:

V=Σj=1NPPjexp[(TT0)2]·exp[i(Δωj)T],
(4)

To determine the length of a sapphire fiber, the dispersion length, LD, and the nonlinear interaction length, LNL, need to be calculated. Those lengths are given as LD = T02/|β 2| and LNL = 1/γP0, where P0 is the peak power of the propagating beam, and β2 is group velocity dispersion [35

35. G. Agrawal, Nonlinear Fiber Optics, 2nd Ed. (Academic Press, New York, 1995).

]. The group velocity dispersion at 784nm, 1290nm, and 2000nm can be calculated from β2=(λ3/2πc2)·(d2n0/2), and the calculated values are 59.21ps2/km, 2.979ps2/km, and -121.5ps2/km, respectively. Based on pulse width of 150fs, the dispersion lengths are 38.01cm for 784nm, 755.34cm for 1290nm, and 18.52 cm for 2000nm. The effective mode area Aeff (10,386µm2) and the nonlinear refractive index n2 (3×10-20m2/W for 784nm, 2.9×10-20m2/W for 1290nm, and 2.8×10-20m2/W for 2000nm [16

16. A. Major, F. Yoshino, I. Nikolakakos, J. Aitchison, and P. Smith, “Dispersion of the nonlinear refractive index in sapphire,” Opt. Lett. 29, 602–604 (2004). [CrossRef] [PubMed]

]) are substituted into γ = n2 ω0/cAeff = 2πn2/ λAeff to find the nonlinear coefficients. The calculated values are 2.268×10-5/m·W, 1.359×10-5/m·W, and 8.466×10-6/m·W for 784nm, 1290nm, and 2000nm, respectively. The calculated nonlinear interaction lengths according to the nonlinear coefficient above and the estimated peak power for our experiment (approximately 1.607×107W) are 0.274cm for 784nm, 0.457cm for 1290nm, and 0.735cm for 2000nm.

ωp1+ωp2=ωs1+ωi1
ωp1+ωp3=ωs2+ωi2
ωp2+ωp3=ωs3+ωi3,
(5a)
kp1+kp2=ks1+ki1+γp1Pp1+γp2Pp2
kp1+kp3=ks2+ki2+γp1Pp1+γp3Pp3
kp2+kp3=ks3+ki3+γp2Pp2+γp3Pp3,
(5b)

where pj is jth pumping source, sj and ij are signal and idler beams generated by the FWM processes, and γpj and Ppj are the nonlinear coefficient and the peak power of jth pumping source.

3. Experimental procedures and results

To verify that FWM processes are involved in the SCG from three pumping sources, we calculated the frequency interaction and phase matching conditions of the three pumping sources. The frequency interaction condition between 1290nm and 2000nm is given as:

ω1290nm+ω2000nm=ωs3+ωi3,
(6)

which is only satisfied when the following phase matching condition is matched [37

37. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St. J. Russell, “Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres,” Opt. Express 12, 299–309 (2004). [CrossRef] [PubMed]

]:

k1290nm+k2000nm=ks3+ki3+(γP)1290nm+(γP)2000nm,
(7)

where kλ = 2πnλ/λ. By using the nonlinear coefficients, the peak power of 1.607×107W, and the refractive indices derived from the sellmeier equation [14

14. S. Yin, J. H. Kim, C. Zhan, J. W. An, J. Lee, P. Ruffin, E. Edwards, C. Brantley, and C. Luo, “Supercontinuum generation in single crystal sapphire fibers,” Opt. Commun. 281, 1113–1117 (2008). [CrossRef]

, 15

15. J. H. Kim, M.-K. Chen, C.-E. Yang, J. Lee, S. Yin, P. Ruffin, E. Edwards, C. Brantley, and C. Luo, “Broadband IR supercontinuum generation using single crystal sapphire fibers,” Opt. Express 16, 4085–4093 (2008). [CrossRef] [PubMed]

] to solve the phase matching condition, we find that the phase matching condition occurs when the signal and idler beams are at 1164nm and 2400nm. Also, two other interactions (784nm and 1290nm, and 784nm and 2000nm) generate the signal and idler peaks located at 595nm and 2700nm, and 727nm and 2500nm, respectively.

To compare the validity of our theory with the experimental results, three pumping sources launch pulses into the sapphire fiber. For the experimental setup shown in Fig. 1, the three sources are the signal and idler beams (1290nm and 2000nm) from the OPA and an additional source at 784nm. The beams have a 1kHz repetition rate and 150fs pulse width. Once the three beams overlap spatially and temporally, they are focused by an achromatic lens (f=5cm) and coupled into the 5cm sapphire fiber. The supercontinuum generated through the sapphire fiber is collimated by a silica lens (for UV, visible, and near-IR ranges) and a Zinc Selenide (ZnSe) IR lens (for near- and mid-IR ranges), and is detected by a monochromator (MicroHR, Horiba Jobin Yvon Inc.).

Fig. 1. Experimental set up for supercontinuum generation in sapphire fiber

Figure 2 shows the experimental results of the supercontinuum spectra generated from the three individual pumping sources (blue dash: 784nm, green dash: 1290nm, and black dash: 2000nm) and the three pumping sources together (red solid). The spectrum produced by each individual pumping source is primarily a result of SPM. The spectra from the 784nm, 1290nm, and 2000nm sources range from 400nm to 1200nm, from 1000nm to 1800nm, and 1300nm to 2800nm, respectively. The supercontinuum generated by the three pumping sources together involves more than SPM. The three main spectra due to SPM are overlapped while the peaks due to nondegenerate FWM processes are created when the pulses from the three sources travel through the sapphire fiber simultaneously. The peaks created by FWM also undergo degenerate FWM processes with other peaks [38

38. J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991). [CrossRef] [PubMed]

] to stack multiple peaks in the UV area, but the later interactions occur over a very short distance due to walk-off. Other effects such as Raman scattering and XPM also contribute to the increase in both ends of spectra. Therefore, idler beams can enhance the intensity level in mid-IR region via nondegenerate FWM processes while signal beams involved in nondegenerate and degenerate FWM processes can increase the intensity level in the UV and visible regions. As a result, an ultra-broadband supercontinuum ranging from the UV to mid-IR regions is generated by employing three pumping sources. The calculated peaks due to nondegenerate FWM processes match well with those of the experimental spectra shown in Fig. 2.

To verify the relevance of our experimental results, a simulation of the NLSE was performed with the same parameters as the experiments. We followed similar procedures in [29

29. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express 12, 124–135 (2003). [CrossRef]

, 30

30. K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989). [CrossRef]

] to numerically simulate the SCG in a sapphire fiber due to the propagation of three pumping sources. The frequency shift of the Raman gain was around 418cm-1 [39

39. W. Jia and W. M. Yen, “Raman scattering from sapphire fibers,” J. Raman Spectroscopy 20, 785–788 (1989). [CrossRef]

]. The fractional contribution of the instantaneous Raman response to the nonlinear refractive index, fR used was 0.25, which was derived from n2 and nR given in [40

40. J. L. Tate, Intense laser propagation in sapphire, Ph. D. Thesis (2004), The Ohio State University.

], and from the equation in [41

41. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989). [CrossRef]

]. Other parameters τ1, and τ2 used to decide delayed Raman response hR were 182fs, and 200fs, respectively [40

4. T. Morioka, K. Mori, and M. Saruwatari, “More than 100-wavelength-channel picosecond optical pulse generation from single laser source using supercontinuum in optical fibres,” Electron. Lett. 29, 862–864 (1993). [CrossRef]

].

Figure 3 shows the simulated spectra of the supercontinuum emitted from the sapphire fiber due to the interaction of the three pumping sources. The spectra of three pumping sources are broadened by SPM and overlapped while peaks and intensity enhancement in the UV, visible, and mid-IR are observed due to complex FWM processes. The peaks due to nondegenerate FWM processes in the simulation results are in good agreement with the experimental results.

To check whether the peaks shown in Figs. 2 and 3 are the nondegenerate FWM caused by each interaction between two pumping sources, we evaluated the interaction between 1290nm and 2000nm with simulation and experimental results. Figure 4(a) shows the simulation spectrum caused by the interaction between 1290nm and 2000nm pumping sources. The peak powers of 8.035×106W and 4.821×106W are utilized for 1290nm and 2000nm peaks, respectively. As shown in Fig. 4(a), signal and idler peaks due to the FWM are observed. To verify that the peaks observed in Fig. 4(a) are due to the FWM, we increased the peak power of 1290nm pumping source to 1.286×107W while the peak power for 2000nm source is unchanged. As shown in Fig. 4(b), the main spectrum caused by 2000nm source is very similar to that in Fig. 4(a) while the intensities of both peaks due to the FWM are increased. Figure 4(c) shows three simulation spectra when 2000nm pumping source is presented alone (dot line), and it is accompanied by 1290nm source with the peak powers of 8.035×106W (dashed line) and 1.286×107W (solid line). While the spectra due to 2000nm pumping source remains very similar, the peak at 2400nm intensifies when the intensity of 1290nm source increases. Also, the peak at 2400nm is not ovservable when 1290nm source is not coupled together. This seems to be due to the increased FWM gain [42

42. J. Fan, A. Migdall, and L. J. Wang, “Increased cross-correlation in cascaded four-wave mixing processes,” Opt. Express 15, 7146–7151 (2007). [CrossRef] [PubMed]

]. According to papers that discuss cross-phase modulation (XPM) effect caused by dual-pumping, the spectrum of an interested source dramatically expands in wavelength when it is affected by another pumping source at different wavelength [25

25. T. Schreiber, T. V. Andersen, D. Schimpf, J. Limbert, and A. Tünnermann, “Supercontinuum generation by femtosecond single and dual wavelength pumping in photonic crystal fibers with two zero dispersion wavelengths,” Opt. Express 13, 9556–9569 (2005). [CrossRef] [PubMed]

, 26

26. E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen, and S. C. Buchter, “Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers,” Opt. Express 14, 7914–7923 (2006). [CrossRef] [PubMed]

, 43

43. V. Tombelaine, P. Leproux, V. Couderc, and A. Barthélémy, “Visible supercontinuum generation in holey fibers by dual-wavelength subnanosecond pumping,” IEEE Photon. Technol. Lett. 18, 2466–2468 (2006). [CrossRef]

]. Therefore, compared to the FWM, the XPM effect does not seem very dominant in this simulation. To verify our simulation results shown in Fig. 4(a)–(c), we experimentally evaluated two pumping sources of 1290nm and 2000nm. The peak power used for this experiment was 8.035×106W. As shown in Fig. 4(d), two peaks due to the FWM are clearly observable. Therefore, many peaks appearing on Figs. 3 and 4 seem to be caused by the FWM effect.

Fig. 2. The experimentally measured spectra generated from the three individual pumping sources (blue dash: 784nm, green dash: 1290nm, and black dash: 2000nm) and the three pumping sources together (red solid)
Fig. 3. The simulation spectra generated from the three pumping sources
Fig. 4. The simulation and experimental spectra of two pumping sources located at 1290nm and 2000nm: (a) simulation spectra of 1290nm source with 8.035×106W and 2000nm source with 4.821×106W, (b) simulation spectra of 1290nm source with 1.286×107W and 2000nm source with 4.821×106W, (c) three simulation spectra when 2000nm pumping source is presented alone (dot line), and it is accompanied by 1290nm source with the peak powers of 8.035×106W (dashed line) and 1.286×107W (solid line), and (d) experimental spectra of 1290nm and 2000nm sources with the peak power of 8.035×106W.

4. Conclusions

We experimentally demonstrated that the spectral bandwidth of SCG, generated from a large mode area sapphire fiber, could be enhanced by employing triple pumping sources. A broad supercontinuum spectrum from the UV to the mid-IR was successfully demonstrated. The mechanisms of SCG using the three pumping sources were theoretically and experimentally investigated. When three pulses at different wavelengths propagated through the sapphire fiber, their spectra were broadened due to SPM and the complex FWM processes. It is also anticipated that by increasing the number of pumping sources in the longer IR wavelengths, this scheme has the potential to create an even broader spectrum. This ultra-broadband source may have a significant impact in variety of applications including multiple region spectroscopy, remote sensing, standoff chemical detection, biomedical researches, and communications.

Acknowledgments

Partial financial support of this work by ONR grant, N00014-05-1-0844 is greatly appreciated.

References and links

1.

S. T. Sanders, “Wavelength-agile fiber laser using group-velocity dispersion of pulsed super-continua and application to broadband absorption spectroscopy,” Appl. Phys. B-Lasers Opt. 75, 799–802 (2002). [CrossRef]

2.

K. Shi, P. Li, S. Yin, and Z. Liu, “Chromatic confocal microscopy using supercontinuum light,” Opt. Express 12, 2096–2101 (2004). [CrossRef] [PubMed]

3.

K. Shi, S. H. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun. 263, 156–162 (2006). [CrossRef]

4.

T. Morioka, K. Mori, and M. Saruwatari, “More than 100-wavelength-channel picosecond optical pulse generation from single laser source using supercontinuum in optical fibres,” Electron. Lett. 29, 862–864 (1993). [CrossRef]

5.

A. A. Ivanov, M. V. Alfimov, A. B. Fedotov, A. A. Podshivalov, D. Chorvat, and A. M. Zheltikov, “An all-solid-state sub-40-fs self-starting Cr4+: Forsterite laser with holey-fiber beam delivery and chirp control for coherence-domain and nonlinear-optical biomedical applications,” Laser Phys. 11, 158–163 (2001).

6.

I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001). [CrossRef]

7.

D. M. Brown, K. Shi, Z. Liu, and R. Philbrick, “Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents,” Opt. Express 16, 8457–8471 (2008). [CrossRef] [PubMed]

8.

P. Weibring, H. Edner, and S. Svanberg, “Versatile mobile lidar system for environmental monitoring,” Appl. Opt. 42, 3583–3594 (2003). [CrossRef] [PubMed]

9.

I. T. Sorokina and K. L. Vodopyanov, Solid-state mid-infrared laser sources (Springer-Verlag, Berlin Heidelberg, 2003). [CrossRef]

10.

J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J.-P. Wolf, Y.-B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille, and L. Wöste, “Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere,” Opt. Lett. 25, 1397–1399 (2000). [CrossRef]

11.

V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto, and A. J. Taylor, “Extruded soft glass photonic crystal fiber for ultraband supercontinuum generation,” Opt. Express 10, 1520–1525 (2002).

12.

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

13.

F. G. Omenetto, N. A. Wolchover, M. R. Wehner, M. Ross, A. Efimov, A. J. Taylor, V. V. R. K. Kumar, A. K. George, J. C. Knight, N. Y. Joly, and P. St. J. Russel, “Spectrally smooth supercontinuum from 350nm to 3µm in sub-centimeter lengths of soft-glass photonic crystal fibers,” Opt. Express 14, 4928–4934 (2006). [CrossRef] [PubMed]

14.

S. Yin, J. H. Kim, C. Zhan, J. W. An, J. Lee, P. Ruffin, E. Edwards, C. Brantley, and C. Luo, “Supercontinuum generation in single crystal sapphire fibers,” Opt. Commun. 281, 1113–1117 (2008). [CrossRef]

15.

J. H. Kim, M.-K. Chen, C.-E. Yang, J. Lee, S. Yin, P. Ruffin, E. Edwards, C. Brantley, and C. Luo, “Broadband IR supercontinuum generation using single crystal sapphire fibers,” Opt. Express 16, 4085–4093 (2008). [CrossRef] [PubMed]

16.

A. Major, F. Yoshino, I. Nikolakakos, J. Aitchison, and P. Smith, “Dispersion of the nonlinear refractive index in sapphire,” Opt. Lett. 29, 602–604 (2004). [CrossRef] [PubMed]

17.

R. W. Waynant, S. Oshry, and M. Fink, “Infrared measurements of sapphire fibers for medical applications,” Appl. Opt. 32, 390–392 (1993). [CrossRef] [PubMed]

18.

R. Nubling and J. Harrington, “Optical properties of single-crystal sapphire fibers,” Appl. Opt. 36, 5934–5940 (1997). [CrossRef] [PubMed]

19.

R. S. Feigelson, “Pulling optical fibers,” J. Cryst. Growth 79, 669–680 (1986). [CrossRef]

20.

G. Merberg and J. Harrington, “Optical and mechanical properties of single-crystal sapphire optical fibers,” Appl. Opt. 32, 3201–3209 (1993). [CrossRef] [PubMed]

21.

G. Genty, T. Ritari, and H. Ludvigsen, “Supercontinuum generation in large mode-area microstructured fibers,” Opt. Express 13, 8625–8633 (2005). [CrossRef] [PubMed]

22.

A. Shirakawa, J. Ota, M. Musha, K. Nakagawa, and K. Ueda, “Large-mode-area erbium-ytterbium-doped photonic-crystal fiber amplifier for high-energy femtosecond pulses at 1.55µm,” Opt. Express 13, 1221–1227 (2005). [CrossRef] [PubMed]

23.

T. A. Birks, W. J. Wadsworth, and P. St. J. Russell, “Supercontinuum generation in tapered fibers,” Opt. Lett. 25, 1415–1417 (2000). [CrossRef]

24.

G. Genty, M. Lehtonen, and H. Ludvigsen, “Route to broadband blue-light generation in microstructured optical fibers,” Opt. Lett. 30, 756–758 (2005). [CrossRef] [PubMed]

25.

T. Schreiber, T. V. Andersen, D. Schimpf, J. Limbert, and A. Tünnermann, “Supercontinuum generation by femtosecond single and dual wavelength pumping in photonic crystal fibers with two zero dispersion wavelengths,” Opt. Express 13, 9556–9569 (2005). [CrossRef] [PubMed]

26.

E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen, and S. C. Buchter, “Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers,” Opt. Express 14, 7914–7923 (2006). [CrossRef] [PubMed]

27.

E. E. Serebryannikov, S. O. Konorov, A. A. Ivanov, M. V. Alfimov, M. Scalora, and A. M. Zheltikov, “Cross-phase-modulation-induced instability in photonic-crystal fibers,” Phys. Rev. E 72, 027601-1–027601-3 (2005). [CrossRef]

28.

E. Räikkönen, S. C. Buchter, and M. Kaivola, “Generation of monochromatic visible light in microstructured optical fiber by nondegenerate four-wave mixing,” Appl. Phys. B 91, 461–465 (2008). [CrossRef]

29.

I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, “Dispersive wave generation by solitons in microstructured optical fibers,” Opt. Express 12, 124–135 (2003). [CrossRef]

30.

K. J. Blow and D. Wood, “Theoretical description of transient stimulated Raman scattering in optical fibers,” IEEE J. Quantum Electron. 25, 2665–2673 (1989). [CrossRef]

31.

N. K. Das, Y. Yamayoshi, and H. Kawaguchi, “Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by the finite-difference beam propagation method,” IEEE J. Quantum Electron. 36, 1184–1192 (2000). [CrossRef]

32.

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

33.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, “Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800nm,” Opt. Lett. 25, 25–27 (2000). [CrossRef]

34.

R. Zhang, J. Teipel, and H. Giessen, “Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation,” Opt. Express 14, 6800–6812 (2006). [CrossRef] [PubMed]

35.

G. Agrawal, Nonlinear Fiber Optics, 2nd Ed. (Academic Press, New York, 1995).

36.

F. G. Omenetto, N. A. Wolchover, M. R. Wehner, M. Ross, A. Efimov, A. J. Taylor, V. V. R. K. Kumar, A. K. George, J. C. Knight, N. Y. Joly, and P. St. J. Russel, “Spectrally smooth supercontinuum from 530nm to 3um in sub-centimeter lengths of soft-glass photonic crystal fibers,” Opt. Express 14, 4928–4934 (2006). [CrossRef] [PubMed]

37.

W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St. J. Russell, “Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres,” Opt. Express 12, 299–309 (2004). [CrossRef] [PubMed]

38.

J. R. Thompson and R. Roy, “Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber,” Phys. Rev. A 43, 4987–4996 (1991). [CrossRef] [PubMed]

39.

W. Jia and W. M. Yen, “Raman scattering from sapphire fibers,” J. Raman Spectroscopy 20, 785–788 (1989). [CrossRef]

40.

J. L. Tate, Intense laser propagation in sapphire, Ph. D. Thesis (2004), The Ohio State University.

41.

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, “Raman response function of silica-core fibers,” J. Opt. Soc. Am. B 6, 1159–1166 (1989). [CrossRef]

42.

J. Fan, A. Migdall, and L. J. Wang, “Increased cross-correlation in cascaded four-wave mixing processes,” Opt. Express 15, 7146–7151 (2007). [CrossRef] [PubMed]

43.

V. Tombelaine, P. Leproux, V. Couderc, and A. Barthélémy, “Visible supercontinuum generation in holey fibers by dual-wavelength subnanosecond pumping,” IEEE Photon. Technol. Lett. 18, 2466–2468 (2006). [CrossRef]

OCIS Codes
(060.7140) Fiber optics and optical communications : Ultrafast processes in fibers
(190.4370) Nonlinear optics : Nonlinear optics, fibers

ToC Category:
Nonlinear Optics

History
Original Manuscript: July 8, 2008
Revised Manuscript: August 29, 2008
Manuscript Accepted: August 31, 2008
Published: September 4, 2008

Citation
Jae Hun Kim, Meng-Ku Chen, Chia-En Yang, Jon Lee, Kebin Shi, Zhiwen Liu, Stuart (Shizhuo) Yin, Karl Reichard, Paul Ruffin, Eugene Edwards, Christina Brantley, and Claire Luo, "Broadband supercontinuum generation covering UV to mid-IR region by using three pumping sources in single crystal sapphire fiber," Opt. Express 16, 14792-14800 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-19-14792


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References

  1. S. T. Sanders, "Wavelength-agile fiber laser using group-velocity dispersion of pulsed super-continua and application to broadband absorption spectroscopy," Appl. Phys. B: Lasers Opt. 75,799-802 (2002). [CrossRef]
  2. K. Shi, P. Li, S. Yin and Z. Liu, "Chromatic confocal microscopy using supercontinuum light," Opt. Express 12, 2096-2101 (2004). [CrossRef] [PubMed]
  3. K. Shi, S. H. Nam, P. Li, S. Yin and Z. Liu, "Wavelength division multiplexed confocal microscopy using supercontinuum," Opt. Commun. 263, 156-162 (2006). [CrossRef]
  4. T. Morioka, K. Mori and M. Saruwatari, "More than 100-wavelength-channel picosecond optical pulse generation from single laser source using supercontinuum in optical fibres," Electron. Lett. 29, 862-864 (1993). [CrossRef]
  5. A. A. Ivanov, M. V. Alfimov, A. B. Fedotov, A. A. Podshivalov, D. Chorvat and A. M. Zheltikov, "An all-solid-state sub-40-fs self-starting Cr4+: Forsterite laser with holey-fiber beam delivery and chirp control for coherence-domain and nonlinear-optical biomedical applications," Laser Phys. 11, 158-163 (2001).
  6. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka and R. S. Windeler, "Ultrahigh resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber," Opt. Lett. 26, 608-610 (2001). [CrossRef]
  7. D. M. Brown, K. Shi, Z. Liu and R. Philbrick, "Long-path supercontinuum absorption spectroscopy for measurement of atmospheric constituents," Opt. Express 16, 8457-8471 (2008). [CrossRef] [PubMed]
  8. P. Weibring, H. Edner and S. Svanberg, "Versatile mobile lidar system for environmental monitoring," Appl. Opt. 42, 3583-3594 (2003). [CrossRef] [PubMed]
  9. I. T. Sorokina and K. L. Vodopyanov, Solid-state mid-infrared laser sources (Springer-Verlag, Berlin Heidelberg, 2003). [CrossRef]
  10. J. Kasparian, R. Sauerbrey, D. Mondelain, S. Niedermeier, J. Yu, J.-P. Wolf, Y.-B. André, M. Franco, B. Prade, S. Tzortzakis, A. Mysyrowicz, M. Rodriguez, H. Wille and L. Wöste, "Infrared extension of the supercontinuum generated by femtosecond terawatt laser pulses propagating in the atmosphere," Opt. Lett. 25, 1397-1399 (2000). [CrossRef]
  11. V. V. Ravi Kanth Kumar, A. K. George, W. H. Reeves, J. C. Knight, P. St. J. Russell, F. G. Omenetto and A. J. Taylor, "Extruded soft glass photonic crystal fiber for ultraband supercontinuum generation," Opt. Express 10, 1520-1525 (2002).
  12. C. Xia, M. Kumar, O. P. Kulkarni, M. N. Islam, and F. J. Terry, Jr, "Mid-infrared supercontinuum generation to 4.5?m in ZBLAN fluoride fibers by nanosecond diode pumping," Opt. Lett. 31, 2553-2555 (2006). [CrossRef] [PubMed]
  13. F. G. Omenetto, N. A. Wolchover, M. R. Wehner, M. Ross, A. Efimov, A. J. Taylor, V. V. R. K. Kumar, A. K. George, J. C. Knight, N. Y. Joly, and P. St. J. Russel, "Spectrally smooth supercontinuum from 350nm to 3?m in sub-centimeter lengths of soft-glass photonic crystal fibers," Opt. Express 14, 4928-4934 (2006). [CrossRef] [PubMed]
  14. S. Yin, J. H. Kim, C. Zhan, J. W. An, J. Lee, P. Ruffin, E. Edwards, C. Brantley and C. Luo, "Supercontinuum generation in single crystal sapphire fibers," Opt. Commun. 281, 1113-1117 (2008). [CrossRef]
  15. J. H. Kim, M.-K. Chen, C.-E. Yang, J. Lee, S. Yin, P. Ruffin, E. Edwards, C. Brantley and C. Luo, "Broadband IR supercontinuum generation using single crystal sapphire fibers," Opt. Express 16, 4085-4093 (2008). [CrossRef] [PubMed]
  16. A. Major, F. Yoshino, I. Nikolakakos, J. Aitchison and P. Smith, "Dispersion of the nonlinear refractive index in sapphire," Opt. Lett. 29, 602-604 (2004). [CrossRef] [PubMed]
  17. R. W. Waynant, S. Oshry and M. Fink, "Infrared measurements of sapphire fibers for medical applications," Appl. Opt. 32, 390-392 (1993). [CrossRef] [PubMed]
  18. R. Nubling and J. Harrington, "Optical properties of single-crystal sapphire fibers," Appl. Opt. 36, 5934-5940 (1997). [CrossRef] [PubMed]
  19. R. S. Feigelson, "Pulling optical fibers," J. Cryst. Growth 79, 669-680 (1986). [CrossRef]
  20. G. Merberg and J. Harrington, "Optical and mechanical properties of single-crystal sapphire optical fibers," Appl. Opt. 32, 3201-3209 (1993). [CrossRef] [PubMed]
  21. G. Genty, T. Ritari and H. Ludvigsen, "Supercontinuum generation in large mode-area microstructured fibers," Opt. Express 13, 8625-8633 (2005). [CrossRef] [PubMed]
  22. A. Shirakawa, J. Ota, M. Musha, K. Nakagawa and K. Ueda, "Large-mode-area erbium-ytterbium-doped photonic-crystal fiber amplifier for high-energy femtosecond pulses at 1.55?m," Opt. Express 13, 1221-1227 (2005). [CrossRef] [PubMed]
  23. T. A. Birks, W. J. Wadsworth and P. St. J. Russell, "Supercontinuum generation in tapered fibers," Opt. Lett. 25, 1415-1417 (2000). [CrossRef]
  24. G. Genty, M. Lehtonen and H. Ludvigsen, "Route to broadband blue-light generation in microstructured optical fibers," Opt. Lett. 30, 756-758 (2005). [CrossRef] [PubMed]
  25. T. Schreiber, T. V. Andersen, D. Schimpf, J. Limbert and A. Tünnermann, "Supercontinuum generation by femtosecond single and dual wavelength pumping in photonic crystal fibers with two zero dispersion wavelengths," Opt. Express 13, 9556-9569 (2005). [CrossRef] [PubMed]
  26. E. Räikkönen, G. Genty, O. Kimmelma, M. Kaivola, K. P. Hansen and S. C. Buchter, "Supercontinuum generation by nanosecond dual-wavelength pumping in microstructured optical fibers," Opt. Express 14, 7914-7923 (2006). [CrossRef] [PubMed]
  27. E. E. Serebryannikov, S. O. Konorov, A. A. Ivanov, M. V. Alfimov, M. Scalora and A. M. Zheltikov, "Cross-phase-modulation-induced instability in photonic-crystal fibers," Phys. Rev. E 72, 027601-1-027601-3 (2005). [CrossRef]
  28. E. Räikkönen, S. C. Buchter, and M. Kaivola, "Generation of monochromatic visible light in microstructured optical fiber by nondegenerate four-wave mixing," Appl. Phys. B 91, 461-465 (2008). [CrossRef]
  29. I. Cristiani, R. Tediosi, L. Tartara, and V. Degiorgio, "Dispersive wave generation by solitons in microstructured optical fibers," Opt. Express 12, 124-135 (2003). [CrossRef]
  30. K. J. Blow and D. Wood, "Theoretical description of transient stimulated Raman scattering in optical fibers," IEEE J. Quantum Electron. 25, 2665-2673 (1989). [CrossRef]
  31. N. K. Das, Y. Yamayoshi, and H. Kawaguchi, "Analysis of basic four-wave mixing characteristics in a semiconductor optical amplifier by the finite-difference beam propagation method," IEEE J. Quantum Electron. 36, 1184-1192 (2000). [CrossRef]
  32. J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006). [CrossRef]
  33. J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air-silica microstructure optical fibers with anomalous dispersion at 800nm," Opt. Lett. 25, 25-27 (2000). [CrossRef]
  34. R. Zhang, J. Teipel, and H. Giessen, "Theoretical design of a liquid-core photonic crystal fiber for supercontinuum generation," Opt. Express 14, 6800-6812 (2006). [CrossRef] [PubMed]
  35. G. Agrawal, Nonlinear Fiber Optics, 2nd Ed. (Academic Press, New York, 1995).
  36. F. G. Omenetto, N. A. Wolchover, M. R. Wehner, M. Ross, A. Efimov, A. J. Taylor, V. V. R. K. Kumar, A. K. George, J. C. Knight, N. Y. Joly, and P. St. J. Russel, "Spectrally smooth supercontinuum from 530nm to 3um in sub-centimeter lengths of soft-glass photonic crystal fibers," Opt. Express 14, 4928-4934 (2006). [CrossRef] [PubMed]
  37. W. J. Wadsworth, N. Joly, J. C. Knight, T. A. Birks, F. Biancalana, and P. St. J. Russell, "Supercontinuum and four-wave mixing with Q-switched pulses in endlessly single-mode photonic crystal fibres," Opt. Express 12, 299-309 (2004). [CrossRef] [PubMed]
  38. J. R. Thompson and R. Roy, "Nonlinear dynamics of multiple four-wave mixing processes in a single-mode fiber," Phys. Rev. A 43, 4987-4996 (1991). [CrossRef] [PubMed]
  39. W. Jia and W. M. Yen, "Raman scattering from sapphire fibers," J. Raman Spectrosc. 20, 785-788 (1989). [CrossRef]
  40. J. L. Tate, Intense laser propagation in sapphire, Ph. D. Thesis (2004), The Ohio State University.
  41. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, and H. A. Haus, "Raman response function of silica-core fibers," J. Opt. Soc. Am. B 6, 1159-1166 (1989). [CrossRef]
  42. J. Fan, A. Migdall, and L. J. Wang, "Increased cross-correlation in cascaded four-wave mixing processes," Opt. Express 15, 7146-7151 (2007). [CrossRef] [PubMed]
  43. V. Tombelaine, P. Leproux, V. Couderc, and A. Barthélémy, "Visible supercontinuum generation in holey fibers by dual-wavelength subnanosecond pumping," IEEE Photon. Technol. Lett. 18, 2466-2468 (2006). [CrossRef]

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