We have experimentally studied supercontinuum generations in highly nonlinear suspended core silica fibers as alternatives to photonic crystal fibers. Octave-spanning spectrum can be easily generated at peak pump power levels as low as ~1.5kW at 1µm and ~1kW at 800 nm, which effectively enables fceo stabilization of mode-locked fiber lasers without further amplification. Experiments also confirm that the blue edge of the supercontinuum undergoes a two-phase growth process, an initial fast growth governed by phase-matched dispersive wave generation and a second slower growth governed by group-velocity-matched cross-phase modulation. We have further experimentally shown that the fundamental solitons generated from the initial fission process can be independent of pump powers and the orders which they are generated. Furthermore, while the fundamental soliton wavelength undergoes continuous red shift by Raman scattering, they continuously lose power to longer wavelength dispersive waves where phase-matching to this long wavelength dispersive wave is allowed and, otherwise, maintain its initial power where phase-matching to long wavelength dispersive wave is not allowed. We also demonstrated that total suppression of dispersive wave generation at short wavelength can be achieved in the absence of dispersion slope at the pump wavelength.
©2008 Optical Society of America
Tremendous amount of studies have been conducted on supercontinuum generation (SCG) in optical fibers since the first demonstration of extremely broad SCG in 2000 in photonic crystal fibers (PCFs) with zero dispersion wavelengths around 800nm . The intense broad band SCG makes it very attractive for a wide range of applications including spectroscopy, coherence tomography and frequency metrology. Despite the complexity of processes involved in SCG, spanning spectral, time and spatial domains, clear understanding of the basic processes have been achieved with the aids of numerical simulations. Generalized nonlinear Schrödinger equation incorporating higher order dispersion effects, instantaneous and retarded optical nonlinearity, and frequency-dependent nonlinear coefficient, has proven to be a very powerful tool for achieving excellent agreement with experimental observations . It has been concluded that a SCG consists of three basic phases, (i) initial spectral broadening and temporal compression, (ii) fission of higher order soliton into fundamental soliton components, and (iii) propagation dynamics of the generated solitons and interactions between the solitons and short wavelength part of the SC.
In phase (iii), the longer wavelength edge of the spectrum is dominated by self frequency shift of the solitons under the influence of Raman scattering while the shorter wavelength edge is dominated by the dispersive wave (DW) generated at the initial phase of the soliton propagation. Interestingly early observations showed that a pulse in normal dispersion regime can undergo continuously blue shift when trapped behind a co-propagating soliton at the longer wavelength [3,4]. This effect would continuously move blue edge of SCG towards shorter wavelength as long as the longer wavelength soliton is continuously shifted towards longer wavelength and is slowing down in its group velocity. Genty et al studied new blue wavelength component generations in the context of cross phase modulations in [5,6]. Recently, Yulin et al have studied interaction between a soliton and a CW wave and concluded that new frequencies can be generated at a number of resonant conditions determined by a FWM-like interaction involving the Fourier components of solitons in fibers with higher order dispersions . A detailed experimental and theoretical study of this phenomenon were performed near the second zero dispersion point of a PCF by Efimov et al . The interactions of a soliton and a co-propagating dispersive wave was well illustrated graphically with carefully planned experiments and simulations in , demonstrating, besides new frequency generations, repulsing and trapping of dispersive waves. Later, a more complete theoretical treatment including coupling efficiencies of the interactions was reported in . This new frequency generation through a soliton and a dispersive wave interaction was also first used to explain the generation of some spectral features at the blue edge of a SCG in . Recently, trapping of a dispersive wave by a co-propagating soliton was theoretically studied in . The dispersive wave is seen as being trapped at the leading edge by the refractive index changes induced by the slowing Raman soliton and on the trailing edge by the inertial force originated from the accelerating soliton. This concept was further refined in  to explain the formation of pulses in the normal dispersion regime with durations similar to that of the solitons at the long wavelength side of a SC and, with FWM-like interaction between a soliton and a CW, to explain the continuous blue shift of the trapped pulses at the short wavelength side of a SC. A recent work has further shown that the blue edge of a SC can be extended by allowing the existence of corresponding group-velocity-matched solitons at the longer wavelength . There are tremendous interests in extending the SCG to visible and UV for spectroscopy and display applications. It is, therefore, very important to fully understand the relevant mechanisms which lead to the generation of blue edge of a SCG.
Recently, we have shown that silica suspended core fibers (SCF) are an excellent alternative for many nonlinear applications to PCFs [14, 15]. Small core silica SCFs have been shown to offer both low transmission loss and low splice loss to conventional single mode fibers. Furthermore, silica SCFs offer a full range of dispersion tailoring as well as potentially shorter zero-dispersion wavelength as a result of the higher numerical aperture (NA) possible with their near 100% air cladding. Such SCFs offer good fabrication controllability, design flexibility and excellent uniformity comparable to that of a PCF, while offering ease of fabrication arising from the much simpler geometry. In this work, we have conducted SCG in these silica SCFs, demonstrating very efficient octave-spanning SCG with peak power as low as 1.5kW at ~1µm and 1kW at ~800 nm thanks to high nonlinearity, low propagation loss and very low splice loss to standard single mode fibers. We have also provided further experimental confirmation of the two separate phases in the growth of the blue SC edge, a fast initial phase dominated by phase-matched dispersive wave generation and a much slower second phase governed by group-velocity-matched interactions between the solitons and shorter wavelength part of SC, leading to a continued blue-shift of the shorter wavelength edge of the SC. We have further experimentally observed that soliton fission process in the initial phase of the SCG in SCFs generates fundamental solitons with power and spectrum features largely independent of the orders of generation and pump powers, somewhat different from previous observations . Furthermore, while the fundamental soliton wavelength undergoes continuous red shift by Raman scattering, they continuously lose power to longer wavelength dispersive waves where phase-matching to this long wavelength dispersive wave is allowed and, otherwise, maintain a constant power where phase-matching to long wavelength dispersive wave is not allowed. Large polarization-dependent soliton wavelength tuning up to 150 nm was also observed in a highly birefringent 1.27µm core SCF.
2. General experimental conditions
Two silica SCFs are used for this study. The cross section of the SCF1 is shown in Fig. 1(a). It has an elliptical core with a dimension of 2.3 µm×2.8 µm (see bottom figure in Fig. 1(a)). The fiber was simulated with 6 circular holes with a Multipole mode solver  (see the bottom figure in Fig. 1(a) for the simulated fiber geometry). The simulation gives dispersion for the two polarization modes (solid and dotted lines in top figure in Fig. 1(a)) very close to the measured dispersion in crosses. This fiber has a 1st zero dispersion wavelength λ01=869 nm and 852 nm for the x and y polarization modes respectively. Group delays of SCF1 are also shown on the right vertical axis in the top figure in Fig. 1(a). Measured birefringence of SCF1 is Δn=9.8×10-4 at 1020 nm, agreeing reasonably well with the predicted 7.9×10-4. SCF2 has a core diameter of ~1.27µm. The core is only slightly elliptical. The web width is ~90nm. Simulation was performed with 6 identical holes. The simulated dispersion in solid line is again very close to measured dispersion in crosses. The first zero dispersion wavelength of SCF2 is λ01=664nm and second zero dispersion wavelength is λ02=1.628µm. Measured birefringence of SCF2 is a much higher Δn=4.5×10-3 at 1020 nm. SCF2 has an effective mode area of 1.1µm2 and 1.75µm2 at 1.05µm and 1.55µm respectively. This gives a nonlinear coefficient γ=~140 W-1 Km-1 and ~60 W-1 Km-1 at 1.05µm and 1.55µm respectively, assuming n2=2.6×10-20 m2/W. SCF1 has an effective mode area of 4.2µm2 and 4.8µm2 at 1.05µm and 1.55µm respectively. This gives γ=~37 W-1 Km-1 at 1.05µm and γ=~22 W-1 Km-1 at 1.55µm. SCF1 has a loss of ~28dB/km at 1550nm and ~320dB/km at the OH absorption peak of 1390nm. SCF2 has a loss of ~77dB/km at 1550nm and ~370dB/km at the OH absorption peak of 1390nm. For all of our experiments, maximum fiber length is slightly over a meter, linear absorption is, therefore, negligible, even at the OH peak of 1390nm.
Two types of pump fiber lasers were used. The first one is IMRA FCPA D400, an ytterbium-doped fiber laser which provides 350fs pulses at 200 kHz repetition rate with a wavelength of 1045 nm. The second laser is a frequency-doubled erbium-doped mode-locked fiber laser, which provides 117fs pulses at 75 MHz repetition rate at 804 nm. We typically splice the SCF to a short length of an intermediate high NA fiber (Nufern, NA=0.35, diameter=2.1µm, 3–5mm long) and then splice to a 10mm Hi1060. In this way high launch efficiency of >75% is easily obtained. The total splice loss is typically ~0.25dB for SCF1 to Hi1060 and ~0.8 dB for SCF2 to Hi1060. We have tested the impact of the length of Hi1060 on SCG at a peak power of 5.7kW at 1045nm. It is found that a very shorter length of Hi1060 does not seriously affect SCG, while longer length Hi1060 degrades SCG spectrum width. We also used 1nm resolution bandwidth on OSA setting and consequently used the unit of dBm/nm for all OSA measurements. All pump powers in this paper are referred to the launched peak pump power in the SCFs.
3. SCG in SCF1
Figure 2 shows SCG in a 17cm SCF1 for the pump at 1045nm. Left plot gives the wavelength-versus-power plot while right plot showing the corresponding 3D plot with input polarization carefully adjusted to align with the major axis of the fiber (x polarization). Two distinct regimes of growth at the short wavelength side can be identified, a low pump power regime where peak pump power <~5kW and a high pump power regime where peak pump power >~10kW. At the low pump power regime, both the short and long wavelength edges of the SCG grow rapidly, while this growth slows to a much lower rate at the high pump power regime. The characteristics of the low and high pump power regimes are further illustrated in Fig. 3 and Fig. 4 where both short and long wavelength edges of the SCG can be seen in more details.
Significant spectrum ripples can be seen at the low pump power regime where peak pump power is less than ~5kW (see Fig. 3), indicating significant overlap in the time domain of the adjacent spectrum components. This is again consistent with the well-understood model of SCG at the initial phase of the growth, where walk-off of various components in time domain is insignificant. This phase of the growth is quite different from that of higher peak pump power, where the smoother spectrum indicates significant walk-off in time domain of adjacent spectrum component (see Fig. 4, please note that it is in a much smaller vertical scale than Fig. 3).
In the high pump power regime (see Fig. 4), the spectrum features are relatively broad and smooth. Raman-shifted solitons at the longer wavelength are clearly visible. The broad short wavelength feature at the short wavelength edge of the SCG is consistent with that of a short pulse. The smooth spectrum is also consistent with well-established observation that both long and short wavelength pulses have significantly walked off from adjacent spectrum features in time domain at this stage. The relative group delay of SCF1 is given in Fig. 1(a), showing that all wavelengths further away from λ01 have increased group delays, i.e. slower group velocity. The continuous blue shift of the shorter wavelength spectrum peak is clearly visible in the high pump power regime. Additional feature to note is that the spectral density of the short wavelength spectrum peak is 1–4dB higher than that of the corresponding long wavelength soliton. The long wavelength soliton spectral density stays remarkably constant despite the pump power increase and continuous red shift by Raman scattering. The spectral density of the short wavelength feature, on the other hand, increases with peak pump power. It should be noted that a higher average power in the short wavelength spectrum was observed by Tartara et al in a micro-structured fiber with a core diameter of 1.5µm and a pump of ~800nm near λ01  and by Ranka et al in their first report of SCG .
To better understand how the dispersive wave at the short wavelength edge and the soliton wave at the long wavelength edge are related in the SCG, group velocity match condition and phase match condition are plotted in Fig. 5 for both polarization modes of SCF1. We used local dispersion and group velocity shown in Fig. 1(a) for this calculation. Nonlinear effect on phase match condition is ignored as this is found to have very little impact at the peak pump powers involved. The peaks of the spectrum feature at the short wavelength edge in the high pump power regime are plotted against the corresponding soliton spectrum peaks in black circles for the major polarization axis (x-polarization). SCG in SCF1 when pump is aligned with the minor polarization axis was also measured. The corresponding shorter wavelength peaks versus the soliton peaks are plotted as red circles. It is evident that the agreement with the group velocity match conditions for both polarization modes is excellent, indicating that the pulse at the short wavelength is indeed trapped behind the slowing corresponding long wavelength soliton and forced to travel at the same group velocity, while its wavelength being continuously blue shifted. This is consistent with what was first observed in [3, 4] and subsequently explained in [10,11,12]. There was, however, no exchange of power between the two pulses. It is worth noting that the trapped dispersive wave pulse can have powers substantially higher than that of the corresponding soliton at the high peak pump powers. This may not be too surprising, considering that only the leading edge of the short wavelength pulse interacts with the soliton. A good physical insight to this process is given in [11, 12].
The peak wavelengths of the shortest wavelength spectrum features in the low pump power regime are also plotted against the corresponding soliton peak wavelengths. This is done for the major axis (x polarization), black diamonds, and the minor axis (y polarization), red diamonds in Fig. 5. This data fits amazingly well with the phase-matching condition, indicating these short wavelength spectrum features were created by phase-matched dispersive wave generation process when a soliton was perturbed by the higher order dispersion. It has been pointed out by Dudley et al  that such dispersive wave is only generated at the initial phase of SCG in the presence of Raman scattering. The excellent fit to the phase match condition also indicates that the soliton wavelength shift over the short fiber length due to Raman scattering is negligible at these low peak pump powers.
Since the dispersive wave power is substantially higher than that of the corresponding soliton at high pump peak powers, large part of its power could only come directly from the pump. Since the pump and dispersive wavelength only overlap in time domain at the initial phase of the SCG before significant walk-off due to their difference in group velocities, it is reasonable to conclude that most of the dispersive power was generated at the initial phase of the propagation, possibly through some interaction involving pump, soliton and dispersive wave, and its wavelength is subsequently continuously blue-shifted while trapped behind the slowing corresponding soliton. The almost constant soliton power despite of peak pump power increase also indicates that the fission process generates the fundamental solitons with substantially similar power and pulse duration, independent pump powers, a new observation to the best of our knowledge. The soliton power also remains remarkably constant during the red shift by Raman scattering from ~1100nm to ~1650nm, indicating very little radiation to the short wavelength dispersive waves. This is consistent with the simulation in .
SCG were further tested in a 1.2m SCF1 with the 1045nm pump. The peak wavelengths of the shortest dispersive wave, 1st dispersive wave, in the high power regime, are plotted against 1st soliton wavelengths as plus signs “+” in Fig. 5. The next dispersive wave can also be clearly identified in this case. Their peak wavelengths are plotted against 2nd soliton wavelengths as multiplication sign “×” in Fig. 5. Pump polarization was not controlled in this case. The data for both 1st and 2nd dispersive waves are very close to the expected group velocity match condition.
SCG was also measured at a low power of 2.6kW with the 1045nm pump while the fiber was progressively cut back. The results are plotted in Fig. 6. The soliton shifts slightly towards longer wavelength over this length of propagation. The dispersive wave at 666nm (see the blue arrow) remained mostly unchanged until ~1m length where it started to interact strongly with the corresponding soliton. A new spectrum component at slight shorter wavelength, see the red arrow, was clearly generated by this interaction from the dispersive wave. This new spectrum component grew rapidly and continuously moves towards shorter wavelength at the same time (see Fig. 7 for fine spectral details). The spectral ripples were developed over the dispersive wave peak at 120 cm, indicating that the new spectrum component overlapped with the original dispersive wave in time domain at this point. The peak wavelengths of the new short wavelength component are plotted against the corresponding soliton wavelengths as black triangles in Fig. 5, where the data fits well with phase match condition, indicating that the new short wavelength component is phase-matched to the long wavelength soliton. Similar new frequency generation has been attributed to interaction of a soliton and a dispersive wave in .
SCG was repeated using a length of 1.35m SCF1 with 1045nm pump and the result is given in Fig. 8. Octave-spanning SCG was observed from 640 nm to 1290 nm at a very low peak pump power of ~1.5kW. This is very important for metrology application. This low threshold implies that the output from a fiber mode-locked oscillator can be directly used without further amplification in fiber fceo-locked systems . The rapid spectral growth at low pump powers and slower spectral growth at high pump powers are also clearly visible. Comparing to the SCG in the 17 cm long SCF1 in Fig. 2, various fundamental solitons are spectrally separated even at relatively low powers due to the much longer fiber length.
4. SCG in SCF2
SCG in a 1m long SCF2 at various peak pump powers from the 1045nm pump is given in Fig. 9(a). The results of SCG in a 0.5 m SCF2 using the 804 nm pump are plotted in Fig. 9(b). Their 3D plots are also given in Fig. 9(c) and Fig. 9(d) respectively. It is important to note that SCF2 has a first zero dispersion wavelength λ01=664nm and second zero dispersion wavelength λ02=1.628µm. Additionally, the dispersion slope is zero around 1075nm and is very small at the pump wavelength of 1045nm. SCF2 also has much larger nonlinear coefficient γ than that of SCF1 due to its much smaller core diameter. Multiple solitons are clearly visible in Fig. 9(a). The long wavelength shifts of the solitons come to a quick stop just before they reach the second zero dispersion wavelength λ02. This effect was observed in an early study . The spectral density of the pulses remained relatively stable after Raman wavelength shift had stopped. The wavelength shift of the next soliton stopped at the same wavelength, adding additional spectral density at this wavelength. It is interesting to note that the long wavelength feature just above the second zero dispersion wavelength λ02 did not appear until much later only after the third soliton wavelength stopped shifting (>4.5kW).
The details of the 1st solitons at low pump powers (before the 2nd soliton reached wavelength stabilized state) are shown in Fig. 10. The wavelengths and peak spectral densities of the 1st soliton at various peak pump powers are shown in Fig. 10(a), re-plotted as peak spectral densities of the 1st soliton versus soliton peak wavelengths in Fig. 10(b), with corresponding spectra shown in Fig. 10(c). The higher rate of wavelength shift just before reaching the wavelength stabilization at ~1600nm is due to the sharply reduced local dispersion despite a reduced soliton peak power (Raman-induced frequency shift scales as P0 2/β2 , where β2 is as normally defined in nonlinear optics and P0 is the soliton power). The spectral density of the 1st soliton decreases at higher peak pump powers and shows a sharp drop at the point of the wavelength stabilization at a pump peak power of ~1.3kW. It is easy to see from Fig. 10(b) that this soliton spectral density drop at high peak pump powers is, in fact, due to a loss of power during red-shift. The peak spectral density at any fixed wavelength for different pump powers is in fact remarkably constant (see Fig. 10(c)), indicating that soliton power is independent of pump powers as in SCF1. While the soliton power remains constant during Raman-induced wavelength shift in SCF1, the soliton loses power in SCF2, possibly due to the radiation into the phase-matched dispersive waves at the long wavelength side of λ02, noting that the linear transmission loss is negligible over this length of propagation in the fiber (see section 2 for details). The generated dispersive is not seen in Fig. 9(a) during this Raman-induced wavelength shift, due to the limit of our OSA to below 1650nm. The soliton has lost a significant amount of power, some ~13dB, before the wavelength shift comes to a stop (see Fig. 10(b)). This loss of power must have played some role in its wavelength stabilization just below λ02. Contrary to the radiation of power to the shorter wavelength dispersive waves below λ01 where the radiation is sharply reduced by the continuous Raman-induced wavelength shift due to a rapid reduction in spectral overlap between the soliton and dispersive wave, the radiation to the longer wavelength dispersive waves above λ02 is actually increased by the continuous Raman-induced wavelength shift.
The acceleration of wavelength shift in a fiber with β3<0 and subsequent wavelength stabilization just below λ02 in Fig. 10(a) was predicted by an analytical study by Tsoy et al using a perturbation theory considering only third order dispersion in  and considering both third and fourth order dispersions in . Our experimental results here also lend support to their suggestion in  that an important contribution to the suppression of self-wavelength shift near λ02 is the energy loss by the soliton to resonant radiation.
A second interesting point to note is that there is a total absence of dispersive wave generated at the short wavelength side of λ01 even at peak powers where multiple fundamental solitons are generated. This is not too surprising considering that there is a near absence of higher order dispersion around the pump wavelength of 1045nm in SCF2 (see Fig. 1(b)) and a dispersive wave can only be generated when soliton is perturbed in the presence of higher order dispersion . The reduction of overlap between the solitons and the dispersive waves due to the larger spectral separation may also have played a part in the suppression of the dispersive wave generation.
SCG with the 804nm pump shows quite a different picture (see Fig. 9(b) and 9(d)). Three short wavelength dispersive waves were clearly generated due to the presence of the higher order dispersion near the pump wavelength. Octave-spanning spectrum was generated at a peak power of ~1kW. Relative group delays and phase versus wavelength of SCF2 are plotted in Fig. 11(a). The presence of the second zero dispersion wavelength λ02 allows the second set of group velocity and phase machining conditions at the longer wavelength side, which shows up as lines at the top of Fig. 11(b). The dispersive wave wavelengths are plotted against the corresponding soliton wavelengths in Fig. 12(a) for the 1st, 2nd and 3rd solitons respectively. The fit to group velocity matching condition is excellent for all three solitons. Soliton wavelengths for the 1st, 2nd and 3rd solitons are plotted in Fig. 12(b) along with their respective peak spectral densities. Peak spectral densities of the three dispersive waves are also plotted in Fig. 12(b). The powers of the three solitons are almost the same and remain largely the same for different peak pump powers. The reduction of the soliton spectral density for pump powers >~4kW in Fig. 12(b) is again from power loss during propagation. This again indicates that power of the fundamental solitons generated from the soliton fission process is largely independent of peak pump power as well as the sequence of its generation. Furthermore, the spectral width of the solitons are also about the same when plotted against frequency (see Fig. 12(c)), implying that all the solitons generated from the fission process are fairly consistent, independence on pump power and the order by which it is generated. Recently Podlipensky et al have studied bound soliton pairs, demonstrating that two solitons can form bound state where they can stably co-propagate even when they undergo red shifts by intra pulse Raman scattering . It is interesting to wonder if three identically spaced solitons with identical powers shown in Fig. 12(c) may suggest some level of interactions among the solitons. Cristiani et al simulated dispersive wave generation and pointed out that the 1st fundamental soliton and 1st dispersive wave are generated at the first temporal compression point of the higher order soliton formed by the spectrum-broadened pump pulse . Our results may suggest that there may be stronger interactions among the solitons during soliton fission. The slow-down in wavelength shifts at higher peak pump powers in Fig. 12(b) is from the soliton power loss during propagation. Wavelength shift deceleration by a loss of power due to radiations of energy to phonons in a Raman process is recently reported in . This loss of soliton power during propagation below λ02 certainly limited the growth of the longer wavelength edge in SCF2. The spectral densities of the dispersive waves show signs of saturation at higher peak pump power levels in this case in Fig. 12b.
Dependence of SCG in SCF2 on polarization was also measured with the 1045nm pump. This is plotted in Fig. 13. The large birefringence of the SCF2 leads to the 1st soliton wavelength to vary from 1050nm to 1200nm at 2.8kW when polarization angle being varied by 90 degree. Some interesting interactions between solitons at 45 degree polarization angle can also be seen where spectral spacing between solitons was minimal.
We have demonstrated efficient SCG in highly nonlinear silica SCFs. We have further experimentally confirmed that continued blue shift of the shorter wavelength edge of the SCG is a result of group-velocity-matched process while the initial dispersive wave generation process is phase-matched to the corresponding soliton. Our experimental study has found that the fundamental solitons generated from the fission process have constant characteristics in terms of power and spectral features, independent of pump powers and sometimes the orders that they are generated. Furthermore, while the soliton wavelength undergoes continuous red shift by Raman scattering, they continuously lose power to longer wavelength dispersive waves where phase-matching to this long wavelength dispersive waves is allowed and, otherwise, maintain a constant power where this phase-matching to long wavelength dispersive waves is not allowed. Furthermore, we have observed significant tuning of soliton wavelength shift by pump polarization change and interesting soliton interactions at 45 degree pump polarization angle. These are new observations to the best of our knowledge and may lead to deeper understanding of the physical processes behind the soliton fission process. Total suppression of the short wavelength dispersive wave generation is also demonstrated in the absence of the dispersion slope at the pump wavelength. We have demonstrated very efficient octave-spanning SCG with peak power as low as 1.5kW at ~1µm and 1kw at ~800 nm thanks to high nonlinearity, low propagation loss and very low splice loss to standard single mode fibers. These new improvements can significantly reduce the complexity of fiber-based frequency-stabilized combs for optical clocks by enabling fceo stabilization of mode-locked fiber lasers without further amplification.
The authors would like to thank Jinzhou Xu, Otho Ulrich, and Gyu Cho for providing IMRA lasers FCPA D400 and Femtolite F-100.
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