Intensity stability and wavelength correlations of near-infrared supercontinuum generation are studied in all-normal flattened dispersion, all-solid soft glass photonic crystal fiber. We use dispersive Fourier transformation method to measure shot-to-shot resolved spectra under pumping from a sub-picosecond, fiber-based chirped pulse amplification (CPA) system. For the first time to our knowledge, we demonstrate how unconverted radiation from pump, propagating in the photonic cladding of the fiber, improves the measured degree of coherence in the spectrum and influences its wavelength correlation by seeding of multiple four-wave-mixing / Raman scattering components. The presented results suggest a convenient and simple way of stabilizing of shot-to-shot coherence in sub-picosecond fiber laser pumped, normal-dispersion supercontinuum sources by direct, pump-related seeding.
© 2014 Optical Society of America
Formation of a supercontinuum spectrum contained entirely within the normal dispersion range of wavelengths attracts increasing attention due to its high shot-to-shot coherence and proven capability of exceeding an octave-spanning bandwidth [1–5]. Ultra-stable, broadband supercontinuum sources would be ideal for characterization of ultrafast or rare-occurring phenomena such as in flow cytometry [6,7] or characterization of rouge waves . Excellent intensity stability of all-normal dispersion supercontinuum (ANDi SC) comes at a cost of specific requirement on the duration of the pump pulse. It has been shown for silica-based nonlinear fibers, that at pump pulse durations over 200 fs, coherence of normal dispersion broadening is deteriorated by Raman scattering . Furthermore, in terms of relative intensity noise, its detrimental influence on ANDi SC was comparable to modulation instability noise in typical anomalous dispersion supercontinuum. From a device perspective, a mode-locked erbium- or thulium-doped fiber laser (FL) would be the pump source of choice for its robustness and wavelength of operation matching state-of-the-art ANDi nonlinear fibers [4,5,10]. However, since in the state-of-the-art FLs with adequate output power levels, pulse durations are in the range of 350-500 fs , Raman scattering can be a possible limiting factor for ultra-stable and robust ANDi SC sources. Control of influence of Raman scattering in ANDi SC generation is of immediate importance, as growing research interest in this type of SC presently involves use of pump pulses with different durations from femtoseconds [1,3–5] to picoseconds , as well as use of photonic crystal fibers (PCFs) drawn from different glasses, including silica glass [1–3] and various oxide  and non-oxide  soft glasses.
In this work, we investigate the dynamics of formation of supercontinuum spectrum in an all-normal dispersion, soft glass photonic crystal fiber (PCF). Our experiment is based on use of the dispersive Fourier transformation (DFT) method . We record trains of 256 shot-to-shot resolved spectra under pumping from a fiber-based CPA laser delivering 390 fs pulses, centered at a wavelength of 1560 nm, with 40 MHz repetition rate. Recorded experimental data is used for analysis of the degree of coherence of the spectrum, defined as:13,14]. The correlation ρ between any two wavelengths λ1 and λ2 in a spectrum takes values in the range –1 < ρ < 1. A positive value indicates that intensities at the two wavelengths both increase or decrease at the same time (are correlated), while a negative value indicates that while the intensity at one wavelength increases, the intensity at the other wavelength decreases (wavelengths are anti-correlated). Obtained experimental results are compared with numerical simulations based on nonlinear Schrödinger equation (NLSE). This allowed for a clear identification of unconverted pump radiation, which co-propagates in the photonic cladding of our ANDi PCF and improves the spectral degree of coherence. For the first time to our knowledge, we demonstrate how unconverted radiation from pump, propagating in the photonic cladding of the fiber, improves the measured degree of coherence in the spectrum and how it influences its wavelength correlation by seeding of multiple, four-wave-mixing and Raman scattering interaction components.
2. Experimental setup
2.1. Mode-locked fiber laser pump and dispersive Fourier transform setup design
The experimental setup is shown in Fig. 1. The normal-dispersion photonic crystal fiber is pumped by a fiber-based chirped pulse amplification system. The CPA is seeded by a dispersion-managed, mode-locked Er-doped fiber laser, delivering 200 fs pulses at a central wavelength of 1560 nm with 40 MHz repetition frequency. The pulses are temporally stretched in a segment of a dispersion compensating fiber with total group delay dispersion (GDD) of 12 ps2. After stretching, the pulses are amplified in a two-stage fiber amplifier. The first stage is a standard Er-doped fiber amplifier (EDFA) which boosts the signal to 15 mW. The second amplifier (high-power stage) is based on an Er/Yb co-doped double-cladding fiber (EYDFA), pumped by a 10W, 976 nm laser diode. Afterwards, the pulses are compressed in a grating-based Treacy-type compressor. The pulse duration after recompression is 390 fs. The whole design is based on single-mode fibers, which allows to maintain almost excellent beam quality, with M2 parameter close to 1 . The maximum average pump power incident on the PCF input facet was limited to 1.0 W. The coupling efficiency estimated by measuring the average power at the output of the small core PCF was around 35%.
As the dispersive element in the DFT measurement, we used 10 km long non-zero dispersion shifted fiber G.655 with dispersion D = 3.5 ps/nm/km at 1550 nm and dispersion slope of 0.033 ps/nm2·km . Spectral widths of the supercontinuum considered in this study were around 400 nm (not optimized for spectral width). The corresponding duration of an individual supercontinuum pulse at the output of the DFT stretching fiber was estimated at Δτ = D·z·Δλ ≈14 ns, where z = 10 km is the stretching fiber length. The 40 MHz pulse repetition corresponds to a pulse shot every 25 ns, hence the stretched supercontinuum pulses would not overlap. Stretched pulses at the output of the G.655 fiber were detected by a 16 GHz photodiode (Discovery Semiconductors DSC2-50S), connected to an oscilloscope with 40 Gsamp/sec sampling rate and a bandwidth of 13 GHz (Agilent Infiniium DSO91304A). The number of the recorded consecutive pulses was limited to 256 shots, since our oscilloscope was not equipped with extended sweep mode. However, comparing different 256-shot traces confirmed this was enough number to characterize the variability in the recorded spectrum. Oscilloscope time-base was converted to wavelengths using formula :Fig. 2.
The anomalous dispersion of the stretching fiber was of practical convenience, as the envelope of pulses monitored at the oscilloscope was exactly of the same shape as the shape of spectrum monitored at the optical spectrum analyzer (OSA, Yokogawa AQ6375), i.e. blue-shifted wavelengths corresponded to the leading edge of pulse and red-shifted wavelengths to the trailing edge of pulse on oscilloscope. The oscillogram trace containing single shot waveforms corresponding to the SC spectra were time-wrapped using a simple computer algorithm. The spectral resolution of the retrieved single-shot spectra was determined by the bandwidth of the detection system – the photodiode and oscilloscope – of which the oscilloscope’s bandwidth was the limiting factor . Hence, the resolution was δdet = 1/(B·|D|·z) ≈2.2 nm, where B = 13 GHz (oscilloscope bandwidth). Generally, this setup can be used for characterization of other types of nonlinear PCFs, i.e. anomalous dispersion fibers for soliton-based supercontinuum generation. Still, attenuation of the stretching fiber at around 1300-1400 nm due to OH¯ content (5-8 dB over 10 km stretcher section) and gradual increase of attenuation at wavelengths longer than 2000-2200 nm typical for silica fibers, is a practical limitation for the investigated spectral range. Other types of dispersive elements, including different types of optical fibers, chirped fiber Bragg gratings, or diffraction gratings for chromo-modal dispersion can be used in a DFT setup, depending on spectral range of interest in a particular application .
2.2. All-solid, all-normal dispersion photonic crystal fiber and femtosecond supercontinuum
The ANDi PCF used in the experiments was an all-solid glass, nonlinear PCF with flattened normal dispersion profile. Details on designing, characterization and femtosecond pulse-pumped supercontinuum performance of this fiber were recently reported in [4,17]. Figure 3 shows the fiber’s dispersion profile – measured up to 1700 nm and calculated using a mode solver based on the finite element method, as well as the real structure of the PCF taken from a scanning electron microscope (SEM) image. Attenuation of the fiber was measured in the 1500-1600 nm range with an amplified spontaneous emission (ASE) source, and found to be approximately 3 dB/m.
We reported recently, that injecting 75 fs pulses centered at 1550 nm enables generation of over an octave spanning SC spectrum with excellent spectral flatness, shown in Fig. 4 . Some unconverted pump radiation, propagating in the photonic cladding, was also observed experimentally, however it was not reproduced by scalar simulations. The nonlinear process has been shown to involve self-phase modulation (SPM), followed by optical wave-breaking (OWB), finalized by four-wave mixing (FWM), in which the OWB and SPM spectral components act as pump and seed signals .
In the correlation map, generated from the numerical data and shown in Fig. 4, this process is manifested by centrally located cross feature stemming from SPM and by oval shapes, extending from the symmetry diagonal (bottom-left to top-right) of the map at wavelengths where OWB sets in (around 1200 nm and 1600 nm). The described process does not depend on Raman scattering to any significant extent. The condition for that is using pump pulse short enough, so there is as little as possible contribution of the delayed Raman response while the pulse lasts. Figure 5(a) shows measured Raman scattering spectrum in a bulk F2 glass, used for the core of the PCF. The spectrum has a peak Raman gain at about 1050 cm−1, corresponding to 31 THz, and a full width at half maximum (FWHM) of roughly 6 THz. For a pump wavelength of 1550 nm, this gives a Stokes Raman signal at 1850 nm and anti-Stokes at 1360 nm. The temporal Raman response, shown in Fig. 5(b) was calculated from the spectrum using formula :4]), only a very limited part of the temporal Raman response can contribute to the nonlinear spectral broadening, and the amount of introduced variability of the Raman scattering contribution as the pump pulse lasts, is very small. The downside of using short pump pulse, is the type of the pump source, that delivers it. Optical parametric amplifiers cannot be considered neither commonly available, nor convenient in the context of robustness and user-friendliness. Mode-locked fiber lasers meet these criteria. However, with devices that deliver sufficient pump power for an octave-spanning spectrum in an ANDi regime, it is difficult to go with pump pulse length below 200 fs. At 390 fs of pulse duration, which was used in this work, most of the temporal Raman response “fits” into the duration of pump pulse, contributing to the nonlinear broadening process with varying intensity as the pulse lasts.
3. Results and discussion
The DFT measurements were performed for ANDi PCF sample, which was 17 cm long. This length was established after running some initial numerical simulations and with a motivation to demonstrate dynamics of SC formation soon after influence of Raman scattering had become clearly distinguishable. We also considered sample handling convenience and wished to avoid limitation of spectral broadening by the fiber’s attenuation over larger propagation lengths.
3.1. DFT supercontinuum measurements
The SC spectrum recorded using an OSA, is show in Fig. 6(a). Average power measured at the output of the PCF was 380 mW, for about 1.0 W of average pump power incident on the PCF input facet. Measurement was performed before launching into the 10 km long G.655 stretching fiber, and the spectrum was also monitored for possible distortions at the exit of stretching fiber. The SC generation setup was by no means optimized with spectral width in mind. On the contrary, pump power was maintained at a level, which was a compromise between reaching expected wavelength location of the Stokes Raman component and at the same time maintaining the spectrum in a wavelength range, in which our stretching fiber would allow correct time-to-wavelength mapping (e.g. avoiding to reach far below 1400 nm, where OH¯ absorption of stretcher is located).
A part of recorded oscilloscope waveform, showing several consecutive SC shots, is shown in Fig. 6(b). The duration of individual stretched pulse was roughly 12-13 ns, against 14 ns estimated with the assumption of a flat dispersion of the stretcher fiber, which supports accuracy the DFT measurement. Superimposed 256 single-shot spectra (and the mean trace) with the oscilloscope time-base converted to wavelength scale using Eq. (3), are shown in Fig. 7 together with spectrum measured with an OSA and spectrum obtained numerically. On top of this graph, a comparison of signal to noise ratio (SNR) is show for the DFT data and for an ensemble of numerical spectra. SNR was calculated as the ratio of the mean to standard deviation of spectral intensity over 256 shots.
It can be noticed, that shot-to-shot fluctuations in the experimental data are small, typically within a 5% range over the entire spectrum. Reconstruction of optical spectrum from the oscillogram is correct with respect to spectral width and location of major intensity peaks. Less accurate reconstruction of intensity ratio among the peaks does not invalidate analysis of degree of coherence and spectral correlation mapping, since these quantities characterize normalized shot-to-shot change of intensity, rather than intensity distribution across the spectrum. DFT spectrum is also more extended toward longer wavelengths, than the OSA-measured spectrum. This discrepancy is assigned to a difference between the dispersion profile of the stretching fiber assumed in the DFT mapping Eq. (3) and its physical dispersion for wavelengths longer than 1700 nm, data on which was unavailable.
For modelling, we used Matlab code published in , because it is easily extendable to include frequency dependence of the effective mode area Aeff(ω) and of the fiber loss α(ω). The statistical data is obtained by running the simulation n-times, where n is number of shots, each time adding pump-laser bandwidth-dependent noise to the complex filed amplitude, as proposed by Frosz in . The nonlinear part of the NLSE is solved in the frequency domain, therefore it was possible to include the Aeff(ω) and the frequency dependent loss in a straightforward way. Temporal Raman response calculated using (4) was included straightforwardly, as well, as its frequency form for the nonlinear part of NLSE is readily obtained by fast Fourier transforming of the time domain data. Experimental and simulated SC spectra are in reasonable agreement. The discrepancies mainly include the area around the pump wavelength, where intensity of the numerical trace is smaller than in the measured trace. Although the spectra share bandwidth and multiple peak structure, the latter is more complex in the measured spectrum. These two main differences will be addressed in detail throughout the section discussing measured and simulated dynamics of SC formation.
Specifically, it comes with a surprise, that any agreement with experimental data disappeared from numerical reconstruction of the degree of coherence, shown in Fig. 8. While numerically generated coherence profile is strongly deteriorated, especially at red-shifted wavelengths, the experimental result remains close to 1.0 over the entire range of generated SC spectrum (around 1450-1700 nm, the remaining wavelengths outside of this range high degree of coherence is related to roughly constant noise floor of the OSA).
Similarly, SNR obtained from the measured data is much higher than in the simulation. Rapid drop of numerically obtained shot-to-shot coherence at red-shifted wavelengths is associated to Stokes-shifted Raman scattering, which introduces oscillations at varying amplitude across the pulse duration. Our theoretical result, where intensity stability of red-shifted wavelengths of spectrum is deteriorated due to Raman scattering, is in agreement with earlier experimental results reported by Aalto et al. for an ultra-violet SC pumped with nanosecond pulses .
3.2. Analysis of wavelength correlations
In order to explain maintained coherence in the experimental data, in connection with reasonable agreement between experimental and simulated SC spectra, wavelength correlation maps were plotted based on ensembles of measured and simulated single-shot spectra. Wavelength correlation maps were recently proposed as a useful tool in characterizing SC dynamics, which are not easily deductible from analysis of vector-like data . The correlation maps, computed using Eq. (2) for experimental and numerical data sets are presented in Fig. 9. The experimental (Fig. 9(a)) and numerical (Fig. 9(b)) maps are very different. Moreover, both maps are different from the numerical map generated from data obtained for supercontinuum spectrum pumped with 75 fs pulses (Fig. 4). The difference between numerical maps in Fig. 9(b) (390 fs long Gaussian pump pulse) and in Fig. 4 (75 fs long Gaussian pump pulse) are easily attributable to different character of involvement of Raman scattering in the broadening process. Under 75 fs pump pulse, Raman scattering has little influence and SPM/OWB features are clearly distinguishable as discussed in previous section. Correlation map generated from numerical data obtained for 390 fs pump pulses shows two pairs of around 50 nm wide, highly correlated wavelength regions, which are blue-shifted and red-shifted from the pump wavelength. Both are assigned to the interplay between FWM and Raman scattering. The characteristic oval features observable in correlation map in Fig. 4, are here replaced by these FWM-Raman related areas. The parametric interaction between SPM and OWB in ANDi fibers is generally not phase-matched and FWM between them takes place only at the limited time window, when these spectral components overlap at the edges of broadening spectrum .
Presence of FWM-Raman components disrupts this interaction and hence surpasses generation of the parametric wing of the spectrum. On the other side of the numerical spectrum (short-wavelengths), observation of anti-Stokes Raman components (blue-shifted against the pump wavelength) is supported by the coupling between the Raman scattering and FWM, which has been shown to facilitate rising of otherwise weak anti-Stokes Raman features [23,24]. Additionally, a broad, correlated area in the top-right corner of the map (1750-1850 nm) corresponds roughly to where first-order Raman shift of the 1560 nm pump should be expected (spectral intensity in that part of the spectrum is however very low at assumed pump pulse energy).
The central area of the experimental correlation map, shown in Fig. 9(a), is uniformly build up with highly correlated “ribbons” aligned parallel to the main symmetry axis and extending from the pump wavelength towards longer wavelengths. In order to explain origin of these highly correlated “ribbon” features in Fig. 9(a) we confront the fiber structure. As hinted earlier, this PCF supports propagation of pump partially in the photonic lattice. This stems from the structure of fiber, where the core made of Schott F2 glass has the highest refractive index of 1.594874, the photonic cladding, composed of F2 capillaries with thermally matched borosilicate glass inclusions has a lower refractive index and the tube around this structure, made only of borosilicate glass, has the lowest refractive index of 1.511304. In the presented case, each of the “ribbons” red-shifted from the pump wavelength is roughly 20 nm in diagonal, which corresponds to the FWHM of the pump laser spectrum. Assignment of a similar wavelength correlation structure to wavelength jitter in the pulse, has been reported before by Godin et al. in . In our case, this jitter is assigned to continuous wavelength shift due to FWM-Raman interaction, while the spectral width of the “ribbons” is a fingerprint of the laser line which seeds this interaction. Involvement of pump as seed in each of these ribbons is further supported by the fact, that the fraction of the pump light propagating along the photonic cladding as higher order modes, does not participate in the nonlinear process at the same terms, as the fundamental mode in the PCF core. These modes experience much less confinement in a 35 µm “core” formed by the photonic cladding and their nonlinear coefficient (Kerr coefficient) would hence be roughly an order of magnitude smaller, than that experienced by the fiber’s fundamental mode in the core. Since this higher order mode radiation does not actually experience nonlinear effects (at least to a non-negligible extent) and its propagation is linear, from the perspective of the nonlinearly propagating mode it can be viewed as a “continuous-wave” seed signal. The blue-shifted area of experimentally obtained correlation map in the range of 1450-1560 nm contains an area of ripple-like structures parallel to the map’s axis. These structures are assigned to anti-Stokes FWM-Raman interaction, which is also seeded by the pump signal. Here, however, the pump “finger-print” is disrupted by beating with the pump-related SPM components, which have higher power spectral density, than at the red-shifted wavelengths.
Involvement of pump light in role of the seed is directly assigned as the cause of maintained experimental degree of coherence over the entire range of SC wavelengths (1450-1800 nm). Seeding of SC generation has been shown to stabilize soliton-broadened spectra in anomalous dispersion pumped PCFs, under the condition that the seed is at least partially coherent with the pump [25,26]. We report on a particular case, where the seed is actually the pump, and specifically part of it, which does not undergo nonlinear conversion. Analogic findings, but for the anomalous dispersion SC were reported by Ren et al. , where seed signal enhanced the spectral coherence, albeit at the cost of delayed soliton fission, which limited obtainable width of spectrum. In our ANDi PCF soliton propagation is not the case, whereas limitation of spectral broadening would be related to the detrimental effect, which Raman scattering has on pump/seed wavelengths for the parametric process generating ANDi SC sidebands, when pumping with tens-of-fs pulses.
The numerical model of nonlinear pulse propagation, used in this study did not take into account the co-propagating seeding pump signal (scalar model). The resulting discrepancies between modelled and measured shot-to-shot coherence profiles, SNR and correlation maps supported identification and discussion of the role of unconverted pump signal as seed in SC formation. At the same time, the SC spectra measured with an OSA and generated numerically were reasonably similar, due to the fact, that Raman scattering was present in both cases. The main limiting factor for spectral broadening was also similar: Raman scattering and/or Raman-FWM disruption of OWB-SPM parametric process. The difference between the experimental and numerical spectrum, revealed with wavelength correlation maps was within the dynamics of SC formation. We finally note, that since Raman scattering reduces the FWM gain by a factor of (1-fR) , the seeding of multiple Raman components from the unconverted pump in the spectrum can be expected to become another limiting factor for spectral broadening as the PCF length increases. Optimization of PCF length in this context should be considered in designing of a practical sub-picosecond pumped ANDi SC.
Results of our work demonstrate a two-fold role of unconverted pump radiation in ANDi SC formation pumped with sub-picosecond pulses. A part of pump radiation, which is not converted in the nonlinear process, seeds the SC generation and stabilizes its shot-to-shot fluctuation of spectral intensity. Excellent shot-to-shot repeatability was observed in the experimental data, as opposed to significant coherence degradation and drop of SNR predicted by scalar simulation, which did not take into account the seeding role of pump signal. This supports cladding propagation of part of unconverted pump power in role of a convenient seeding-based, noise-cleaning method in ANDi SC sources pumped with robust sub-picosecond fiber lasers. At the same time, seeding of new Raman components increases the detrimental effects of Raman scattering on ANDi SC generation, through replacement of an efficient SPM-OWB parametric process observed in tens-of-femtoseconds pump regime, with FWM-Raman components. It is to be noted, that the design of the all-solid ANDi PCF used in this work, was by no means optimized to make the most out of the presented idea for coherence enhancement. After longer propagation distance, the unconverted pump radiation can be expected to either deteriorate spectral width of SC due to limiting effect of generated Raman components on the FWM gain bandwidth, or due to gradual leaking out of the cladding, which would cancel the seeding effect. Investigation of the seeding efficiency for different propagation lengths and larger bandwidths of spectrum is the topic of our current study.
The reported results suggest, that during the design of ANDi fibers for SC generation pumped by pulses long enough to allow Raman scattering to influence the spectral dynamics, measures can be taken in order to limit this detrimental effect. These should be focused on finding optimum parameters enabling efficient, direct seeding of ANDi SC from the pump, including a PCF layout with photonic cladding enabling linear propagation of part of the pump radiation, as well as optimum PCF length, at which the seeding of additional Raman components disrupting the FWM contribution to spectral broadening does not outbalance the benefit of enhanced degree of coherence.
This work was supported the project TEAM/2012-9/1 operated within the Foundation for Polish Science Team Programme co-financed by the European Regional Development Fund, Operational Program Innovative Economy 2007-2013 and by the Polish Ministry of Science and Higher Education under the project entitled “Amplification of femtosecond pulses from fiber lasers utilizing graphene” (project no. IP2012 056772). The authors wish to acknowledge Mariusz Zdrojek from Warsaw University of Technology for measuring the Raman scattering spectrum of the fiber glass, as well as Ryszard Stępień and Dariusz Pysz from Institute of Electronic Materials Technology for synthesis of thermally matched glasses and for drawing of the all-solid glass photonic crystal fiber.
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