Abstract

Based on induced modulation instability, we present a numerical study on harnessing rogue wave for supercontinuum generation in cascaded photonic crystal fibers. By selecting optimum modulation frequency, we achieve supercontinuum with a great improvement on spectrum stability when long-pulse is used as the pump. In this case, rogue wave can be obtained in the first segmented photonic crystal fiber with one zero dispersion wavelength in a controllable manner. Numerical simulations show that spectral range and flatness can be regulated in an extensive range by cascading a photonic crystal fiber with two zero dispersion wavelengths. Some novel phenomena are observed in the second segmented photonic crystal fiber. When the second zero dispersion wavelength is close to the first one, rogue wave is directly translated into dispersion waves, which is conducive to the generation of smoother supercontinuum. When the second zero dispersion wavelength is far away from the first one, rogue wave is translated into the form of fundamental soliton steadily propagating in the vicinity of the second zero dispersion wavelength. Meanwhile, the corresponding red-shifted dispersion wave is generated when the phase matching condition is met, which is beneficial to the generation of wider supercontinuum. The results presented in this work provide a better application of optical rogue wave to generate flat and broadband supercontinuum in cascaded photonic crystal fibers.

© 2017 Optical Society of America

1. Introduction

Supercontinuum (SC) generation in optical fibers has attracted a multitude of attention as a significant research area in nonlinear optics over the last decades. Since the first report by Alfano and Shapiro [1], SC has been applied in such diverse fields as optical frequency metrology [2], pulse compression [3], optical coherent tomography [4] and so on. Up to now, numerical simulations and experiments both have shown that SC can be obtained by using unamplified pump pulses of durations ranging from femtosecond to picosecond, nanosecond, and even continuous wave (CW) [5]. As is well known, the distinguishing features of SC are related to the spectral stability, spectral range and spectral flatness, all of which are vital to promote the technical applications of SC. Spectral stability can be largely enhanced by using femtosecond pump pulse, while such short pulse requires specialized dispersion control and is sensitive to perturbations [6]. Furthermore, soliton-related dynamics play a dominate role in the process of femtosecond pulse evolution, which go against the generation of smooth SC [7,8]. On the other hand, SC generated with longer pump pulse has some advantages, including higher spectral power density and smoother spectrum, and hence it can be better utilized in a wide range [9,10].

With a long pulse as the pump, the generated spectrum suffers from shot-to-shot variations on account of modulation instability (MI), which is initiated spontaneously from stochastic noise [11]. Noise-seeded MI dynamics dominate the initial stage of spectral broadening through phase-matched four-wave mixing (FWM). High-order dispersion and stimulated Raman scattering (SRS) play an important role in further modifying the nonlinear dynamics [12–14]. The perturbed dynamics drive the emergence of optical rogue wave (RW) – statistically rare event associated with extreme red-shift and high-intensity of long-wavelength Raman soliton pulse [15,16]. Due to the importance of RW to SC generation, there has been a lot of work done related to the regulation of RW in the process of SC generation. For example, Solli et al. experimentally investigated the transition between MI gain and induced soliton fission in nonlinear fiber, which produced SC spectra displaying persistent, fine modulation from seeding-induced noise reduction [17]. A. Kudlinski et al. demonstrated a significant reduction of SC pulse-to-pulse fluctuations in the visible wavelength range by using a photonic crystal fiber (PCF) with longitudinally tailored guidance properties [18]. Q. Li et al. showed that the RW occurring in SC generation can exhibit high-degree of temporal coherence and pulse-to-pulse intensity stability by selecting appropriate CW-trigger wavelengths [19]. Sørensen et al. numerically investigated that seeding with the optimum modulation frequency near MI gain peak can give a considerable improvement on the spectral stability [20]. Therefore, spectral stability can be dramatically improved by changing the incident conditions, which is in favor of RW utilization, as shown in Ref [21]. However, high-intensity RW located at the long wavelength leads to the uneven distribution of total energy [21–23]. Note that spectral flatness and range would be influenced to a great degree. Although many methods have been applied for the improvement of RW stability, little work is done on harnessing RW to generate smooth and wide SC. The advent of PCFs provides a new possibility because of their single-mode operation over a wide wavelength range as well as controllable dispersion and nonlinear properties [24,25]. Meanwhile, the zero dispersion wavelength (ZDW) can be shifted to the desired location by adjusting the geometry structure of a PCF. Previously, cascaded fibers were mainly used to regulate spectral shape and range [26,27]. However, there is not yet an investigation on harnessing RW for SC generation in cascaded fibers. In this paper, we present a fiber-cascading method to deal with the uneven energy distribution and accordingly obtain a SC spectrum with large-bandwidth and high-flatness. Here, the first segmented PCF with one ZDW is used to generate RW in a controllable manner by induced MI. Then another PCF with two ZDWs is chosen as the second segmented fiber to change the propagation state of RW. Interestingly, RW can be converted into other forms such as dispersion waves (DWs) and fundamental soliton by adjusting the ZDW position of the second segmented fiber. The energy conversion can give rise to SC spectra with different bandwidths and flatness.

2. Propagation model and modulation instability gain

2.1 Propagation model

It is well known that the generalized nonlinear Schrödinger equation (GNLSE) is suitable for modeling propagation of broadband unidirectional fields, which gives a good understanding of RW nonlinear dynamics [5,20,28]. The GNLSE reads:

A(z,T)z=k2ik+1βkk!kATk+iγ(1+iω0T)×(A(z,T)[+R(T)|A(z,TT)|2dT+iΓR(z,T)]).
Here A(z,T) is the field envelope.Tand z present the time in a reference frame moving at the pulse group velocity and longitudinal coordinate along the fiber axis, respectively.βk is the kth-order dispersion coefficient at the central frequencyω0, and γ is the nonlinear coefficient. The nonlinear response function R(t)=fRhR(t)+(1fR)σ(t) includes the delayed Raman contribution and the instantaneous Kerr-contribution [3,5]. We usefR=0.18and hR determined from the fused silica Raman cross-section [5]. High-order dispersion as well as nonlinear effects such as self-phase modulation (SPM) and SRS have non-ignorable impact on the pulse propagation dynamics, while the fiber loss is neglected. Noise is included in the frequency domain through a one photon per mode spectral density on each spectral discretization bin, and via the term ΓR which describes thermally-driven spontaneous Raman scattering [3,5,28]. The specific value of the noise amplitude is not critical as it only influences the RW generation rate [15,19]. The noise amplitude is chosen to be 10-5 of the pump amplitude.

In this paper, RW dynamics are studied under the effect of induced MI, and hence we model a Gaussian pump pulse (T0 = 500 fs, λ0 = 1060 nm) and a seed pulse propagating in cascaded PCFs. The modulated Gaussian input pulse envelope is:

A(0,T)=(Pp+a0Ppei2πfmodT)exp(T2/2T02),
wherePp=150Wis the peak power of the pump, and the power of the seed is defined as a02Pp. a0=0.1is the modulation depth. The seed is temporally overlapped with the pump, and gives a frequency offsetfmod, wherefmod>0corresponds to seeding at a wavelength shorter than that of the pump. The cascaded PCF consists of two parts, namely, the first for a 15-m-long single ZDW PCF1 and the second for a 10-m-long dual ZDW PCF. In order to illustrate the effect of ZDW position on RW evolution, we select PCF2 and PCF3 as the second segmented fiber, respectively. In addition, the OH-absorption of these PCFs is ignored because their OH-ion level is less than one part in one hundred million [5]. The dispersion curves and relative group delay curves of PCF1, PCF2, and PCF3 as a function of the wavelength are illustrated in Fig. 1. The PCF1 has one ZDW located at 1055 nm [28]. The dual ZDW PCF2 has two ZDWs located at 1053 nm and 1289 nm, respectively. By reducing the core size of PCF2, we obtain the PCF3 with two ZDWs located at 1054 nm and 1105 nm.

 figure: Fig. 1

Fig. 1 (a) The dispersion profiles and (b) the related group delay curves of PCF1 (blue curve), PCF2 (green curve), and PCF3 (red curve) as a function of the wavelength.

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2.2 Modulation instability gain

We take the nonlinear response function and high-order dispersion into account to obtain the MI gain g(Ω), which is calculated for the pump power alone [24,29]:

g(Ω)=Im{Δko±Δke+2γPpR˜(Ω)Δke}.
Here Ω is the modulation frequency, and R˜(Ω) is the Raman response for silica.Δko and Δke are sums over odd and even order derivatives of the propagation constant β, respectively:
Δko=m=1β¯2m+1(2m+1)!Ω2m+1,Δke=m=1β¯2m2m!Ω2m,
where β¯m=mβ/Ωm|Ω=0. PCF1, PCF2 and PCF3 have the same nonlinear parameter ofγ=0.015W1m1. Figure 2 shows how the MI gain spectrum changes with the modulation frequency at pump power.

 figure: Fig. 2

Fig. 2 The related MI gain spectra of PCF1 (blue curve), PCF2 (green curve), and PCF3 (red curve) as a function of seed frequency offset.

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Because RW generation is unstable with noise-seeded MI, in order to ensure a deterministic pulse breakup, the method of providing a seed within the MI gain spectrum is proposed. By pumping highly nonlinear fibers in the anomalous dispersion regime, the reduction of pulse-to-pulse fluctuations has been obtained with a single seed in the simulation [30] and experiment [16]. Besides, Genty et al. have showed that seeding with the modulation frequency at approximately three-fifths of MI gain peak can give an optimum improvement of SC stability [28]. Remarkably, our group has shown that 6 THz is the optimum modulation frequency for PCF1 under the same input condition [21]. In 2009, B. Kibler et al. demonstrated soliton and RW statistics during SC generation in PCF with two ZDWs [31]. According to the Ref [16,30,32], spectral stability still can be improved with a single seed when pumping PCF2 and PCF3 in the anomalous dispersion regime. Because the MI gain peak of PCF1 is close to those of PCF2 and PCF3, 6 THz should also approach the corresponding optimum modulation frequencies, which can ensure the SC spectrum with high stability in PCF2 and PCF3. Therefore, we adopted 6 THz as the modulation frequency in the process of SC generation in cascaded PCFs.

3. Numerical results in cascaded PCFs

To harness RW in the process of SC generation, we simulate the propagation of the pump and the seed launched into the anomalous dispersion regime of cascaded PCFs. Here, providing a 6 THz seed can improve the spectral stability and reduce the pulse-to-pulse fluctuations to a considerable extent in cascaded PCFs. Therefore, we just present the simulations of individual events with the same input condition in this section. In addition, all the intensity plots use the same logarithmic density scale in order to better analyze the pulse evolution under different conditions.

3.1 Harness RW in PCF1 cascaded with PCF2

Figure 3 presents the dynamical evolution of input pulse in cascaded PCF, which consists of a 15-m-long single ZDW PCF1 and a 10-m-long dual ZDW PCF2. Figure 3(a2) shows the typical temporal evolution. The related pulse shapes at the propagation distance of 0 m, 15 m, and 25 m are plotted in Fig. 3(a1). In the first segmented PCF, the breakup of input pulse is initiated by the FWM process, which results from induced MI. Subsequently, a train of fundamental solitons with different durations and peak powers are ejected after propagating a few meters. The most powerful fundamental soliton undergoes the strongest Raman self-frequency shift under the effect of SRS. With the propagation of fundamental solitons to a longer wavelength, the dispersion increases and the group velocity decreases. Due to the discrepancies in group velocities of solitons with different power levels, collisions occur between these solitons. Significant energy exchange associated with the collisions yields one higher-energy RW and a lower-amplitude residual pulse. Besides, the collision between DWs and fundamental solitons is another important mechanism for the generation of RW. In the spectral evolution, a single set of sidebands is amplified by the FWM effect at about 2 m in Fig. 3(b2). Next, distinct RW emerges and the related spectral asymmetry is enhanced as the RW undergoes the Raman self-frequency shift.

 figure: Fig. 3

Fig. 3 In the propagation medium of a 15-m-long single ZDW PCF1 cascaded with a 10-m-long dual ZDW PCF2, we illustrate (a1) the temporal intensity at the propagation distance of 0 m (blue curve), 15 m (green curve), 25 m (red curve), (b1) the output spectrum intensity, as well as the (a2) temporal and (b2) spectral evolution as the function of fiber length, where the red dotted line presents the cascaded position of two PCFs.

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When the propagation distance increases to 15 m, the RW enters into the anomalous dispersion regime of the second segmented PCF. Obviously, the dispersion slope and related group velocity slope that RW experiences change due to the different dispersion parameters from those of PCF1. These changes are indicated by a bend after 15 m during temporal evolution of RW, as shown in Fig. 3(a2). In the spectral domain, the RW has a larger red-shift rate resulting from Raman induced frequency shift (RIFS). In this process, the intensity of RW is very unstable since multiple collisions occur under the effect of SRS and high-order dispersion. When the propagation distance increases to 18 m, a large proportion of energy of RW is effectively converted to the new generated component, namely, red-shifted dispersion wave (R-DW). As the central frequency of RW gradually approaches the second ZDW with negative dispersion slop, the wavelength of R-DW begins to blue shift with respect to the wavelength of RW according to phase matching condition. When meeting the balance between Raman self-frequency shift and spectral recoiling from the amplification of R-DW, RW ceases to shift in the vicinity of the second ZDW. Unexpectedly, RW eventually evolves into the form of a fundamental soliton due to energy dissipation. In addition, multiple collisions occur in the second segmented fiber owing to these fundamental solitons with different group velocities, which lead to the generation of a new RW at 21 m. When increasing the length of the second segmented PCF to a certain degree, the new RW will be translated into another fundamental soliton due to the existence of the second ZDW. At the same time, the corresponding R-DW is radiated out when phase matching condition is met. In cascaded fiber, 6 THz as the optimum modulation frequency is sufficient to achieve spectral stability. According to the Ref [16,30], the fluctuations at the edge of SC can be significantly reduced with a single seed when pumping in the anomalous dispersion region. Hence, the generation of DW is able to maintain the initial stability with a 6 THz seed.

Furthermore, the intriguing phenomenon that RW is translated into the form of fundamental soliton can also be observed in Fig. 3(a1). The input pulse is with the shape of a modulated Gaussian, and thus the normalized peak intensity is relatively low. When the propagation distance increases to 15 m, the first RW emerges at the time delay of 11.5 ps, whose intensity is more than twice that of the average amplitude of the significant wave height. When the propagation distance reaches 25 m, the first RW is translated into the form of fundamental soiton by radiating its partial energy to R-DW. However, there is still a new RW obtained at the time delay of 15 ps since multiple collisions occur again in the second segmented PCF. The output spectrum is presented in Fig. 3(b1), which has a relatively large bandwidth and complex frequency components.

3.2 Harness RW in PCF1 cascaded with PCF3

When the PCF3 as the second segmented PCF shown in Fig. 4, temporal and spectral evolution have some evident differences compared with those shown in Fig. 3. With 6 THz modulation frequency, the evolution of input pulse is controllable in the first segmented PCF. As a result, the output pulse shape at the end of the first segmented PCF in Fig. 4 is similar to that in Fig. 3. Accordingly, the RW with a 11.5 ps time delay is found at 15 m in Fig. 4(a1).

 figure: Fig. 4

Fig. 4 In the propagation medium of a 15-m-long single ZDW PCF1 cascaded with a 10-m-long dual ZDW PCF3, we illustrate (a1) the temporal intensity at the propagation distance of 0 m (blue curve), 15 m (green curve), 25 m (red curve), (b1) the output spectrum intensity, as well as the (a2) temporal and (b2) spectral evolution as the function of fiber length, where the red dotted line presents the cascaded position of two PCFs.

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When the RW enters the second segmented PCF, its time delay has a large variation in Fig. 4(a2) because of the change of dispersion profile. At the same time, the energy of RW is radiated out as the form of DWs, which results from the RW directly located at the normal dispersion regime of the second segmented PCF. Besides, there are some fundamental solitons directly translated into the form of DWs based on the same reason. With the increase of propagation distance, the new generated DWs derived from the RW have some special features such as the gradually increasing group velocities, as shown in Fig. 4(a2). In this case, these DWs with increasing velocities can eventually catch up with the other fundamental solitons at the anomalous dispersion regime, which will play a non-ignorable role in changing the shapes of these fundamental solitons. Subsequently, some remarkable variation is observed, where the time delay of these fundamental solitons begins to be sporadic. Such phenomenon indicates that these fundamental solitons at the anomalous dispersion regime also are translated into the DWs in the end. Soliton-related dynamics are the main factors that affect spectral flatness. While in this cascaded PCF, the fundamental solitons and RW generated in the first segmented PCF are all converted into the form of DWs at the end of the second segmented PCF, as illustrated in Fig. 4(a1). Therefore, this cascaded PCF provides the possibility to obtain the SC with much smoother spectrum by harnessing RW. The special phenomenon can also be seen from Fig. 4(b1), where smoother SC is generated at the expense of bandwidth compared with that in Fig. 3(b1).

4. Impact of cascading

In order to better present the advantages of cascaded PCF on harnessing RW, we plot the output spectrograms at different PCFs in Fig. 5. Figure 5(a) shows the output spectrogram at the medium of 15-m-long PCF1, where a high-intensity RW is generated at the longest wavelength due to multiple collisions. When the length of PCF1 increases to 25 m, there is a new RW generated in Fig. 5(b), which does harm to spectral flatness. At the same time, the first-ejected RW occurs red-shift resulting from Raman effect. Nevertheless, the red-shifted range of RW is not big, which has little impact on the spectral expansion. Figure 5(c) shows the output spectrogram of the pulse propagating in 15-m-long PCF1 cascaded with 10-m-long PCF2. Due to the existence of the second ZDW in PCF2, the RW generated in Fig. 5(a) is translated into a fundamental soliton in Fig. 5(c). Moreover, R-DW is radiated from the RW at the wavelength that meets phase matching condition. However, there are still other fundamental solitons with different group velocities and powers located at the anomalous dispersion regime of the second segmented PCF. Consequently, multiple collisions occur again, which lead to a new RW generated in Fig. 5(c). On this occasion, SC spectrum has a much wider bandwidth and more frequency components compared with that shown in Fig. 5(b). Figure 5(d) shows the output spectrogram of the pulse propagating in 15-m-long PCF1 cascaded with 10-m-long PCF3. There isn’t distinct soliton shape discovered under this condition, which leads to the SC with much smoother spectrum in contrast with those in Figs. 5(b) and 5(c). By comparing among the four spectrograms, one can clearly see that cascaded PCFs are beneficial to the generation of SC with different spectral ranges and flatness.

 figure: Fig. 5

Fig. 5 The output spectrograms at the medium of (a) 15-m-long PCF1, (b) 25-m-long PCF1, (c) a 15-m-long PCF1 cascaded with a 10-m-long PCF2, and (d) a 15-m-long PCF1 cascaded with a 10-m-long PCF3, respectively.

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Figure 6 shows the evolution of normalized peak intensity as a function of fiber length in 25-m-long PCF1, 15-m-long PCF1 cascaded with 10-m-long PCF2, and 15-m-long PCF1 cascaded with 10-m-long PCF3, respectively. In Fig. 6, it is clear that the normalized peak intensity at certain points of PCFs is much higher than that at the output. According to the Ref [33], such phenomenon suggests that the relatively high peak intensity events correspond to the collisions. At the first 15 m of three PCFs, the evolution of peak power is similar because they all adopt the PCF1 as the propagation medium under the same modulation frequency. In this stage, the evolution of peak intensity begins to present very sharp variation until a length of about 5.5 m. With the increase of propagation distance, the relatively high peak intensity emerges at about 11.5 m, which corresponds to the position of soliton collisions. Shortly afterwards, the peak intensity is quickly decreased within a very short fiber length. For Figs. 6(a) and 6(b), the output normalized peak intensities are both beyond the value of 2, which shows that RW still exists in the two kinds of PCFs. Interestingly, there are some new intense crests emerging from 15 m to 21 m in Fig. 6(b). In this case, the RW with high-intensity begins to red-shift under the effect of SRS when entering the second segmented PCF. Since the RW is very unstable in the process of red-shift, multiple collisions occur between the RW and DWs, which leads to new intense crests generated from 15 m to 18 m. When the RW reaches the vicinity of the second ZDW, the corresponding peak intensity is gradually reduced because part of its energy is transferred to R-DW. The generation of R-DW is beneficial to obtain a broader SC spectrum. While, there is still a new intense crest generated at 21 m because of soliton collisions, which indicates the emergence of a new RW. For Fig. 6(c), the normalized peak intensity is decreased at a very rapid rate when entering into the second segmented PCF. During the pulse propagating at the second segmented PCF, the normalized peak intensity of the pulse has remained at about the value of 1. Such low peak intensity indicates that there are only a number of DWs generated in this cascaded PCF, which is beneficial to the generation of a smoother SC spectrum. Therefore, one can obtain SC with much smoother and wider spectrum by harnessing RW in cascaded PCFs.

 figure: Fig. 6

Fig. 6 The evolution of normalized peak intensity as a function of fiber length in (a) 25-m-long PCF1, (b) 15-m-long PCF1 cascaded with 10-m-long PCF2, and (c) 15-m-long PCF1 cascaded with 10-m-long PCF3, respectively. The relatively high peak intensity events correspond to the collisions.

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5. Statistics with spectral bandwidth

From Fig. 1(a), we can learn that the short wavelength ZDWs of PCF2 and PCF3 are extremely close while the long wavelength ZDWs are very different. Therefore, the position of the second ZDW is crucial to the behavior of spectral range and flatness. In Fig. 7, we show the output spectral variation of 100 individual simulations when only changing the position of the second ZDW in the second segmented PCF. The bandwidth is defined as the range of 30 dB down from the peak intensity. Thus SC bandwidth can be obtained by subtracting the shortest wavelength from the longest wavelength.

 figure: Fig. 7

Fig. 7 The evolution of the shortest wavelength and the longest wavelength of 100 individual simulations (gray) as a function of the second ZDW in the second segmented PCF. The red line with dot presents the average longest wavelength, while the blue line with asterisk presents the average shortest wavelength.

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From Fig. 7, one can see that for the shortest and longest wavelengths in every fiber structure, the gray range is narrow on behalf of 100 numerical simulations. In other words, the value of each simulation is relatively close, which further proves that providing a single seed can improve the spectral stability and reduce the noise effect to a considerable extent in cascaded PCFs. By comparison, the shortest wavelength is nearly constant along with the increase of the second ZDW, which results from stable location of the first ZDW. On the contrary, the longest wavelength has a great variation with the increase of the second ZDW. When the second ZDW is less than 1180 nm, the longest wavelengths are located around 1220 nm, and such phenomena are similar to that in Fig. 4. In this case, because RW generated in the first segmented PCF enters into the normal dispersion regime of the second segmented PCF, it is directly translated into DWs, which makes SC bandwidth kept in a certain range. When the second ZDW increases from 1180 nm to 1460 nm, the longest wavelength is gradually increased since the generation of R-DW facilitates the spectral expansion. While, when the second ZDW increases from 1460 nm to 1600 nm, the longest wavelength is quickly decreased since the second ZDW is far away from pump wavelength. In this case, RW still has some red-shift under the effect of SRS, while it needs a relatively long fiber length to reach the second ZDW. With the increase of propagation distance, it is also translated into fundamental soliton in the end because of the energy consumption. As a result, the RW doesn’t have enough energy to reach the second ZDW and the corresponding R-DW can’t be ejected at a finite PCF length, which limits spectral expansion. When the second ZDW exceeds 1600 nm, the longest wavelengths are steadily located around 1285 nm. In this case, RW just red-shift within a small range when the second ZDW is so far away from the pump pulse. As a consequence, the spectral evolution is similar to that in the PCF only with the first ZDW. In a word, spectrum bandwidth can be changed by harnessing RW in cascaded PCFs.

6. Conclusion

In this work, we have numerically shown how rogue wave can be harnessed in cascaded photonic crystal fiber for the generation of supercontinuum with much broader and smoother spectrum. In the first segmented photonic crystal fiber with one zero dispersion wavelength, rogue wave can be generated in a controlled manner with a 6 THz seed, which contributes to the improvement of spectral stability. In the second segmented photonic crystal fiber with two zero dispersion wavelengths, rogue wave can be translated into other forms, which can deal with the uneven distribution of total energy. In addition, spectral bandwidth and flatness can be changed over a wide range by cascading different photonic crystal fibers. What’s more, the negative effect of rogue wave on spectral expansion and flatness can also be reduced to a considerable extent when propagating in fiber system because of the energy conversion in cascaded photonic crystal fiber. These numerical simulations and analysis presented here may open up a new possibility of generating wide and flat supercontinuum in cascaded photonic crystal fiber by harnessing rogue wave.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 61275137).

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23. J. Peng, N. Tarasov, S. Sugavanam, and D. Churkin, “Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser,” Opt. Express 24(19), 21256–21263 (2016). [CrossRef]   [PubMed]  

24. P. Russell, “Photonic Crystal Fibers,” Science 299(5605), 358–362 (2003). [CrossRef]   [PubMed]  

25. J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003). [CrossRef]   [PubMed]  

26. T. Sylvestre, A. Vedadi, H. Maillotte, F. Vanholsbeeck, and S. Coen, “Supercontinuum generation using continuous-wave multiwavelength pumping and dispersion management,” Opt. Lett. 31(13), 2036–2038 (2006). [CrossRef]   [PubMed]  

27. J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011). [CrossRef]  

28. G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009). [CrossRef]  

29. M. H. Frosz, S. T. Sørensen, and O. Bang, “Nanoengineering of photonic crystal fibers for supercontinuum spectral shaping,” J. Opt. Soc. Am. B 23(8), 1692–1699 (2006). [CrossRef]  

30. G. Genty and J. M. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45(11), 1331–1335 (2009). [CrossRef]  

31. B. Kibler, C. Finot, and J. M. Dudley, “Soliton and rogue wave statistics in supercontinuum generation in photonic crystal fibre with two zero dispersion wavelengths,” Eur. Phys. J. Spec. Top. 173(1), 289–295 (2009). [CrossRef]  

32. K. Hammani, C. Finot, R. Habert, A. Mussot, and A. Kudlinski, “Active reduction of fluctuations in fourth-order modulation instability,” Opt. Lett. 37(20), 4305–4307 (2012). [CrossRef]   [PubMed]  

33. A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17(19), 17010–17015 (2009). [CrossRef]   [PubMed]  

References

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  1. R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
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  2. B. Washburn and N. Newbury, “Phase, timing, and amplitude noise on supercontinua generated in microstructure fiber,” Opt. Express 12(10), 2166–2175 (2004).
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  3. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
    [Crossref]
  4. D. L. Marks, A. L. Oldenburg, J. J. Reynolds, and S. A. Boppart, “Study of an ultrahigh-numerical-aperture fiber continuum generation source for optical coherence tomography,” Opt. Lett. 27(22), 2010–2012 (2002).
    [Crossref] [PubMed]
  5. G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012)
  6. J. M. Dudley and J. R. Taylor, Supercontinuum Generation In Optical Fibers (Cambridge University, 2010)
  7. S. Zhao, H. Yang, N. Chen, X. Fu, and C. Zhao, “Soliton trapping of dispersive waves in photonic crystal fiber with three zero-dispersion wavelengths,” IEEE Photonics J. 7(5), 7102701 (2015).
  8. W. Wang, H. Yang, P. Tang, C. Zhao, and J. Gao, “Soliton trapping of dispersive waves in photonic crystal fiber with two zero dispersive wavelengths,” Opt. Express 21(9), 11215–11226 (2013).
    [Crossref] [PubMed]
  9. M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
    [Crossref]
  10. C. Lin and R. H. Stolen, “New nanosecond continuum for excited-state spectroscopy,” Appl. Phys. Lett. 28(4), 216–218 (1976).
    [Crossref]
  11. V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: The beginning,” Physica D 238(5), 540–548 (2009).
    [Crossref]
  12. S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. S. J. Russell, “Supercontinuum generation by stimulated Raman scattering and parametric four-wave mixing in photonic crystal fibers,” J. Opt. Soc. Am. B 19(4), 753–764 (2002).
    [Crossref]
  13. S. Kobtsev and S. Smirnov, “Modelling of high-power supercontinuum generation in highly nonlinear, dispersion shifted fibers at CW pump,” Opt. Express 13(18), 6912–6918 (2005).
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  14. E. J. R. Kelleher, J. C. Travers, S. V. Popov, and J. R. Taylor, “Role of pump coherence in the evolution of continuous-wave supercontinuum generation intiated by modulation instability,” J. Opt. Soc. Am. B 29(3), 502–512 (2012).
    [Crossref]
  15. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
    [Crossref] [PubMed]
  16. D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
    [Crossref] [PubMed]
  17. D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105(23), 233902 (2010).
    [Crossref] [PubMed]
  18. A. Kudlinski, B. Barviau, A. Leray, C. Spriet, L. Héliot, and A. Mussot, “Control of pulse-to-pulse fluctuations in visible supercontinuum,” Opt. Express 18(26), 27445–27454 (2010).
    [Crossref] [PubMed]
  19. Q. Li, F. Li, K. K. Y. Wong, A. P. T. Lau, K. K. Tsia, and P. K. A. Wai, “Investigating the influence of a weak continuous-wave-trigger on picosecond supercontinuum generation,” Opt. Express 19(15), 13757–13769 (2011).
    [Crossref] [PubMed]
  20. S. T. Sørensen, C. Larsen, U. Møller, P. Moselund, C. L. Thomsen, and O. Bang, “Influence of pump power and modulation instability gain spectrum on seeded supercontinuum and rogue wave generation,” J. Opt. Soc. Am. B 29(10), 2875–2885 (2012).
    [Crossref]
  21. S. Zhao, H. Yang, N. Chen, and C. Zhao, “Controlled generation of high-intensity optical rogue waves by induced modulation instability,” Sci. Rep. 7, 39926 (2017).
    [Crossref] [PubMed]
  22. K. Hammani, C. Finot, J. M. Dudley, and G. Millot, “Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers,” Opt. Express 16(21), 16467–16474 (2008).
    [Crossref] [PubMed]
  23. J. Peng, N. Tarasov, S. Sugavanam, and D. Churkin, “Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser,” Opt. Express 24(19), 21256–21263 (2016).
    [Crossref] [PubMed]
  24. P. Russell, “Photonic Crystal Fibers,” Science 299(5605), 358–362 (2003).
    [Crossref] [PubMed]
  25. J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
    [Crossref] [PubMed]
  26. T. Sylvestre, A. Vedadi, H. Maillotte, F. Vanholsbeeck, and S. Coen, “Supercontinuum generation using continuous-wave multiwavelength pumping and dispersion management,” Opt. Lett. 31(13), 2036–2038 (2006).
    [Crossref] [PubMed]
  27. J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011).
    [Crossref]
  28. G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
    [Crossref]
  29. M. H. Frosz, S. T. Sørensen, and O. Bang, “Nanoengineering of photonic crystal fibers for supercontinuum spectral shaping,” J. Opt. Soc. Am. B 23(8), 1692–1699 (2006).
    [Crossref]
  30. G. Genty and J. M. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45(11), 1331–1335 (2009).
    [Crossref]
  31. B. Kibler, C. Finot, and J. M. Dudley, “Soliton and rogue wave statistics in supercontinuum generation in photonic crystal fibre with two zero dispersion wavelengths,” Eur. Phys. J. Spec. Top. 173(1), 289–295 (2009).
    [Crossref]
  32. K. Hammani, C. Finot, R. Habert, A. Mussot, and A. Kudlinski, “Active reduction of fluctuations in fourth-order modulation instability,” Opt. Lett. 37(20), 4305–4307 (2012).
    [Crossref] [PubMed]
  33. A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17(19), 17010–17015 (2009).
    [Crossref] [PubMed]

2017 (1)

S. Zhao, H. Yang, N. Chen, and C. Zhao, “Controlled generation of high-intensity optical rogue waves by induced modulation instability,” Sci. Rep. 7, 39926 (2017).
[Crossref] [PubMed]

2016 (1)

2015 (1)

S. Zhao, H. Yang, N. Chen, X. Fu, and C. Zhao, “Soliton trapping of dispersive waves in photonic crystal fiber with three zero-dispersion wavelengths,” IEEE Photonics J. 7(5), 7102701 (2015).

2013 (1)

2012 (3)

2011 (2)

Q. Li, F. Li, K. K. Y. Wong, A. P. T. Lau, K. K. Tsia, and P. K. A. Wai, “Investigating the influence of a weak continuous-wave-trigger on picosecond supercontinuum generation,” Opt. Express 19(15), 13757–13769 (2011).
[Crossref] [PubMed]

J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011).
[Crossref]

2010 (2)

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105(23), 233902 (2010).
[Crossref] [PubMed]

A. Kudlinski, B. Barviau, A. Leray, C. Spriet, L. Héliot, and A. Mussot, “Control of pulse-to-pulse fluctuations in visible supercontinuum,” Opt. Express 18(26), 27445–27454 (2010).
[Crossref] [PubMed]

2009 (5)

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: The beginning,” Physica D 238(5), 540–548 (2009).
[Crossref]

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[Crossref]

A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17(19), 17010–17015 (2009).
[Crossref] [PubMed]

G. Genty and J. M. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45(11), 1331–1335 (2009).
[Crossref]

B. Kibler, C. Finot, and J. M. Dudley, “Soliton and rogue wave statistics in supercontinuum generation in photonic crystal fibre with two zero dispersion wavelengths,” Eur. Phys. J. Spec. Top. 173(1), 289–295 (2009).
[Crossref]

2008 (2)

K. Hammani, C. Finot, J. M. Dudley, and G. Millot, “Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers,” Opt. Express 16(21), 16467–16474 (2008).
[Crossref] [PubMed]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
[Crossref] [PubMed]

2007 (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

2006 (3)

2005 (1)

2004 (1)

2003 (2)

P. Russell, “Photonic Crystal Fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
[Crossref] [PubMed]

2002 (2)

2001 (1)

M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
[Crossref]

1976 (1)

C. Lin and R. H. Stolen, “New nanosecond continuum for excited-state spectroscopy,” Appl. Phys. Lett. 28(4), 216–218 (1976).
[Crossref]

1970 (1)

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[Crossref]

Alfano, R. R.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[Crossref]

Bang, O.

Barviau, B.

Boppart, S. A.

Chau, A. H. L.

Chen, N.

S. Zhao, H. Yang, N. Chen, and C. Zhao, “Controlled generation of high-intensity optical rogue waves by induced modulation instability,” Sci. Rep. 7, 39926 (2017).
[Crossref] [PubMed]

S. Zhao, H. Yang, N. Chen, X. Fu, and C. Zhao, “Soliton trapping of dispersive waves in photonic crystal fiber with three zero-dispersion wavelengths,” IEEE Photonics J. 7(5), 7102701 (2015).

Churkin, D.

Coen, S.

Cotlet, M.

M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
[Crossref]

De Schryver, F. C.

M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
[Crossref]

Desevedavy, F.

J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011).
[Crossref]

Douay, M.

Dudley, J.

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[Crossref]

Dudley, J. M.

G. Genty and J. M. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45(11), 1331–1335 (2009).
[Crossref]

B. Kibler, C. Finot, and J. M. Dudley, “Soliton and rogue wave statistics in supercontinuum generation in photonic crystal fibre with two zero dispersion wavelengths,” Eur. Phys. J. Spec. Top. 173(1), 289–295 (2009).
[Crossref]

K. Hammani, C. Finot, J. M. Dudley, and G. Millot, “Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers,” Opt. Express 16(21), 16467–16474 (2008).
[Crossref] [PubMed]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Eggleton, B.

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[Crossref]

El-Amraoui, M.

J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011).
[Crossref]

Fatome, J.

J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011).
[Crossref]

Finot, C.

Frosz, M. H.

Fu, X.

S. Zhao, H. Yang, N. Chen, X. Fu, and C. Zhao, “Soliton trapping of dispersive waves in photonic crystal fiber with three zero-dispersion wavelengths,” IEEE Photonics J. 7(5), 7102701 (2015).

Gadret, G.

J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011).
[Crossref]

Gao, J.

Genty, G.

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[Crossref]

G. Genty and J. M. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45(11), 1331–1335 (2009).
[Crossref]

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Habert, R.

Hammani, K.

Harvey, J. D.

Héliot, L.

Hofkens, J.

M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
[Crossref]

Jalali, B.

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105(23), 233902 (2010).
[Crossref] [PubMed]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
[Crossref] [PubMed]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

Jules, J. C.

J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011).
[Crossref]

Kelleher, E. J. R.

Kibler, B.

J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011).
[Crossref]

B. Kibler, C. Finot, and J. M. Dudley, “Soliton and rogue wave statistics in supercontinuum generation in photonic crystal fibre with two zero dispersion wavelengths,” Eur. Phys. J. Spec. Top. 173(1), 289–295 (2009).
[Crossref]

Knight, J. C.

Kobtsev, S.

Kolobov, M.

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

Krueger, A.

M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
[Crossref]

Kudlinski, A.

Larsen, C.

Lau, A. P. T.

Leonhardt, R.

Leray, A.

Li, F.

Li, Q.

Lin, C.

C. Lin and R. H. Stolen, “New nanosecond continuum for excited-state spectroscopy,” Appl. Phys. Lett. 28(4), 216–218 (1976).
[Crossref]

Louvergneaux, E.

Maillotte, H.

Marks, D. L.

Maus, M.

M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
[Crossref]

Millot, G.

Møller, U.

Moselund, P.

Mussot, A.

Newbury, N.

Oldenburg, A. L.

Ostrovsky, L. A.

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: The beginning,” Physica D 238(5), 540–548 (2009).
[Crossref]

Peng, J.

Popov, S. V.

Reynolds, J. J.

Ropers, C.

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105(23), 233902 (2010).
[Crossref] [PubMed]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
[Crossref] [PubMed]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

Rousseau, E.

M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
[Crossref]

Russell, P.

P. Russell, “Photonic Crystal Fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

Russell, P. S. J.

Schweitzer, C.

M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
[Crossref]

Shapiro, S. L.

R. R. Alfano and S. L. Shapiro, “Emission in the region 4000 to 7000 Å via four-photon coupling in glass,” Phys. Rev. Lett. 24(11), 584–587 (1970).
[Crossref]

Smektala, F.

J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011).
[Crossref]

Smirnov, S.

Solli, D. R.

D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105(23), 233902 (2010).
[Crossref] [PubMed]

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
[Crossref] [PubMed]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

Sørensen, S. T.

Spriet, C.

Stolen, R. H.

C. Lin and R. H. Stolen, “New nanosecond continuum for excited-state spectroscopy,” Appl. Phys. Lett. 28(4), 216–218 (1976).
[Crossref]

Sugavanam, S.

Sylvestre, T.

Taki, M.

Tang, P.

Tarasov, N.

Taylor, J. R.

Thomsen, C. L.

Travers, J. C.

Tsia, K. K.

Van der Auweraer, M.

M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
[Crossref]

Vanholsbeeck, F.

Vedadi, A.

Wadsworth, W. J.

Wai, P. K. A.

Wang, W.

Washburn, B.

Wong, K. K. Y.

Yang, H.

S. Zhao, H. Yang, N. Chen, and C. Zhao, “Controlled generation of high-intensity optical rogue waves by induced modulation instability,” Sci. Rep. 7, 39926 (2017).
[Crossref] [PubMed]

S. Zhao, H. Yang, N. Chen, X. Fu, and C. Zhao, “Soliton trapping of dispersive waves in photonic crystal fiber with three zero-dispersion wavelengths,” IEEE Photonics J. 7(5), 7102701 (2015).

W. Wang, H. Yang, P. Tang, C. Zhao, and J. Gao, “Soliton trapping of dispersive waves in photonic crystal fiber with two zero dispersive wavelengths,” Opt. Express 21(9), 11215–11226 (2013).
[Crossref] [PubMed]

Zakharov, V. E.

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: The beginning,” Physica D 238(5), 540–548 (2009).
[Crossref]

Zhao, C.

S. Zhao, H. Yang, N. Chen, and C. Zhao, “Controlled generation of high-intensity optical rogue waves by induced modulation instability,” Sci. Rep. 7, 39926 (2017).
[Crossref] [PubMed]

S. Zhao, H. Yang, N. Chen, X. Fu, and C. Zhao, “Soliton trapping of dispersive waves in photonic crystal fiber with three zero-dispersion wavelengths,” IEEE Photonics J. 7(5), 7102701 (2015).

W. Wang, H. Yang, P. Tang, C. Zhao, and J. Gao, “Soliton trapping of dispersive waves in photonic crystal fiber with two zero dispersive wavelengths,” Opt. Express 21(9), 11215–11226 (2013).
[Crossref] [PubMed]

Zhao, S.

S. Zhao, H. Yang, N. Chen, and C. Zhao, “Controlled generation of high-intensity optical rogue waves by induced modulation instability,” Sci. Rep. 7, 39926 (2017).
[Crossref] [PubMed]

S. Zhao, H. Yang, N. Chen, X. Fu, and C. Zhao, “Soliton trapping of dispersive waves in photonic crystal fiber with three zero-dispersion wavelengths,” IEEE Photonics J. 7(5), 7102701 (2015).

Appl. Phys. B (1)

G. Genty, J. Dudley, and B. Eggleton, “Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime,” Appl. Phys. B 94(2), 187–194 (2009).
[Crossref]

Appl. Phys. Lett. (1)

C. Lin and R. H. Stolen, “New nanosecond continuum for excited-state spectroscopy,” Appl. Phys. Lett. 28(4), 216–218 (1976).
[Crossref]

Electron. Lett. (1)

J. Fatome, B. Kibler, M. El-Amraoui, J. C. Jules, G. Gadret, F. Desevedavy, and F. Smektala, “Mid-infrared extension of supercontinuum in chalcogenide suspended core fibre through soliton gas pumping,” Electron. Lett. 47(6), 398–400 (2011).
[Crossref]

Eur. Phys. J. Spec. Top. (1)

B. Kibler, C. Finot, and J. M. Dudley, “Soliton and rogue wave statistics in supercontinuum generation in photonic crystal fibre with two zero dispersion wavelengths,” Eur. Phys. J. Spec. Top. 173(1), 289–295 (2009).
[Crossref]

IEEE J. Quantum Electron. (1)

G. Genty and J. M. Dudley, “Route to coherent supercontinuum generation in the long pulse regime,” IEEE J. Quantum Electron. 45(11), 1331–1335 (2009).
[Crossref]

IEEE Photonics J. (1)

S. Zhao, H. Yang, N. Chen, X. Fu, and C. Zhao, “Soliton trapping of dispersive waves in photonic crystal fiber with three zero-dispersion wavelengths,” IEEE Photonics J. 7(5), 7102701 (2015).

J. Opt. Soc. Am. B (4)

Nature (2)

J. C. Knight, “Photonic crystal fibres,” Nature 424(6950), 847–851 (2003).
[Crossref] [PubMed]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature 450(7172), 1054–1057 (2007).
[Crossref] [PubMed]

Opt. Express (8)

S. Kobtsev and S. Smirnov, “Modelling of high-power supercontinuum generation in highly nonlinear, dispersion shifted fibers at CW pump,” Opt. Express 13(18), 6912–6918 (2005).
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A. Kudlinski, B. Barviau, A. Leray, C. Spriet, L. Héliot, and A. Mussot, “Control of pulse-to-pulse fluctuations in visible supercontinuum,” Opt. Express 18(26), 27445–27454 (2010).
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Q. Li, F. Li, K. K. Y. Wong, A. P. T. Lau, K. K. Tsia, and P. K. A. Wai, “Investigating the influence of a weak continuous-wave-trigger on picosecond supercontinuum generation,” Opt. Express 19(15), 13757–13769 (2011).
[Crossref] [PubMed]

W. Wang, H. Yang, P. Tang, C. Zhao, and J. Gao, “Soliton trapping of dispersive waves in photonic crystal fiber with two zero dispersive wavelengths,” Opt. Express 21(9), 11215–11226 (2013).
[Crossref] [PubMed]

B. Washburn and N. Newbury, “Phase, timing, and amplitude noise on supercontinua generated in microstructure fiber,” Opt. Express 12(10), 2166–2175 (2004).
[Crossref] [PubMed]

K. Hammani, C. Finot, J. M. Dudley, and G. Millot, “Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers,” Opt. Express 16(21), 16467–16474 (2008).
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J. Peng, N. Tarasov, S. Sugavanam, and D. Churkin, “Rogue waves generation via nonlinear soliton collision in multiple-soliton state of a mode-locked fiber laser,” Opt. Express 24(19), 21256–21263 (2016).
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A. Mussot, A. Kudlinski, M. Kolobov, E. Louvergneaux, M. Douay, and M. Taki, “Observation of extreme temporal events in CW-pumped supercontinuum,” Opt. Express 17(19), 17010–17015 (2009).
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Opt. Lett. (3)

Phys. Rev. Lett. (3)

D. R. Solli, C. Ropers, and B. Jalali, “Active control of rogue waves for stimulated supercontinuum generation,” Phys. Rev. Lett. 101(23), 233902 (2008).
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D. R. Solli, B. Jalali, and C. Ropers, “Seeded supercontinuum generation with optical parametric down-conversion,” Phys. Rev. Lett. 105(23), 233902 (2010).
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[Crossref]

Physica D (1)

V. E. Zakharov and L. A. Ostrovsky, “Modulation instability: The beginning,” Physica D 238(5), 540–548 (2009).
[Crossref]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78(4), 1135–1184 (2006).
[Crossref]

Rev. Sci. Instrum. (1)

M. Maus, E. Rousseau, M. Cotlet, C. Schweitzer, J. Hofkens, M. Van der Auweraer, F. C. De Schryver, and A. Krueger, “New Picosecond laser system for easy tenability over the whole ultraviolet/visible/near infrared wavelength range based on flexible harmonic generation and optical parametric oscillation,” Rev. Sci. Instrum. 72(1), 36–40 (2001).
[Crossref]

Sci. Rep. (1)

S. Zhao, H. Yang, N. Chen, and C. Zhao, “Controlled generation of high-intensity optical rogue waves by induced modulation instability,” Sci. Rep. 7, 39926 (2017).
[Crossref] [PubMed]

Science (1)

P. Russell, “Photonic Crystal Fibers,” Science 299(5605), 358–362 (2003).
[Crossref] [PubMed]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Academic, 2012)

J. M. Dudley and J. R. Taylor, Supercontinuum Generation In Optical Fibers (Cambridge University, 2010)

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Figures (7)

Fig. 1
Fig. 1 (a) The dispersion profiles and (b) the related group delay curves of PCF1 (blue curve), PCF2 (green curve), and PCF3 (red curve) as a function of the wavelength.
Fig. 2
Fig. 2 The related MI gain spectra of PCF1 (blue curve), PCF2 (green curve), and PCF3 (red curve) as a function of seed frequency offset.
Fig. 3
Fig. 3 In the propagation medium of a 15-m-long single ZDW PCF1 cascaded with a 10-m-long dual ZDW PCF2, we illustrate (a1) the temporal intensity at the propagation distance of 0 m (blue curve), 15 m (green curve), 25 m (red curve), (b1) the output spectrum intensity, as well as the (a2) temporal and (b2) spectral evolution as the function of fiber length, where the red dotted line presents the cascaded position of two PCFs.
Fig. 4
Fig. 4 In the propagation medium of a 15-m-long single ZDW PCF1 cascaded with a 10-m-long dual ZDW PCF3, we illustrate (a1) the temporal intensity at the propagation distance of 0 m (blue curve), 15 m (green curve), 25 m (red curve), (b1) the output spectrum intensity, as well as the (a2) temporal and (b2) spectral evolution as the function of fiber length, where the red dotted line presents the cascaded position of two PCFs.
Fig. 5
Fig. 5 The output spectrograms at the medium of (a) 15-m-long PCF1, (b) 25-m-long PCF1, (c) a 15-m-long PCF1 cascaded with a 10-m-long PCF2, and (d) a 15-m-long PCF1 cascaded with a 10-m-long PCF3, respectively.
Fig. 6
Fig. 6 The evolution of normalized peak intensity as a function of fiber length in (a) 25-m-long PCF1, (b) 15-m-long PCF1 cascaded with 10-m-long PCF2, and (c) 15-m-long PCF1 cascaded with 10-m-long PCF3, respectively. The relatively high peak intensity events correspond to the collisions.
Fig. 7
Fig. 7 The evolution of the shortest wavelength and the longest wavelength of 100 individual simulations (gray) as a function of the second ZDW in the second segmented PCF. The red line with dot presents the average longest wavelength, while the blue line with asterisk presents the average shortest wavelength.

Equations (4)

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A( z,T ) z = k2 i k+1 β k k! k A T k +iγ( 1+ i ω 0 T )× ( A( z,T )[ + R( T ) | A( z,T T ) | 2 d T +i Γ R ( z,T ) ] ).
A( 0,T )=( P p + a 0 P p e i2π f mod T )exp( T 2 /2 T 0 2 ),
g(Ω)=Im{ Δ k o ± Δ k e +2γ P p R ˜ ( Ω )Δ k e }.
Δ k o = m=1 β ¯ 2m+1 ( 2m+1 )! Ω 2m+1 ,Δ k e = m=1 β ¯ 2m 2m! Ω 2m ,

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