infrared supercontinuum from a large mode area pcf under...

Opt Quant Electron (2007) 39:1297–1309DOI 10.1007/s11082-008-9207-8

Infrared supercontinuum from a large mode area PCFunder extreme picosecond excitation

V. G. Savitski · K. V. Yumashev · V. L. Kalashnikov ·V. S. Shevandin · K. V. Dukel’skii

Received: 11 February 2008 / Accepted: 18 March 2008 / Published online: 8 April 2008© Springer Science+Business Media, LLC. 2008

Abstract Evolution of the long-wavelength edge of supercontinuum (SC) in a largemode-area photonic crystal fiber (LMA PCF) under extreme (close to the fiber damagethreshold) picosecond excitation is analyzed for the first time to our knowledge. The obtainedresults are interpreted on the basis of the numerical simulations explaining both spectral andtemporal characteristics of SC in dependence on the pulse power and the fiber length. Anexistence of the minimum LMA PCF length providing the broadest spectrum under the high-est picosecond excitations is predicted. The multimode cross-modulation inside the LMAPCF is analyzed, as well.

Keywords Photonic crystal fiber · Supercontinuum · Nonlinear optics · Optical solitons

PACS 42.72.Ai · 42.65.Sf · 42.65.Tg

1 Introduction

Compact sources of coherent emission within a wide spectral range are of interest for alot of applications such as spectroscopy, gas sensing, optical coherence tomography, testingof optical fibres, metrology, etc. Phenomenon of the laser pulse spectrum broadening, as itpropagates inside a transparent medium, was observed in CS2, at first (Jones and Stoicheff1964). Later, a considerable spectral broadening (few hundred nanometers), the so-called

V. G. Savitski (B)Institute of Photonics, Wolfson Centre, University of Strathclyde, 106 Rottenrow, Glasgow G4 ONW, UKe-mail: [email protected]

K. V. YumashevInstitute for Optical Materials and Technologies BNTU, 65 Nezavisimosti Ave., bldg. 17, 220013 Minsk,Belarus

V. L. KalashnikovInstitut für Photonik, TU Wien, Gusshausstr. 27/387, 1040 Vienna, Austria

V. S. Shevandin · K. V. Dukel’skiiS. I. Vavilov Federal Optical Institute, 36/1 Babushkin Str., 192171 St.-Petersburg, Russia

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1298 V. G. Savitski et al.

white-light or supercontinuum (SC) generation, was demonstrated in a number ofcondensed media (Alfano and Shapiro 1970a,b; Alfano 1989), liquids (Weinberg 1969,Penzkofer et al. 1973; Penzkofer 1974; Lee Smith et al. 1977), gases (Alfano and Shap-iro 1970b; Corkun et al. 1986; François et al. 1993; Ilkov et al. 1993), and fibers, includingmulti-mode (Baldeck et al. 1987), dispersion-shifted (Mori et al. 1995), and photonic crystalfibers (PCFs; Dudley et al. 2006; Genty et al. 2007; Birks et al. 1997; Ranka et al. 2000;Rulkov et al. 2005; Provino et al. 2001; Cherif et al. 2008).

The advantages of SC generated by long (picosecond) pulses or even by CW are thesmoothness of its average spectral profile and the high average output power (Seefeldt et al.2003; Serebryannikov and Zheltikov 2007). The bandwidth of the picosecond SC generatedin a PCF could be enhanced by growth of both fiber length and power coupled into a fiber.However, the growth of fiber length worsens the temporal characteristics of the SC, whichare essential for the probe emission in the pump-probe experiments. An alternative approachis the fiber core growth aimed to increase the coupled pump power. Hence, it is preferableto use a short fiber with a large mode area (LMA) for the spectroscopic applications. Forthis aim, such a convenient source of SC as the heavy water (D2O) is widely used in non-stationary and nonlinear spectroscopy (Yumashev et al. 2000). However, the absorption fea-tures of D2O (Kou et al. 1993) limit its’ emission long-wavelength edge at ≈1,350 nm.Therefore, comparison of the SC spectrum generated within the near-IR spectral range inD2O and the LMA PCF is useful from the standpoint of practical applications in spectroscopy.

Recently, the SC in a 100 m long single-mode LMA PCF under nanosecond excitation hasbeen reported with a long-wavelength emission edge at 1.7 µm (Genty et al. 2005). Althoughthe infrared (IR) SC generation in the LMA PCF under picosecond excitation is expectable,still there are some issues to address. An information about the IR edge of SC generated in theLMA PCF was limited by the spectral sensitivity edge of the optical detector at ≈1,750 nm(Genty et al. 2005). It is of interest to analyze the SC spectrum generated in such a PCF atlonger wavelengths (up to 2 µm). Another issue is the effect of the high-energy pulse prop-agation on the SC characteristics. In particular, the multimode properties of the LMA PCFscan contribute to the SC structure (Kalashnikov et al. 2004).

The primary issues addressed in this paper are: (i) how far the long-wavelength edge ofthe SC generated in the LMA PCF could be shifted into IR-range under excitation by pico-second pulses with energies up to optical damage threshold; (ii) what is the minimum LMAPCF length for a fixed extreme excitation providing the sufficiently broad IR SC withoutconsiderable temporal broadening of the pulse; and (iii) what is an impact of the multimodepropagation on the SC structure. The study can be useful for application of the LMA PCFas the broad-band source of probe emission in picosecond pump-probe spectrophotometrywithin the 1–2 µm spectral range.

2 Experimental setup

Fibers under consideration (LMA-10, below) were produced by the two-step method from apolycapillary preform described in Dukel’skii et al. (2005). The LMA-10 fibers are charac-terized by the core diameter of 10 ± 1 µm and d/� ≈ 0.9 (d is the capillary hole diameter,� is the pitch of the structure). Such a high level of the air-filling fraction results in thehigh numerical apperture (NA) [≈0.36, estimated in accordance with Issa (2004)] that is theadvantage for coupling emission into a fiber. However, the PCF with such a NA parametercannot be characterized as the endlessly single-mode fiber, because it does not satisfy therequirement of d/� ≤ 0.43 (Nielsen and Mortensen 2003).

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Infrared supercontinuum from a large mode area PCF 1299

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pers

ion,

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Fig. 1 Calculated dispersion profiles of the LMA-10 fiber (for the fundamental mode—solid line, and for thefirst higher-order mode—dashed line). Inset: Measured attenuation spectrum of the LMA-10 PCF

Fig. 2 Scheme of the experimental setup (MO is the microscope objective, �tp is the pulse duration, λ is thepulse wavelength)

The LMA-10 fiber dispersion curves, calculated with the Mode Solutions software(Lumerical Solutions, Inc.) are presented in Fig. 1. The zero-dispersion wavelength for thefundamental (zero-order) mode of the LMA-10 PCF with core diameter of 10 ± 1 µm is1179 ± 16 nm. The measured attenuation spectrum of the LMA-10 PCF is shown in Fig. 1(inset). The considered fiber lengths are 0.5, 1.5, and 5 m. The fiber attenuation at 1,079 nmequals to 39 dB/km and is about of two times higher than that of commercial multimodePCF.1 The reason for high optical losses within the short wavelength range (<1,000 nm) incomparison with the long wavelength one (1,600 nm) is a fundamental leakage of the modeswhen the �-parameter exceeds ≈8 µm (Dukel’skii et al. 2006). A mentioned phenomenonhas not been observed in the conventional fibers made of bulk glasses.

The experimental setup scheme is presented in Fig. 2. The SC generation in the LMA-10PCF was excited with the 15 ps pulses from a passively mode-locked Nd:YAlO3 oscillator,operating at the 1 Hz repetition rate and at the wavelength of 1,079 nm. The pumping emis-sion was collimated into the fiber by a 10X microscope objective (MO). The SC spectrumafter the monochromator was detected with the Hamamatsu G8180-256 W linear sensors

1 Passive High NA Photonic Crystal Fibres, http://www.crystal-fibre.com/datasheets/MM-HNA-5.pdf

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http://www.crystal-fibre.com/datasheets/MM-HNA-5.pdf


(spectral sensitivity within 900–2,500 nm). The spectral resolution of the registration systemwas 8 nm.

3 Experimental results

Growth of the pump peak power coupled into the 0.5 m long LMA-10 PCF results in a gradualbroadening of the SC spectrum (Fig. 3a). It develops from the Raman band at ≈1,130 nm[line (1) in Fig. 3a] to a broad spectrum [lines (2) and (3) in Fig. 3a]. Frequency shift ofthe observed band is rather close to the Raman peak at 440 cm−1 in SiO2. With the cou-pled pump peak power of 300 kW, the IR edge of SC from the 0.5-m-long PCF reaches≈1,800 nm. The corresponding energy density inside the PCF was ≈3 J/cm2. It is somewhatlower than the damage threshold of the LMA-10 PCF, which was estimated experimentally(≈5 J/cm2). At the short wavelength side of the pump, the observed spectrum was limitedby the spectral sensitivity of the detector and the low efficiency (<40% for the wavelengthsshorter than 1,335 nm) of the grating used in the monochromator. The blue side (from thepump at 1.08 µm) of the SC spectrum has been investigated earlier for such a type of theLMA PCF (Genty et al. 2005) and is beyond the scope of this work.

Tenfold increasing of the fiber length does not lead to a substantial shift of the IRSC edge: the spectrum edge shifts from 1,800 to 1,875 nm under the same highest peakpump power (see Fig. 3b). Therewith the holes, associated with the OH-absorption bands(see Fig. 1, inset) became more pronounced. The spectral profile of the generated SC inthe LMA-10 PCF with the lengths of 1.5 and 5 m was almost independent on the energycoupled into fiber. We only observe the SC narrowing with the pump energy decrease. Themaximum conversion efficiency of the pump emission to the SC is estimated to be 33% inthe 1.5-m-long PCF with the coupled peak power of 300 kW.

The inset in Fig. 3a demonstrates the SC generated in the D2O-cell under excitation bysame oscillator with the pulse energy density inside the liquid to be 70 J/cm2. D2O allowsthe emission with the long-wavelength edge at only ≈1,350 nm due to strong absorption in

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Fig. 3 (a) SC spectra from the 0.5-m-long LMA-10 fiber with the coupled powers of 25 (1) and 50 (2) and300 kW (3). Inset: SC spectrum from D2O under excitation with the same oscillator. The energy density insidethe D2O cell is 70 J/cm2. (b) SC spectra from the 0.5 m (1), 1.5 m (2), and 5 m (3) long LMA-10 PCF with thecoupled power of 300 kW

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water at the longer wavelengths (Kou et al. 1993). Besides, the absorption produces the holesin the D2O emission spectrum. Nevertheless, an employment simplicity and a regenerationproperty of a liquid are the advantages of the D2O utilization in the spectroscopic pump-probeexperiments.

The long-wavelength edge of SC at the maximum coupled power of 300 kW in the5-m-long LMA-10 PCF is situated at ≈1,875 nm. The evolution of the SC spectrum in asingle-mode PCF with different lengths was observed by Wadsworth et al. (2004). Underthe fixed pumping conditions, the fiber length growth leads to a gradual broadening of theSC spectrum and to a shifting of its long-wavelength edge (Wadsworth et al. 2004). Thereis a certain optimal fiber length, above which the substantial shift of the SC spectrum edgewas not observed and the SC bandwidth did not grow any more (Wadsworth et al. 2004;Sorokin et al. 2003). Since the optimal fiber length is unknown in our case, one can expectthat growth of the LMA-10 fiber length broadens the SC and shifts its long-wavelength edgebeyond 2,000 nm. To analyze such a possibility, we use the numerical simulations presentedin the next section.

Fig. 4 Power profiles of thefundamental (a) and firsthigher-order (b) modes

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Fig. 5 SC profiles from the 50 cm section of PCF. The pump powers are (a) 300 kW and (b) 50 kW. All poweris contained in either zero (black curves) or first higher-order (gray curves) modes (see Fig. 4). �ω is thefrequency shift from the central frequency corresponding to 1,079 nm

4 Numerical analysis of the picosecond multimode SC and discussion

It has been established, that the basic mechanism of the picosecond SC formation is thefour-wave mixing (FWM), which is strongly enhanced when the pump wavelength issituated within the anomalous dispersion range (Serebryannikov and Zheltikov 2007; Stolenand Bjorkholm 1982; Coen et al. 2001, 2002; Dudley et al. 2002). Such an enhancementresults from the phase-matched FWM over a broad range of wavelengthes. The pulse prop-agation inside this spectral range causes the strong modulational instability (MI) driving thefield dynamics and initiating the SC formation (Stolen et al. 1989; Demircan and Bandelow2005). When the pulse wavelength is located within the negative dispersion range and isclose to the zero-dispersion wavelength, the soliton effects and the dispersion waves contrib-ute substantially to the SC, as well (Tamura et al. 2000; Schreiber et al. 2003; Mussot et al.2004; Kutz et al. 2005; Vanholsbeeck et al. 2005; Kobtsev and Smirnov 2005).

Let us consider the multimode propagation ( j and l are the indexes related to the differentmodes) inside a fiber on the basis of the extended coupled nonlinear Schrödinger equations(Agrawal 2001):

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Fig. 6 The temporal profiles of zero-order mode after the 50 cm section of PCF. The pump powers are (a)50 kW and (b) 300 kW. Inset shows an enlarged region in the vicinity of a soliton

∂a j

∂z+ δ j

∂a j

∂t−

N∑

m=2

im+1βm, j

m!∂ma j

∂tm= i

(n2ω

c

)

×∑

l �= j

{(1 − ζ )

[(f j j

∣∣a j∣∣2 + 2 f jl |al |2

)a j + f jla

2j a

∗l ei�kz

]

+ ζ

∞∫

0

dt ′ h(t ′) ×

[a j

(t ′) (

f j j∣∣a j

(t − t ′

)∣∣2 + 2 f jl∣∣al

(t − t ′

)∣∣2)

+ f jla j(t − t ′

)a∗

l

(t − t ′

)al (t)

]}, (1)

where z and t are the propagation distance and the time, respectively; a j and al are theslowly-varying complex field amplitudes of the modes; δ j is the inverse group-velocity, βm, j

is the mth-order group-velocity dispersion coefficient, n2 is the nonlinear refraction coeffi-cient, ω is the central frequency of the pump pulse, ζ is the Raman fraction in the nonlinearrefraction coefficient, f j j is the inverse effective mode-area, f jl is the overlapping integralof the modes, �k is the phase-mismatch between the modes resulting from the differenceof their propagation constants; h(t) is the Raman responce function. System (1) has beensolved on the basis of the split-step symmetrized Fourier method on the time-mesh containing218 points with the 1 fs time-step. The propagation step amounts to 1/100 of the nonlinear

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Fig. 7 SC after the 150 cm (black) and 500 cm (gray) sections of PCF. 300 kW power inside the zero-ordermode

length (minimal for a given mode set). N = 9 and the dispersion coefficients correspond tothe Taylor approximations of the curves shown in Fig. 1. We consider only two lowest modes,which intensity profiles are shown in Fig. 4. For these modes, the parameters γ ≡ n2ω f j j

/c

equal to 3.128 × 10−5 W−1 cm−1 and 2.788 × 10−5 W−1 cm−1, respectively. The modeoverlapping is 16%.

Our simulations demonstrate that the stimulated Raman scattering affects the dynamicsonly on the initial propagation stage and almost does not affect the final structure of SC forthe pump powers exceeding 50 kW. This corresponds to the fact that the FWM gain exceedsthat for the stimulated Raman scattering (Stolen and Bjorkholm 1982). Therefore, the resultswith only ζ = 0 will be presented below.

The calculated SC spectra for the case, when the total pump is concentrated in eitherzero- or first-order modes, are shown in Fig. 5. One can see, that for the maximum pumppower of 300 kW (Fig. 5a), there is no substantial difference between the spectra of twolowest modes. The FWM is so efficient that the spectra are almost flat and range up to 2 µm.The experimental spectrum is narrower (Fig. 3a) and we explain this discrepancy by theenergy leaking into higher-order modes.

Figure 5b demonstrates the effect of MI, which is clearly visible for the small pumppowers. The IR spike for the zero-order mode (black curve), possessing a larger negativeGDD satisfies completely the equation for the spectral shift due to MI (Agrawal 2001):

=√

2γ P0/|β2| (P0 is the peak pump power). For the higher-order mode (gray curve),

such an agreement is worse because the β2-parameter is almost zero in this case. As a result,the phase-matched FWM and the higher-order dispersions contribute to the SC formation.One can suppose that smoothness of the experimental spectrum at this pump power level

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Fig. 8 SC for 240 kW pump power, 50 cm PCF section. The first-order mode (gray curves) contains 4% ofenergy (black curves—zero-order mode). (a) noninteracting modes, (b) interacting modes

results from the superposition of multiple modes. The minor broadening of the experimentalSC in comparison with the calculated one can be caused by the stimulated Raman scattering,which is pronounced for the low pump powers (see also curve 1 in Fig. 3a).

Figure 6 shows the temporal profiles after propagation inside the 50 cm section of PCF,when all power is concentrated into the zero-order mode. One can see that the FWM result-ing in the spectrum broadening causes a strong fragmentation of the pulse temporal profile(Stolen and Bjorkholm 1982). As a result of beating between the strongly differentfrequencies inside the SC, the modulational structure is very fine and strengthens withthe SC broadening, when the power grows (Fig. 6a, b). Inset in Fig. 6b demonstrates thatthe high-power SC contains both solitons and dispersive waves radiated from a region of thestrong MI.

Figure 7 demonstrates that the propagation length growth does not cause a substantialbroadening of SC. Tenfold PCF lengthening in comparison with that in Fig. 5a gives onlya slight effect. Thus, the picosecond SC can be characterized by some optimal propagationlength like that in the case of the femtosecond SC (Sorokin et al. 2003).

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Fig. 9 As in Fig. 8. Temporal profiles for the first-order mode: (a) noninteracting modes, (b) interactingmodes

Since the LMA PCF is multimode, the nonlinear coupling between modes affects theSC characteristics (Cherif et al. 2008). Figure 8 illustrates the situation, when only 4%of total energy propagates into the first-order mode. In the absence of the nonlinear cou-pling (i.e., the mode overlapping parameter in Eq. 1 equals to zero), the first-order modespectrum does not broaden at all (Fig. 8a). However, the cross-modulation between thezero- and first-order modes causes the noticeable spectral broadening of the latter (Fig. 8b).Such a broadening results from a strong MI of the higher-order mode induced by thehigh-power field propagating into the zero-order mode (compare the temporal profiles inFig. 9a, b). Such a nonlinear intermode coupling has been observed in the femtosecond SC(Kalashnikov et al. 2006) and allows controlling the SC characteristics. For instance, con-trol of the beam focusing changes the energy portion into higher-order modes. Growth ofthis portion will reduce slightly the SC width, but enhance its smoothness owing to spectralbroadening of the higher-order modes caused by the intermode cross-modulation.

5 Conclusion

In conclusion, for the first time to our knowledge, the IR edge of the SC generated in the LMAPCF with the numerical aperture of 0.36, core diameter of 10 µm, and air-filling fraction of

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0.9 is studied under excitation by 15 ps pulses at 1.08 µm with the energies up to fiber damagethreshold (≈5 J/cm2).

It is shown both experimentally and numerically that the long-wavelength edge of SC at≈ 1.9 µm does not shift significantly into infrared with the 10-fold PCF length growth (from0.5 to 5 m) under pumping with the coupled peak powers (300 kW) up to the PCF damagethreshold. This effect results from an existence of the optimal PCF length providing the bora-dest SC under maximum (close to the damage threshold) pump power. For the first time to ourknowledge, the spatial-temporal structure of the picosecond SC is analyzed on the basis ofthe extended coupled nonlinear Schrödinger equations. It is found that the cross-modulationbetween the modes enhances the spectral broadening and the modulational instability ofhigher-order modes. As a result, the smoothness of SC in a multimode PCF under picosec-ond excitation can be controlled by means of manipulation with the pump energy portioninto higher-order modes, when the pump beam focusing changes. The obtained results areof interest for applications of the LMA PCF as a broad-band source of probe emission inpicosecond pump-probe spectrophotometry within the 1–2 µm spectral range.

Acknowledgements Author (V.L.K.) was supported by the Austrian “Fonds zur Förderung derWissenschaftlichen Forschung” (FWF), Projects No. P20293 and P17973.

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infrared supercontinuum from a large mode area pcf under...

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