Enhanced soliton self-frequency shift and CWsupercontinuum generation in GeO2-doped

core photonic crystal fibers

B. Barviau,1,* O. Vanvincq,1 A. Mussot,1 Y. Quiquempois,1 G. Mélin,2 and A. Kudlinski1

1Université Lille 1, IRCICA, Laboratoire PhLAM, 59655 Villeneuve d’Ascq, France2DRAKA, route de Nozay, 91460 Marcoussis, France

*Corresponding author: benoit.barviau@ircica.univ‐lille1.fr

Received January 31, 2011; revised March 3, 2011; accepted March 13, 2011;posted March 16, 2011 (Doc. ID 141978); published April 19, 2011

We investigate the impact of germanium oxide (GeO2) doping on the linear and nonlinear properties of photoniccrystal fibers. We propose some design rules allowing a strong enhancement of the Raman and Kerr nonlinearitieswith little impact on the fiber dispersive properties. It is experimentally and numerically demonstrated that usingGeO2-doped core photonic crystal fibers allows a significant enhancement of the soliton self-frequency shift ascompared to pure silica photonic crystal fibers with comparable dispersion. We found that the high nonlinearcoefficient (due to a good mode confinement) obtained in the GeO2-doped core fiber plays a more importantrole on the soliton self-frequency shift enhancement than the intrinsic Raman gain. © 2011 Optical Societyof America

OCIS codes: 060.2280, 060.4005, 060.5295, 190.4370, 190.5530.

1. INTRODUCTIONIntrapulse Raman scattering is an inelastic nonlinear (NL) pro-cess in which low-frequency photons of a solitary pulse areamplified through Raman scattering from optical phonons[1]. Its impact on the propagation of solitons in optical fiberswas experimentally observed for the first time by Golovchen-ko et al. [2] in 1985. This mechanism was later called solitonself-frequency shift (SSFS) [3,4], because it manifests itselfthrough a continuous redshift of the central soliton wave-length with respect to propagation distance. The discoveryof the SSFS phenomenon immediately attracted much atten-tion because of its potential applications in high bit-rate soli-ton communication systems [5,6] or in tunable short-pulsefiber sources [7,8]. More recently, it has been identified asone of the main mechanisms involved in the generation ofoctave-spanning supercontinua (SC) [9]. Indeed, in both theshort- and long-pulse pumping regimes [10], the long-wavelength part of the SC spectrum is composed of redshift-ing fundamental solitons initially created by pulse fission ormodulation instability (MI), respectively [9]. Given that thespectral extent in the visible is intimately linked to the infraredone through a group index matching between solitons andtrapped dispersive waves [11,12], the SSFS dynamics lies atthe heart of the SC generation process. The improvementof the SC bandwidth thus relies on a careful optimizationof the SSFS process, whose rate increases with pump power[1,4]. In the case of a CW pumping with MI, the SSFS rate in-creases with the CW pump power squared [13]. Its optimiza-tion is thus especially important in this regime, becausetypical CW pump powers (of a few hundreds of watts atthe maximum) are much lower than the peak power of pulsedpumps (of at least several kilowatts) [13]. Moreover, the SSFSrate strongly depends on both the dispersive and NL proper-ties of the fiber [1,4]. The adjustment of the soliton wavelength

or optimization of the SC spectral extent in the experimentsdescribed above therefore require the simultaneous control ofthe fiber linear and NL properties. The photonic crystal fiber(PCF) technology allows the group-velocity dispersion (GVD)to be tailored [14,15] by adjusting the geometry of the air/silicacladding or to enhance the Kerr nonlinearity by reducing thecore size while increasing the air hole size [16,17]. However,since the adjustment is done through a control of the micro-structured cladding in both cases, the simultaneous control ofdispersive properties and enhancement of the Kerr nonlinear-ity is tricky to achieve over a large range.

We demonstrate here that doping the PCF core with GeO2

provides an additional degree of freedom in designing PCFswith targeted dispersive and NL properties. The GeO2 dopingis of great interest in optical fiber technology, because the pre-form fabrication technology is very mature and allows highdoping content with a controlled refractive index radialprofile [18]. Moreover, it provides a high gain for Raman am-plification in telecommunication networks [19]. It has alsoproven to be an efficient way of enhancing parametric fre-quency conversion [20,21] or SC generation [22,23]. However,the impact of GeO2 doping on the processes involved in SCgeneration, and in particular on soliton propagation, wasnot studied in detail in [22,23].

In this paper, we first show in Section 2 that doping the corewith GeO2 allows a further degree of freedom in designing andfabricating PCFs with greatly enhanced Kerr and Raman re-sponses, while tailoring the GVD, and in particular the posi-tion of the zero dispersion wavelength (ZDW). In Section 3,we experimentally demonstrate that such GeO2-doped corePCFs allow a significant enhancement of the SSFS. We showwith help of numerical simulations that this is mainly due tothe enhancement of the NL coefficient rather than the one ofthe intrinsic material Raman gain. Finally, in Section 4, we

1152 J. Opt. Soc. Am. B / Vol. 28, No. 5 / May 2011 Barviau et al.

0740-3224/11/051152-09$15.00/0 © 2011 Optical Society of America

highlight the benefit of GeO2-doped core PCFs in the contextof CW SC generation, and we propose an explanation of therecent unprecedented report of white-light CW SC generationin such fibers [24].

2. IMPACT OF GeO2 DOPING ON LINEARAND NL PROPERTIES OF PHOTONICCRYSTAL FIBERSA. Optical Properties of Bulk GeO2-Doped GlassesIt is well known that the incorporation of GeO2 into a silicamatrix alters the intrinsic dispersive properties of the material[25–27] as well as the instantaneous Kerr [28,29] and delayedRaman NL responses [30,31]. In this section, we provide anoverview of the methods used to determine the optical proper-ties of GeO2-doped silica from the data of the literature.

The refractive index dispersion of GeO2-doped bulk silicaglasses can be calculated from the empirical relations pro-posed by Fleming [27]. It depends on the Sellmeier coeffi-cients deduced from experiments for pure SiO2 and GeO2

bulk glasses, as well as on the mole fraction of GeO2. Figure 1shows the material GVD curves calculated from these data forpure silica (dashed curve) and GeO2 mole concentrations of10 and 20mol:% (dotted and solid curves, respectively). Thematerial GVD curve is shifted toward long wavelengths for in-creasing GeO2 mole fraction, and the material ZDW increasesfrom about 1270 nm in pure silica to 1360 nm in a 20mol:%GeO2-doped glass.

The estimation of the Kerr NL index n2 as a function ofGeO2 mole concentration in bulk germanosilicate glassescan be made by using the empirical relationship of Eq. 1 in[29] combined with the previous refractive index data from[27]. The evolution of n2 with the GeO2 mole concentrationcalculated at 1064nm is plotted in Fig. 2. It increases from2:53 × 10−20 m2=W for pure silica to 3:14 × 10−20 m2=W for aGeO2 content of 20mol:% Note that the NL refractive indexdispersion is less than 2% over the transparency window ofsilica and will consequently be neglected in the following.

The determination of the third-order Raman susceptibilityχð3Þ of GeO2-doped glasses can be made using the followingsimple relation proposed by Sylvestre et al. in [32]:

χð3ÞðωÞ ¼hχð3ÞSiO2

ðωÞð1 − xÞ þ χð3ÞGeO2ðωÞðx − 0:03Þ

i=0:97; ð1Þ

where χð3ÞSiO2and χð3ÞGeO2

are the third-order Raman susceptibil-ities of pure silica and pure GeO2, respectively, and x is the

mole fraction of GeO2 (x ≥ 0:03). The Raman gain parametergR is proportional to the imaginary part of the Raman suscept-ibility χð3ÞðωÞ as

gRðωÞ ∝ ℑ½χð3ÞðωÞ� × ωP; ð2Þ

where ωP is the pump frequency, and the symbolℑ representsthe imaginary part. The Raman gain is normalized so thatgR ¼ 7 × 10−14 m=W in pure silica for a 1550nm pump [1].The Raman gain spectrum can thus be calculated for anyGeO2 content, and it is represented in Fig. 3 for pure silica(dashed curve), and GeO2 mole concentrations of 10 and20mol:% (dotted and solid curves, respectively), for a pumpwavelength of 1064 nm. It is worth noting that there are twoimportant differences between these three curves. First, themaximum gain (obtained for a detuning of about 13THz fromthe pump in all cases) increases with the GeO2 content, asexpected. This is highlighted in Fig. 3(b) where the evolutionof the maximum gain as a function of the GeO2 mole concen-tration is represented. Second, the GeO2 doping modifies theoverall shape of the gain spectrum, especially for low-frequency shifts, as can be seen from the inset of Fig. 3. Animportant consequence is that the simple linear approxima-tion of the Raman gain spectrum for low-frequency detuningusually employed in analytical calculations [1,4] is not validanymore when GeO2 is added to the glass matrix.

B. Design and Properties of GeO2-Doped Core PCFs1. Influence of the GeO2 Doping ContentAs shown above, the GeO2 doping allows the enhancement ofboth the Kerr (n2 in Fig. 2) and Raman (gR in Fig. 3) NL re-sponses of silica glasses, with a simultaneous redshift of theZDW. The aim of this section is to find GeO2-doped core PCFstructures with a ZDW arbitrarily fixed to 1060� 1 nm, suita-ble for SC experiments with widely used 1064 nm pump lasers.Design simulations are performed with commercial finite-element software (COMSOL). The control of the ZDW locationis done through a careful adjustment of the microstructuredcladding parameters [33], namely the air hole diameter d andthe hole-to-hole separation Λ, keeping in mind the limitationsimposed by the fabrication process. The GeO2-doped region[represented in red in Fig. 4(a)] is located in the core center.In the results reported in this paragraph, the diameter of theGeO2-doped area, labeled dGeO2

, was fixed to 0:53 ×Λ in orderto match the one of previous reports [21]. We only considerhere GeO2-doped areas with a parabolic refractive index

Fig. 1. Material GVD curve calculated from [27] for a pure silica glass(dashed curve), and GeO2 mole concentrations of 10 and 20mol:%(dotted and solid curves, respectively).

Fig. 2. NL index n2 of bulk GeO2-doped glasses versus GeO2 molefraction.

Barviau et al. Vol. 28, No. 5 / May 2011 / J. Opt. Soc. Am. B 1153

profile (corresponding to preforms widely used for standardmultimode fibers), and a maximum GeO2 content of 20mol:%,which corresponds to a maximum refractive index differenceΔn of 32 × 10−3, with respect to the pure silica background. Inthe following, GeO2 mole fractions correspond to the dopinglevel at the top of the parabolic profile.

Figs. 4(b)–4(d) show the PCF quarter structures designedto have a ZDW of 1060� 1nm, for core doping levels of0mol:% (pure silica), 10mol:%, and 20mol:%, respectively.The corresponding parameters of the microstructured clad-ding (d and Λ) are summarized in Table 1. For increasingdoping levels, the position of the ZDW was adjusted to 1060�1 nm by reducing the pitch Λ and increasing the d=Λ ratio.The corresponding computed GVD curves are plotted in Fig. 5as a dashed curve for the pure silica PCF, as a dotted curve fora GeO2 level of 10mol:%, and as a solid curve for a GeO2 levelof 20mol:%. Although the ZDW is about the same for all fibers,the GVD slope β3 slightly increases with the doping content ata fixed wavelength (see Table 1).

The adjustment of the cladding parameters to controlthe ZDW location implies a change in the mode confine-ment in the core, as can be seen from the plot colors ofFigs. 4(b)–4(d). In particular, since the pitch Λ is reduced

and the d=Λ ratio is increased, the effective mode areaAeff (defined from [1]) decreases from 15.9 to 4:8 μm2 at1064 nm, for doping levels increasing from 0 to 20mol:%(see Table 1). This enhancement of the optical mode confine-ment combined with an increase of the NL index for increas-ing GeO2 doping contents (see Fig. 2) leads to a strongenhancement of the NL coefficient γ. In fibers with a nonuni-form NL refractive index profile, the NL coefficient γ is calcu-lated using the following Eq. (3):

γ ¼ 2π�n2

λAeff: ð3Þ

In Eq. (3), �n2 represents the NL refractive index of the fiber,and is defined as [29,34]

�n2 ¼RRþ∞−∞

n2ðx; yÞI2ðx; yÞdxdyRRþ∞−∞

I2ðx; yÞdxdy ; ð4Þ

where Iðx; yÞ is the transverse intensity distribution of the op-tical field, deduced from finite-element calculations. Values of�n2 calculated for each of the three fibers under investigationare reported in Table 1, which shows that �n2 increases withincreasing doping content. Figure 6 shows the spectral

Fig. 4. (Color online) (a) Scheme representing the PCF structure,with the GeO2-doped area depicted in red color. (b)–(d) Quarter sec-tion of the pure silica (b) and GeO2-doped core PCFs with a GeO2content of 10 (c) and 20mol:% (d). The colored scale representsthe fundamental mode distribution at 1064nm in logarithmic scale.

Fig. 3. (a) Raman gain spectra gR of pure silica glass (dashed curve),and GeO2-doped silica glasses with a mole fraction of 10 and 20mol:%(dotted and solid curves, respectively), for a pump wavelength of1064nm. Inset : close-up on the low detuning region. (b), (c) Evolutionof the maximum Raman gain gR (b) and fractional contribution f R (c)as a function of GeO2 doping content for a 1064nm pumping. Notethat plots (b) and (c) can only be done for doping contents≥3mol:% according to the model of [32].

Table 1. Summary of the Optogeometrical Properties

of the Three Designed PCFs

Pure Silica 10mol:% 20mol:%

Λ ðμmÞ 3.60 3.26 3.05d ðμmÞ 1.80 1.96 2.49�n2 at 1064nm ðm2=WÞ 2:5 × 10−20 2:6 × 10−20 2:9 × 10−20

Aeff at 1064nm ðμm2Þ 15.9 8.8 4.8γ at 1064nm ðW−1 · km−1Þ 9.4 17.8 34.8GVD at 1064nm ðps=nm=kmÞ 0.78 0.92 1.16

1154 J. Opt. Soc. Am. B / Vol. 28, No. 5 / May 2011 Barviau et al.

evolution of the corresponding NL coefficient calculated withEq. (3). Its value at 1064 nm increases from 9:4W−1 · km−1 forthe pure silica PCF to 34:8W−1 · km−1 for a GeO2 contentof 20mol:%.

All simulation results obtained for these investigated PCFstructures are summarized in Table 1 for the sake of clarity.They illustrate the possibility of a significant enhancement ofthe NL coefficient (almost fourfold in our case), with littleinfluence on the GVD curve, with a realistic GeO2 contentof 20mol:%.

2. Influence of the Relative Diameter of theGeO2-Doped AreaSince the GeO2 doping content plays an important role on theoptical mode confinement, and thus on the NL coefficient, onecan wonder how the size of the GeO2-doped region (relative tothe pitch Λ) affects these properties. To clarify this, we per-formed numerical simulations in GeO2-doped core PCF struc-tures by varying the diameter of the GeO2-doped area dGeO2

normalized to Λ, for the two doping levels of 10mol:% and20mol:% investigated above. For these simulations, thed=Λ ratio was fixed (to 0.6 and 0.815 for the 10 and20mol:% doping levels, respectively), but the pitch Λ wasslightly adjusted so that all PCF designs exhibit the sameZDW of 1060� 1 nm. The required pitch variations to do thiswere about 20% for both investigated doping contents. Figure 7shows the evolution of the NL coefficient calculated withEq. (3) at 1064 nm as a function of the dGeO2

=Λ ratio, for dop-ing levels of 10mol:% (open circles) and 20mol:% (solid cir-cles). These curves present an optimum in the NL coefficient

value at 1064nm for a dGeO2=Λ ratio of about 0.95 and 0.7, re-

spectively. The variations of the NL coefficient for dGeO2=Λ

varying from 0.3 to 0.95 are significant and reach about45% in both cases, which can be understood as follows. Letus first consider the case of the 20mol:% doping content.For the smallest dGeO2

=Λ values, the optical field is not wellconfined in the GeO2-doped region, because its size is of theorder of the light wavelength (the diameter of the GeO2-dopedregion is 1:1 μm for dGeO2

=Λ ¼ 0:3). In this case, the mode ef-fective area is relatively large, which makes the NL coefficientquite low. As the diameter of the GeO2-doped region increasesto about twice the light wavelength (for a dGeO2

=Λ of 0.7), thefield confinement and thus the NL coefficient are enhanced.For higher dGeO2

=Λ values for which the GeO2-doped regiondiameter is more than twice the light wavelength, the field isconfined in a larger region, so that the NL coefficientdecreases. For a lower doping content of 10mol:%, the fieldconfinement due to the GeO2 refractive index is reduced, sothat the optimum in the NL coefficient is shifted toward higherdGeO2

=Λ values, for which the confinement due to the micro-structured cladding becomes more important.

3. SSFS IN GeO2-DOPED CORE PHOTONICCRYSTAL FIBERSA. Fiber PropertiesTo illustrate the benefit of such GeO2-doped core PCFs forSSFS and CW SC generation, we fabricated a PCF with adoping level of 20mol:% and a ZDW of 1060 nm, as well asa pure silica PCF with the same ZDW for comparison.Figures 8(a) and 8(b) show the scanning electron microscope(SEM) images of the fabricated pure silica PCF andGeO2-doped core PCF, respectively. The profile of the GeO2-doped preform used to form the core is shown in Fig. 8(c). Ithas a parabolic profile with a maximum GeO2 content of20mol:% at the center, which corresponds to a refractive in-dex difference of about 32 × 10−3. The GeO2-doped regionappears as a lighter area at the core center in the image ofFig. 8(b). We chose the available GeO2-doped preform thatprovides a dGeO2

=Λ ratio as close as possible to the optimalvalue of the NL coefficient (see Fig. 7). The dGeO2

=Λ ratiois 0.53 and corresponds to only an 8% reduction of the NLcoefficient from the optimum value reported in Fig. 7.

Fig. 6. NL coefficient curves calculated for a pure silica-core PCF(dashed curve), and two PCFs with GeO2 doping levels of10mol:% (dotted curve) and 20mol:% (solid curve).

40

35

30

25

20

15

10

NL

coef

ficie

nt (

W-1

.km

-1)

0.80.60.4dGeO2

/ Λ

Fig. 7. NL coefficient calculated at 1064nm as a function of the dia-meter of the GeO2-doped region dGeO2

relative to the pitch Λ for twoPCFs with GeO2 doping levels of 10mol:% (dotted curve) and20mol:% (solid curve). The d=Λ ratio was fixed to 0.6 and 0.815for the 10 and 20mol:% doping levels, respectively, and the pitchwas adjusted so that all PCF designs exhibit the same ZDW of1060� 1 nm. Lines are guides for the eye.

800 1000 1200 1400 1600−150

−100

−50

0

50

100

GV

D (

ps/n

m/k

m)

Wavelength (nm)

PCF

Fig. 5. GVD curves calculated for a pure silica-core PCF (dashedcurve), and two PCFs with GeO2 doping levels of 10mol:% (dottedcurve) and 20mol:% (solid curve).

Barviau et al. Vol. 28, No. 5 / May 2011 / J. Opt. Soc. Am. B 1155

GVD curves of both fibers were calculated with a finite-element method using high-resolution SEM images and takinginto account the parabolic profile of the GeO2-doped region.They are plotted in Fig. 9(a) in dashed and solid curves for thepure silica and GeO2-doped core fiber, respectively. The re-sults of GVD measurements performed with a standardlow-coherence interferometry setup [15,35] are displayed inmarkers for both fibers. They show an excellent agreementwith the calculated curves, confirming that the ZDW is locatedat 1060nm and that the third-order dispersion β3 is higher inthe GeO2-doped core fiber at a fixed wavelength. The spectralevolution of the NL coefficient γ is displayed in Fig. 9(b) for

both fibers. It has been deduced from the effective mode areacomputed from digitalized high-resolution SEM images, takinginto account the enhancement of the NL refractive index n2

along the GeO2-doped profile. The NL coefficient taken at1064 nm reaches 38W−1 · km−1 in the GeO2-doped corePCF, versus only 10W−1 · km−1 in the pure silica PCF, whichalmost corresponds to a fourfold enhancement. Note that theNL coefficient of the fabricated GeO2-doped core PCF isslightly higher than the one of the corresponding designpresented in Subsection 2.B due to slightly different micro-structured cladding parameters and air hole deformationaround the core.

B. Experiments and Numerical SimulationsTo investigate the impact of GeO2 doping on the SSFS, weperformed experiments by launching 75 fs pulses with a repe-tition rate of 1 kHz at 1308nm in 1m long samples of bothfibers previously described. The pump wavelength has beenchosen relatively far from the ZDW in order to avoid super-continuum generation. The GVD values at the pump wave-length were 35ps=nm=km in the pure silica PCF, and55ps=nm=km in the GeO2-doped one. The input peak powerwas adjusted so that the initial pump pulse breakup led tothe ejection of a single fundamental soliton in the fiber lengthsinvestigated here. In these conditions, the injected pumppeak power was estimated to 9:8kW and 6:5 kW in the puresilica and GeO2-doped PCFs, respectively. The solitonspectral dynamics was investigated as a function of fiberlength for a fixed pump power with a cutback experiment.Figs. 10(a) and 10(c) show the experimental measurementsof the soliton evolution as a function of fiber length L normal-ized to the pump peak power P, in the pure silica andGeO2-doped core PCFs, respectively. In the pure silicaPCF, the central wavelength of the ejected soliton reaches1600 nm after a normalized length L × P of 28m · kW, which

100

80

60

40

20

0

NL

coef

ficie

nt (

W-1

.km

-1)

140012001000800

Wavelength (nm)

-200

-100

0

100

GV

D (

ps/n

m/k

m)

(a)

(b)

Fig. 9. (a) Calculated GVD curves for the pure silica PCF (dashedcurve) and GeO2-doped core PCF (solid curve). Markers depict thecorresponding GVD measurements performed with a low-coherenceinterferometry setup. (b) Calculated spectral evolution of the NL coef-ficient γ in the pure silica PCF (dashed curve) and GeO2-doped corePCF (solid curve).

Fig. 8. (Color online) (a) SEM image of the fabricated pure silicaPCF and (b) of the GeO2-doped core PCF with a maximum contentof 20mol:% at the center. Both images are at the same scale. (c) Radialevolution of the GeO2 mole fraction measured in the preform used toform the core of the GeO2-doped PCF.

Fig. 10. (Color online) (a), (c) Experimental measurement of the so-liton evolution as a function of length normalized to the pump peakpower in the pure silica PCF (a) and in the GeO2-doped core PCF (c).(b), (d) Corresponding numerical simulations with the GNLSE bytaking into account all available experimental conditions in the puresilica PCF (b) and in the GeO2-doped core PCF (d).

1156 J. Opt. Soc. Am. B / Vol. 28, No. 5 / May 2011 Barviau et al.

corresponds to a frequency shift of 41:8THz from the pump. Inthe GeO2-doped core PCF, it reaches 1733 nm at the same nor-malized length, which corresponds to a frequency shift of59:5THz from the pump. In other words, the GeO2 dopingleads to a SSFS enhancement of 30% as compared to the puresilica PCF. These experimental results are in very good agree-ment with numerical simulations [represented in Figs. 10(b)and 10(d)] performed with the generalized NL Schrödingerequation (GNLSE) taking into account all available experi-mental parameters (see Appendix A for details). Moreover,numerical simulations were carried out in order to investigatelonger propagation distances. Figure 11 displays the fre-quency shift from the pump measured on spectra resultingfrom the simulated propagation in the pure silica PCF (dashedcurve) and in the GeO2-doped core PCF (solid curve) for nor-malized fiber lengths up to 300m · kW. The comparison of thetwo evolutions shows that, for a fixed fiber length and pumppower, the SSFS remains much more efficient in theGeO2-doped core PCF than in the pure silica one.

All results from Figs. 10 and 11 thus show that the useof GeO2-doped core PCFs allows the significant enhancementof the SSFS as compared to pure silica PCFs with thesame ZDW, but yet slightly lower GVD value at the pumpwavelength.

C. Discussion: Relative Weight of γ and R�t� in the SSFSThe theoretical expression of the SSFS rate with fiber length[1,4,36] indicates that this SSFS enhancement observed in theGeO2-doped core PCF can be due to its higher NL coefficient γand/or Raman gain gR, as compared to the pure silica PCF. It isnot theoretically possible to completely dissociate the Kerrand the Raman effect, so we chose to investigate the relativeinfluence of the NL coefficient γ and the response functionRðtÞ on the SSFS in GeO2-doped core PCFs. The term RðtÞis defined in Appendix A. It contains the proportion of the in-stantaneous Kerr and delayed Raman effect via f R and alsotakes into consideration the Raman temporal responsehRðtÞ associated with the doped material. The method devel-oped to deduce f R and hRðtÞ from the Raman gain gR is ex-plained in Appendix A. For the sake of our demonstration,we consider the simplest case in which a short pulse islaunched into PCFs with different parameter couples [γ, f R,hRðtÞ]. We consider Gaussian pulses of 75 fs (FWHM) at1308 nmwith 6:5 kW peak power into the PCF. The GVD curvehas been assumed to be fixed in all cases and correspondsto an average between the ones of fabricated PCFs of

Subsection 3.A. The ZDW is 1060 nm, and the GVD value atthe pump wavelength is 45:2 ps=nm=km. In order to dissociatethe contribution of the NL coefficient from the one of the re-sponse function RðtÞ on the SSFS enhancement, four caseswere investigated. Cases 1 and 4 are realistic and correspondto the NL coefficient and to the Raman gain of pure silica(case 1) and GeO2-doped core (case 4) PCFs, while cases 2and 3 are didactic. They illustrate the SSFS obtained inunrealistic PCFs presenting different material properties[γSiO2

, f R−GeO2and hR−GeO2

ðtÞ] for case 2 and vice versa for case3 [γGeO2

, f R−SiO2and hR−SiO2

ðtÞ].Figure 12 shows the spectra obtained after a lossless pro-

pagation [α ¼ 0 in Eq. (A1)] over 4:3m, in each case. First ofall, as expected, the SSFS in the GeO2-doped core PCF(case 4,Δν ¼ −56:6THz) is much larger than the one achievedin the pure silica PCF (case 1, Δν ¼ −26:8THz). Now if weonly consider the enhancement of RðtÞ due to GeO2 doping(case 2, Δν ¼ −28THz), the SSFS is not significantly en-hanced as compared to the pure silica PCF. On the contrary,the enhancement of the NL coefficient alone (case 3,Δν ¼ −53:5THz) leads to a SSFS almost as efficient as inthe GeO2-doped core PCF. All these results are summarizedin Table 2 for the sake of clarity. One can conclude that, con-trary to what could be expected a priori, the enhancement ofthe SSFS in the GeO2-doped core PCF under investigation ascompared to the pure silica PCF is mainly due to the NL

Fig. 12. Simulated spectrum after 4:3mpropagation in the four caseslisted in Table 2. The vertical dashed line depicts the wavelengthwhere the soliton was initially injected.

-80

-60

-40

-20

0

Freq

uenc

y sh

ift (

TH

z)

3002001000

Normalized length L×P (m.kW)

Fig. 11. Numerical simulation of the frequency shift from the pumpversus fiber length normalized to the pump power in the pure silicaPCF (dashed curve) and in the GeO2-doped core PCF (solid curve).

Table 2. Frequency Shifts of Redshifted Solitons

from the Pump at 1308 nm in Each of the Four

Investigated Casesa

Case γ f R hRðtÞ γ ðW−1 · km−1Þ f R Δν ðTHzÞ1 SiO2 SiO2 7.4 0.22 −26:82 SiO2 GeO2 7.4 0.32 −283 GeO2 SiO2 23.8 0.22 −53:54 GeO2 GeO2 23.8 0.32 −56:6

af R and hRðtÞ were calculated such that gRmax

ðSiO2Þ ¼8:3 × 10−14 m=W, gRmax

ðGeO2Þ ¼ 13 × 10−14 m=W. Numerical values ofgR and γ are recalled at a wavelength of 1308nm.

Barviau et al. Vol. 28, No. 5 / May 2011 / J. Opt. Soc. Am. B 1157

coefficient enhancement (due to a better mode confinement)rather than the one of the intrinsic Raman gain. Note that theinjected pulse characteristics correspond to the real case in-vestigated in Subsection 3.B. Other simulations performedwith different pulse widths and energies confirm that theNL coefficient enhancement still plays a major role in theSSFS enhancement.

4. CW SUPERCONTINUUM GENERATIONIN GeO2-DOPED CORE PHOTONICCRYSTAL FIBERSAs explained in the introduction, the SSFS mechanism plays akey role in the process of the supercontinuum generation [9].In the case of long-pulse or CW pumping regime, the initialpump field is transformed into a train of solitonic pulsesthrough the MI process. In Subsection 3.B, we demonstratedthe benefit of using GeO2-doped fibers for enhancing the SSFSeffect. However, one can wonder about the impact of theGeO2 doping on the MI process, which is at the origin of so-liton generation. In order to obtain a rapid insight, we fol-lowed the procedure described in Chapter 8 of [13]. Byconsidering that the energy within a MI period entirely endsup in one soliton, the characteristic duration of solitonsemitted from MI can be expressed as [13]

T0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2jβ2j

π2γPCW

s; ð5Þ

where PCW is the initial pump power. By considering the threefibers designed in Subsection 2.B, we found that T0 decreasesfrom about 30% in the pure silica-core PCF as compared toGeO2 doping of 20mol:%, for a pump power PCW of 10W.Since the SSFS rate is inversely proportional to T4

0 [4](or T0 for shorter solitons [37]), the redshift experiencedby solitons formed from MI is expected to be much more effi-cient in the GeO2-doped core PCF. This has been rigorouslyinvestigated numerically by using the GNLSE described inAppendix A. The input CW pump field was modeled by addinga random spectral phase to each component, as introduced in[38,39]. The average pump power was fixed to 13W and has aGaussian shape with a 0:7nm linewidth at FWHM to matchexperimental conditions of [24]. Quantum noise was modeledby adding a half photon per mode with random phase andintensity on each spectral discretization bin of the input field.Numerical simulations were performed with use of an adap-tative split-step Fourier method with a local error of 10−6.Simulations were performed with 216 sampling points, andthe temporal window was set to 130ps (leading to a temporalresolution of 1:98 fs). An averaging was performed over onlyfive simulation runs corresponding to five different initialnoise conditions, because the computation time was veryimportant (360h on a four-core 2:9GHz PC). Figure 13 showssimulated SC spectra obtained after a propagation length of300m in the pure silica PCF (top curve) and in theGeO2-doped core PCF (bottom curve). Spectra resulting fromeach single simulation shot are plotted in gray, and averagespectra are displayed in black. Note that, in order to get a faircomparison, the exact same set of five random initial condi-tions was used for the pure silica and GeO2-doped core PCFs.

Comparing both simulated SC spectra immediately showsthat the CW SC generation is very efficient in the GeO2-doped

core PCF, as previously reported experimentally in [24].Indeed, the spectrum extent covers 1000 nm in the GeO2-doped core PCF (from 700 to 1700 nm), against 600nm inthe pure silica PCF (from 800 to 1400 nm). The numerical si-mulation performed here highlights that the unique combina-tion of GVD tailoring and NL coefficient enhancement in theGeO2-doped core PCF leads to a much more efficient SSFS atthe origin of the great increase of SC spectral bandwidth.

5. CONCLUSIONIn conclusion, we have numerically and experimentally stu-died the potential of highly GeO2-doped PCFs in the contextof soliton propagation and CW SC generation. We have pro-vided some examples of PCF structures with different dopinglevels yet having very close GVD properties. This was done byadjusting the parameters of the microstructure so that the wa-veguide GVD compensates for the material one. The NL prop-erties (Kerr and Raman responses) of these fibers have beencalculated and were found to be enhanced with increasingdoping levels due to a combination of material intrinsic prop-erties and strong mode confinement. The SSFS has been ex-perimentally and numerically studied in a pure silica and aGeO2-doped core PCF, and we found a SSFS enhancementof 30% in the GeO2-doped core PCF with a doping level of20mol:% as compared to the pure silica fiber. Contrary towhat could be expected a priori, this enhancement is mainlydue to the NL coefficient enhancement due to a strong modeconfinement (imposed by the waveguide geometry) ratherthan to an increase of the intrinsic material Raman gain.We finally numerically illustrate the benefit of GeO2-dopedcore PCFs in the context of CW SC generation. This providesan explanation for the recent unprecedented report of white-light SC generation from a CW pump [24].

APPENDIX AAll simulations were performed using the following GNLSEform:

∂Ψðz; tÞ∂z

¼X∞m≥2

imþ1βmm!

∂mΨðz; tÞ∂tm

−12

X∞m¼0

�imαmm!

∂m

∂tm

�Ψðz; tÞ

þX∞m¼0

�imþ1γmm!

∂m

∂tm

�

×

�Ψðz; tÞ

ZRðt0ÞjΨðz; t − t0Þj2dt0

�ðA1Þ

(a)

(b)

Pow

er (

20 d

B/d

iv.)

Wavelength (nm)1000 1400 1800600

Fig. 13. Spectra resulting from each single simulation shot (graycurves) and obtained from an averaging over five simulation shots(black curves) (a) in the pure silica PCF and (b) in the GeO2-dopedcore PCF. See Section 4 for details about the simulation parameters.

1158 J. Opt. Soc. Am. B / Vol. 28, No. 5 / May 2011 Barviau et al.

where αm ¼ ðdmα=dωmÞω¼ω0, γm ¼ ðdmγ=dωmÞω¼ω0

, andRðtÞ ¼ ð1 − f RÞδðtÞ þ f R · hRðtÞ.

βm are the mth-order derivative of the dispersion curve ex-pressed around the pump frequency. Since the equation iswritten in the temporal domain, losses and nonlinearity arealso included through a Taylor expansion in order to taketheir spectral dependence into account. Note that, duringthe numerical integration, those terms are included in theFourier space in the form of αðωÞ and γðωÞ. Finally, RðtÞ isdefined such that f R is the fractional contribution of the de-layed temporal Raman response hRðtÞ to the NL effects. Theseparameters are evaluated from Eq. (1) and from [1] with

f R · hRðtÞ ¼2

n2π

Z∞

0ℑ½χð3ÞðωÞ� × sinðωtÞdω; ðA2Þ

and by considering that

Z∞

0hRðtÞdt ¼ 1: ðA3Þ

The fractional contribution of the delayed Raman response(f R) then depends on the GeO2 doping, and its evolution isrepresented in Fig. 3(c) for pure silica, as well as for GeO2

of 10mol:% and 20mol:%.For the sake of simplicity, parabolic GeO2 profiles with a

doping level of X mol:% at the top of the parabolic profileare modeled by considering a constant doping of0:66X mol:% in the GNLSE, so that their integrals over thedoped area are equal. We checked that this approximationhas negligible influence.

ACKNOWLEDGMENTSWe acknowledge Remi Habert for experimental assistance,Karen Delplace for assistance in fiber fabrication. This workwas partly supported by the Agence Nationale de la Re-cherche through the IMFINI ANR-09-BLAN-0065 project, bythe French Ministry of Higher Education and Research, theNord-Pas de Calais Regional Council and Fonds Européende Développement Régional through the “Contrat de ProjetsEtat Région (CPER) 2007-2013” and the “Campus IntelligenceAmbiante (CIA)”.

REFERENCES AND NOTES1. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Aca-

demic, 2007).2. E. A. Golovchenko, E. M. Dianov, A. M. Prokhorov, and V. N.

Serkin, “Decay of optical solitons,” JETP Lett. 42, 87–91 (1985).3. F. Mitschke and L. Mollenauer, “Discovery of the soliton self-

frequency shift,” Opt. Lett. 11, 659–661 (1986).4. J. P. Gordon, “Theory of the soliton self-frequency shift,” Opt.

Lett. 11, 662–664 (1986).5. P. Mamyshev, S. Chernikov, and E. Dianov, “Generation of fun-

damental soliton trains for high-bit-rate optical fiber communi-cation lines,” IEEE J. Quantum Electron. 27, 2347–2355(1991).

6. J. Lucek and K. Blow, “Soliton self-frequency shift in telecom-munications fiber,” Phys. Rev. A 45, 6666–6674 (1992).

7. B. Zysset, P. Beaud, and W. Hodel, “Generation of optical soli-tons in the wavelength region 1:37–1:49 μm,” Appl. Phys. Lett.50, 1027–1029 (1987).

8. K. Blow, N. Doran, and D. Wood, “Generation and stabilizationof short soliton pulses in the amplified nonlinear Schrödingerequation,” J. Opt. Soc. Am. B 5, 381–391 (1988).

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

10. The long-pulse pumping regime refers to cases in which thepump pulse duration ΔT is much longer than the MI oscillationperiod ΔTMI, given by ΔTMI ¼ 2π

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffijβ2j=ð2γPÞp

, with β2 thesecond-order dispersion coefficient, γ the NL coefficient, andP the pump peak power. Cases in which ΔT is of the orderof or less than ΔTMI correspond to the short-pulse pumpingregime.

11. A. V. Gorbach and D. V. Skryabin, “Light trapping in gravity-likepotentials and expansion of supercontinuum spectra inphotonic-crystal fibres,” Nat. Photon. 1, 653–657 (2007).

12. J. M. Stone and J. C. Knight, “Visibly “white” light generation inuniform photonic crystal fiber using a microchip laser,” Opt.Express 16, 2670–2675 (2008).

13. J. M. Dudley and J. R. Taylor, Supercontinuum Generation in

Optical Fibers (Cambridge University, 2010), Chap. 8.14. D. Mogilevtsev, T. Birks, and P. Russell, “Group-velocity disper-

sion in photonic crystal fibers,” Opt. Lett. 23, 1662–1664(1998).

15. J. Knight, J. Arriaga, T. Birks, A. Ortigosa-Blanch, W. Wads-worth, and P. Russell, “Anomalous dispersion in photonic crys-tal fiber,” IEEE Photon. Technol. Lett. 12, 807–809 (2000).

16. N. Broderick, T. Monro, P. Bennett, and D. Richardson, “Nonli-nearity in holey optical fibers: measurement and future oppor-tunities,” Opt. Lett. 24, 1395–1397 (1999).

17. J. Ranka, R. Windeler, and A. Stentz, “Optical properties ofhigh-delta air-silica microstructure optical fibers,” Opt. Lett.25, 796–798 (2000).

18. T. Izawa and S. Sudo,Optical Fibers: Materials and Fabrication

(KTK Scientific, 1987).19. C. Headley and G. P. Agrawal, Raman Amplification in Fiber

Optical Telecommunication Systems (Academic, 2005).20. Y. P. Yatsenko and A. D. Pryamikov, “Parametric frequency con-

version in photonic crystal fibres with germanosilicate core,”J. Opt. A 9, 716–722 (2007).

21. Y. P. Yatsenko, A. F. Kosolapov, A. E. Levchenko, S. L. Semjo-nov, and E. M. Dianov, “Broadband wavelength conversion in agermanosilicate-core photonic crystal fiber,” Opt. Lett. 34,2581–2583 (2009).

22. K. Schuster, J. Kobelke, S. Grimm, A. Schwuchow, J. Kirchhof,H. Bartelt, A. Gebhardt, P. Leproux, V. Couderc, and W. Urbanc-zyk, “Microstructured fibers with highly nonlinear materials,”Opt. Quantum Electron. 39, 1057–1069 (2007).

23. V. Tombelaine, A. Labruyere, J. Kobelke, K. Schuster, V. Reichel,P. Leproux, V. Couderc, R. Jamier, and H. Bartelt, “Nonlinearphotonic crystal fiber with a structured multi-component glasscore for four-wave mixing and supercontinuum generation,”Opt. Express 17, 15392–15401 (2009).

24. A. Kudlinski, G. Bouwmans, O. Vanvincq, Y. Quiquempois, A. LeRouge, L. Bigot, G. Melin, and A. Mussot, “White-light cw-pumped supercontinuum generation in highly GeO2-doped-corephotonic crystal fibers,” Opt. Lett. 34, 3631–3633 (2009).

25. J. Fleming, “Material dispersion in lightguide glasses,” Electron.Lett. 14, 326–328 (1978).

26. F. Galeener, A. Leadbetter, and M. Stringfellow, “Comparison ofthe neutron, Raman, and infrared vibrational-spectra of vitreousSiO2, GeO2, and BeF2,” Phys. Rev. B 27, 1052–1078 (1983).

27. J. Fleming, “Dispersion in GeO2–SiO2 glasses,” Appl. Opt. 23,4486–4493 (1984).

28. N. Boling, A. Glass, and A. Owyoung, “Empirical relationshipsfor predicting non-linear refractive-index changes in opticalsolids,” IEEE J. Quantum Electron. 14, 601–608 (1978).

29. P. Sillard, P. Nouchi, J.-C. Antona, and S. Bigo, “Modeling thenon-linear index of optical fibers,” in Optical Fiber Communi-

cation Conference and Exposition and The National Fiber

Optic Engineers Conference, Technical Digest (CD) (OpticalSociety of America, 2005), paper OFH4.

30. T. Nakashima, S. Seikai, and M. Nakazawa, “Dependence ofRaman gain on relative index difference for GeO2-dopedsingle-mode fibers,” Opt. Lett. 10, 420–422 (1985).

31. S. Davey, D. Williams, B. Ainslie, W. Rothwell, and B. Wakefield,“Optical gain spectrum of GeO2–SiO2 Raman fiber amplifiers,”IEE Proc. J. 136, 301–306 (1989).

Barviau et al. Vol. 28, No. 5 / May 2011 / J. Opt. Soc. Am. B 1159

32. T. Sylvestre, P. Dinda, H. Maillotte, E. Lantz, A. Moubissi, andS. Pitois, “Wavelength conversion from 1:3 μm to 1:5 μm in sin-gle-mode optical fibres using Raman-assisted three-wavemixing,” J. Opt. A 2, 132–141 (2000).

33. J. Kobelke, K. Schuster, R. Spittel, A. Hartung, A. Schwuchow, J.Kirchhof, and H. Bartelt, “Dispersion tailored microstructuredfibers—core dopant effects,” Proc. SPIE 7714, 771–416(2010).

34. T. Kato, Y. Suetsugu, andM. Nishimura, “Estimation of nonlinearrefractive-index in various silica-based glasses for optical fi-bers,” Opt. Lett. 20, 2279–2281 (1995).

35. M. Tateda, N. Shibata, and S. Seikai, “Interferometric method forchromatic dispersion measurement in a single-mode optical fi-ber,” IEEE J. Quantum Electron. 17, 404–407 (1981).

36. A. C. Judge, O. Bang, B. J. Eggleton, B. T. Kuhlmey, E. C. Magi, R.Pant, and C. M. de Sterke, “Optimization of the soliton self-fre-quency shift in a tapered photonic crystal fiber,” J. Opt. Soc. Am.B 26, 2064–2071 (2009).

37. M. H. Frosz, O. Bang, and A. Bjarklev, “Soliton collision and Ra-man gain regimes in continuous-wave pumped supercontinuumgeneration,” Opt. Express 14, 9391–9407 (2006).

38. F. Vanholsbeeck, S. Martin-Lopez, M. Gonzalez-Herraez, and S.Coen, “The role of pump incoherence in continuous-wave super-continuum generation,” Opt. Express 13, 6615–6625 (2005).

39. B. Barviau, S. Randoux, and P. Suret, “Spectral broadening of amultimode continuous-wave optical field propagating in thenormal dispersion regime of a fiber,” Opt. Lett. 31, 1696–1698(2006).

1160 J. Opt. Soc. Am. B / Vol. 28, No. 5 / May 2011 Barviau et al.