OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 23 — Nov. 8, 2010
  • pp: 24352–24360
« Show journal navigation

Significant reduction of power fluctuations at the long-wavelength edge of a supercontinuum generated in solid-core photonic bandgap fibers

O. Vanvincq, B. Barviau, A. Mussot, G. Bouwmans, Y. Quiquempois, and A. Kudlinski  »View Author Affiliations


Optics Express, Vol. 18, Issue 23, pp. 24352-24360 (2010)
http://dx.doi.org/10.1364/OE.18.024352


View Full Text Article

Acrobat PDF (973 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We show that the infrared edge of supercontinua generated in solid core photonic bandgap fibers is characterized by a very different temporal behavior than the one obtained in standard fibers. In particular, pulse-to-pulse spectral power fluctuations are significantly reduced near the bandgap edge, and the statistical distribution is quasi-gaussian. The spectral dynamics of this process and statistical properties are investigated experimentally and confirmed by numerical simulations. The reduction of power fluctuations originates from the cancellation of the soliton self-frequency shift near the bandgap edge.

© 2010 Optical Society of America

1. Introduction

Recent research in the field of supercontinuum (SC) generation in optical fibers has pointed out the key role of noise in the temporal stability of such sources [1

1. J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002). [CrossRef]

, 2

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

]. In the long-pulse regime, the spectral broadening originates from the modulation instability (MI) process which is seeded by noise and the long-wavelength SC edge is characterized by statistically-rare optical rogue waves [3

3. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1058 (2007). [CrossRef]

], originating from soliton dynamics [3

3. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1058 (2007). [CrossRef]

6

6. G. Genty, C.M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J.M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010). [CrossRef]

]. Consequently, the SC is characterized by a low coherence, and pulse-to-pulse fluctuations of the spectral power at the long-wavelength SC edge are very high [3

3. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1058 (2007). [CrossRef]

,7

7. F. Vanholsbeeck, S. Martin-Lopez, M. González-Herráez, and S. Coen, “The role of pump incoherence in continuous-wave supercontinuum generation,” Opt. Express 13, 6615–6625 (2005). [CrossRef] [PubMed]

]. This is a major issue for a number of applications requiring dynamics measurements. A straightforward way to control these instabilities is to seed the SC with a coherent signal rather than leaving it self-starting from noise [4

4. J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008). [CrossRef] [PubMed]

, 8

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

10

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

]. Although this has been demonstrated experimentally [10

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

], the setup requires a seed laser whose properties (in terms of power and wavelength) must be very precisely adjusted for an efficient MI control. This makes this solution inadequate for a large number of applications and hardly compatible with commercialization aspects.

In this paper, we demonstrate that spectral power fluctuations usually characterizing the long-wavelength edge of SC sources can be reduced by the use of an optimized solid-core photonic bandgap (PBG) fiber. Although it has already been demonstrated that such fibers allow a spectral shaping of SC sources [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

, 12

12. B. Kibler, T. Martynkien, M. Szpulak, C. Finot, J. Fatome, J. Wojcik, W. Urbanczyk, and S. Wabnitz, “Nonlinear femtosecond pulse propagation in an all-solid photonic bandgap fiber,” Opt. Express 17, 10393–10398 (2009). [CrossRef] [PubMed]

], we show here that they also allow a control of their temporal properties. We demonstrate a significant reduction of statistically rare rogue events at the long-wavelength SC edge which results in a greatly improved pulse-to-pulse stability. This phenomenon is interpreted in terms of soliton self-frequency shift (SSFS) suppression thanks to the specific guiding properties of the PBG fiber. These explanations are supported by numerical simulations. The remaining of the paper is organized as follows. In section 2, we provide the experimental evidence for the reduction of pulse-to-pulse fluctuations at the SC long-wavelength edge in solid-core PBG fibers as compared to standard fibers. The first part of section 3 is devoted to experimental results about the dynamics of this phenomenon in solid-core PBG fibers, while the second part focuses on their confirmation by numerical simulations. In section 4, we discuss our results and provide a physical interpretation based on numerical spectrograms, before summarizing our study.

2. Experimental evidence

The solid-core PBG fiber used in the experiments is based on the same design than those previously employed for efficient SC generation [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

]. It is characterized by a double-periodicity cladding structure incorporating germanium-doped inclusions and air holes, depicted respectively in light grey and black regions in the inset of Fig. 1(c). This ensures light to be guided by a PBG mechanism while keeping relatively low confinement losses in the first-order PBG of interest here [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

,13

13. A. Bétourné, G. Bouwmans, Y. Quiquempois, M. Perrin, and M. Douay, “Improvements of solid-core photonic bandgap fibers by means of interstitial air holes,” Opt. Lett. 32, 1719–1721 (2007). [CrossRef] [PubMed]

]. Figure 1(a) shows the computed group-velocity dispersion (GVD) and nonlinear (NL) coefficient curves (deduced from the computed effective area) calculated with a finite-elements method. As previously reported [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

], the GVD slightly increases from its zero value (located around 920 nm) to about 1580 nm where the increase suddenly becomes much more important because of the vicinity of the PBG edge. In this region (delimited by the vertical dotted line), the GVD slope β3 reaches extreme values of about 10−37 s3/m (i.e. about three orders of magnitude larger than in standard fibers), and the NL coefficient drastically drops down to less than 1 W−1.km−1. These strong spectral dependencies of guiding properties are typical of the PBG guidance in fibers [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

, 14

14. V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber and Integrated Optics 28, 27–50 (2009). [CrossRef]

].

Fig. 1 (a), (d) Computed GVD (left axis) and NL coefficient curves (right axis) of the solid-core PBG fiber (a) and standard PCF (d). (b), (e) Experimental SC spectra (left axis) and measurement of pulse-to-pulse variations (right axis) in the solid-core PBG fiber (b) and standard PCF (e). (c), (f) Corresponding histograms of the measured pulse amplitude over 10,000 shots at 1550 nm. Inset : scanning electron microscope (SEM) images of the fibers cross section.

SC generation experiments were performed using a microchip laser at 1064 nm delivering 600 ps pulses with a peak power of a few kilowatts, at a repetition rate of 7 kHz. Figure 1(b) shows the spectrum measured for a launched peak power of 3 kW and a fiber length of 7 m. In these conditions, the infrared spectral broadening is limited to about 1580 nm by the PBG edge as demonstrated in Ref. [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

]. The peak centered around 1555 nm corresponds to an accumulation of solitons for which the SSFS effect has been cancelled [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

, 15

15. O. Vanvincq, A. Kudlinski, A. Bétourné, Y. Quiquempois, and G. Bouwmans, “Extreme deceleration of the soliton self-frequency shift by the third-order dispersion in solid-core photonic bandgap fibers,” J. Opt. Soc. Am. B 27, 2328–2335 (2010). [CrossRef]

]. Our aim here is to quantify pulse-to-pulse fluctuations of the SC spectral power as a function of wavelength in the solid-core PBG fiber, and to compare it with a SC generated in a standard photonic crystal fiber (PCF). We thus fabricated an air/silica PCF whose linear properties were designed to produce a SC with approximately the same spectral extent. Its computed GVD and NL coefficient are plotted in Fig. 1(d). In order to generate a spectral broadening mainly on the long-wavelength side of the pump, the zero-GVD wavelength is located at 950 nm, i.e. relatively far from the pump wavelength to minimize the dispersive wave generation on the short-wavelength edge of the SC. The NL coefficient is 25 W−1.km−1 at 1064 nm, which is much higher than the one of the solid-core PBG fiber. The pump peak power launched in the standard PCF was adjusted so that the spectral extent of the SC (calculated for a 20 dB power drop from the spectral power at 1200 nm) was similar to the one produced in the solid-core PBG fiber. The pump peak power was thus 1.5 kW in the standard PCF (against 3 kW in the PBG fiber). Although SC extensions are very similar in both fibers, their spectrum shape at long wavelengths is very different.

Full squares in Fig. 1(b) and (e) correspond to pulse-to-pulse variations measured every 50 nm over the whole SC spectrum in the solid-core PBG fiber and in the standard PCF, respectively. For both fibers, it slightly increases from 10 % at 1100 nm to about 25 % at 1400 nm. For higher wavelengths, the temporal behavior becomes drastically different : pulse-to-pulse fluctuations significantly increase in the standard PCF to reach σ values of about 90 % at 1550 nm, while in the solid-core PBG fiber, σ values remain lower than 40 % until 1500 nm, and significantly drop down to 10 % at 1550 nm. Note that increasing the launched pump peak power in the standard PCF would result in a larger spectral broadening towards the infrared, and would reduce shot-to-shot fluctuations at the fixed wavelength of 1550 nm. We arbitrarily chose to compare both fibers for a fixed spectral width, which required a lower pump peak power in the standard PCF due to its higher NL coefficient, so that the NL phase shift γPL was comparable in both fibers. Besides, the statistical power distributions of the pulses at 1550 nm have very different features, as shown in Figs. 1(c) and (f). These figures show histograms obtained over 10,000 pulses at 1550 nm in the solid-core PBG fiber and in the standard PCF, respectively. In the standard PCF, the statistical distribution is highly asymmetric and presents a long-tail profile, which means that the most powerful events have a higher probability of apparition than in a gaussian distribution. In fact, this corresponds to the spectral region of instabilities identified as so-called optical rogue waves [3

3. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1058 (2007). [CrossRef]

]. On the contrary, the statistical distribution measured at 1550 nm in the solid-core PBG fiber presents a quasi-gaussian shape, which is the signature of good SC pulse-to-pulse stability.

These experiments show that, besides offering the possibility of controlling the SC spectral extent [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

, 12

12. B. Kibler, T. Martynkien, M. Szpulak, C. Finot, J. Fatome, J. Wojcik, W. Urbanczyk, and S. Wabnitz, “Nonlinear femtosecond pulse propagation in an all-solid photonic bandgap fiber,” Opt. Express 17, 10393–10398 (2009). [CrossRef] [PubMed]

], solid-core PBG fibers allow SC fluctuations to be drastically reduced at the long-wavelength edge of the spectrum, as compared to standard PCFs.

3. Dynamics of the SC stabilization in solid-core PBG fibers

3.1. Experimental investigation

Following the experimental evidence of the reduction of pulse-to-pulse fluctuations in the solid-core PBG fiber, we experimentally studied the dynamics of this phenomenon as a function of fiber length for a fixed peak pump power of 3 kW. A cutback experiment was performed to record the spectral evolution of the SC, as well as pulse-to-pulse fluctuations across the spectrum every 0.5 m. First of all, Fig. 2(a) shows the evolution of the spectral broadening along fiber length. For propagation distances longer than 3 m, the spectrum is limited by the long-wavelength PBG edge located at 1580 nm, as previously reported in Ref. [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

]. Corresponding spectra measured at 2.5 m, 3 m and 7 m are reported in Fig. 2(b). Although the spectral extent is comparable in each case, the shape of the spectrum is slightly different. Indeed, while the long-wavelength edge is relatively smooth for a fiber length of 2.5 m, it becomes much sharper after 3 m, where the cancellation of the SSFS imposes a saturation of the spectral broadening [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

,15

15. O. Vanvincq, A. Kudlinski, A. Bétourné, Y. Quiquempois, and G. Bouwmans, “Extreme deceleration of the soliton self-frequency shift by the third-order dispersion in solid-core photonic bandgap fibers,” J. Opt. Soc. Am. B 27, 2328–2335 (2010). [CrossRef]

]. This phenomenon causes a soliton accumulation whose spectral signature is the peak located at 1555 nm that clearly appears in the spectrum recorded after 7 m.

Fig. 2 (a) Measurement of the spectral broadening as a function of propagation distance in the solid-core PBG fiber. (b) Measured spectra for fiber lengths of 2.5, 3 and 7 m (from bottom to top). Dotted lines depict the PBG edge. (c) Samples of corresponding pulse train after spectral filtering at 1550 nm. (d) Spectral evolution of pulse-to-pulse fluctuations σ for fiber lengths of 2.5 m (blue), 3 m (red) and 7 m (grey). (e) Corresponding histograms at 1550 nm. The signal is normalized to the average over 10,000 pulses.

3.2. Confirmation with numerical simulations

In order to confirm these results, we performed numerical simulations by integrating the generalized nonlinear Schrödinger equation (GNLSE) in the frame of the model firstly proposed by J. Laegsgaard [18

18. J. Laegsgaard, “Mode profile dispersion in the generalized nonlinear Schrödinger equation,” Opt. Express 15, 16110–16123 (2007). [CrossRef] [PubMed]

]. Our aim at this point is to try to reproduce both the experimental spectral and temporal features. To do this, all available fiber characteristics and experimental conditions have been taken into account with no free parameter, with the exception of the pulse duration that has been reduced to 50 ps (against 600 ps in experiments). Indeed, shortening the pulse duration in simulations (while staying in the long-pulse regime though) allows to significantly reduce the computation time without significantly affecting the SC dynamics. The input pump peak power was 3 kW, and quantum noise was modeled by adding one photon per mode with random phase on each spectral discretization bin of the input field [2

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

]. In order to study the statistical behavior of the pulse train, we performed 200 simulations with random initial noise conditions.

Simulations results are displayed in Fig. 3, with the same organization as Fig. 2 for easy comparison. Figures 3(a) and (b), which show the dynamics of the SC formation, correspond to the averaged spectrum over 200 simulations shots. The agreement with experiments is excellent, and the typical spectral features discussed above about the spectrum shape at its long-wavelength edge are accurately reproduced. Temporal properties shown in Fig. 3(c) and (d) have been respectively calculated by using a numerical gaussian filter of 10 nm (FWHM) centered at 1562 nm, which corresponds to the maximum of the spectral power peak observed near the PBG edge [plot (c)], or using a sliding 10 nm filter across the spectrum [plot (d)]. Taking the inverse Fourier transform gives the temporal profile of the SC filtered at the corresponding wavelength, whose average power has been calculated. A sample of the modeled pulse train corresponding to 40 simulation shots is displayed in Fig. 3(c), and shows good agreement with the measured one represented in Fig. 2(c). Simulated shot-to-shot fluctuations σ are represented in Fig. 3(d) as a function of wavelength, and show qualitative agreement with experiments. In particular, the inset of Fig. 3(d) shows that the σ value at 1562 nm (depicted by squares) strongly decreases from about 100 % to 20 % for fiber lengths increasing from 2.5 m to 7 m, respectively. Note that pulse-to-pulse fluctuations do not further decrease for a longer fiber of 8 m. Corresponding statistical distributions calculated from all the 200 simulations are shown in Fig. 3(e), and also show a good agreement with experiments. Note that in simulations, the σ parameter is calculated with Vmax and Vmin corresponding respectively to the maximum and minimum power of the filtered SC for 1 occurrence of the 200 simulations shots. This explains the slightly higher fluctuations obtained in simulations as compared to experiments (in which they are defined for 10 occurrences over 10,000 measurements).

Fig. 3 (a) Simulation of the spectral broadening as a function of propagation distance in the solid-core PBG fiber (averaged over 200 shots). (b) Simulated averaged spectra for fiber lengths of 2.5, 3 and 7 m (from bottom to top). Dotted lines depict the PBG edge. (c) Samples of corresponding pulse train after spectral filtering at 1562 nm. (d) Spectral evolution of pulse-to-pulse fluctuations σ for fiber lengths of 2.5 m (blue), 3 m (red) and 7 m (grey). Inset : evolution of σ at 1562 nm with fiber length. (e) Corresponding histograms over 200 pulses at 1562 nm.

All these simulation results therefore allow to reproduce the main spectral features observed in the experiments (dynamics of the SC formation, typical spectral shape at the long-wavelength edge), but also the measured statistical features of the pulse train (pulse-to-pulse fluctuations as a function of wavelength and propagation distance, shape of the distribution). At this point however, numerical simulations of Fig. 3 do not allow to discuss on the physical mechanisms responsible for the enhanced pulse-to-pulse stability near the PBG edge.

4. Discussion

As shown above, numerical simulations using the GNLSE accurately reproduce our experiments and can consequently be used to discuss the physical mechanisms causing the enhanced stability of the SC long-wavelength edge. To this end, the spectro-temporal representation has proved to be a powerful tool in studying the dynamics of SC generation [2

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

]. Figure 4 shows the evolution of a simulated spectrogram for fiber lengths of 2.5 m, 3 m and 7 m (from top to bottom). Figure 4(a) shows how MI initially generates solitons that subsequently red-shifts through Raman-induced SSFS. In such a long-pulse pumping regime, the presence of statistically rare temporal events in SC experiments can find two complementary physical origins in the recent literature. Firstly, it can be due to a single high peak power soliton generated from MI for particular initial noise conditions [3

3. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1058 (2007). [CrossRef]

, 4

4. J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008). [CrossRef] [PubMed]

]. Because of its higher peak power, it experiences a more efficient SSFS than other solitons, and consequently becomes statistically rare at highest wavelengths due to the low probability for these particular noise conditions to happen [3

3. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1058 (2007). [CrossRef]

]. Note that, in this case, the requirement for a soliton to be statistically rare at the long-wavelength SC edge, is only to experience a slightly more efficient SSFS than the other ones [19

19. M. Erkintalo, G. Genty, and J.M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. Phys. J. Special Topics 185, 135–144 (2010). [CrossRef]

]. Secondly, following these early interpretations, it has been suggested that rare and brief events can arise from the collision of two or more solitons travelling with different group-velocities [5

5. 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, 17010–17015 (2009). [CrossRef] [PubMed]

,6

6. G. Genty, C.M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J.M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010). [CrossRef]

,19

19. M. Erkintalo, G. Genty, and J.M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. Phys. J. Special Topics 185, 135–144 (2010). [CrossRef]

,20

20. K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374, 3585–3589 (2010). [CrossRef]

] because of the convective nature of the system [21

21. M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, “Third-order dispersion for generating optical rogue solitons,” Phys. Lett. A 374, 691–695 (2010). [CrossRef]

]. Note that these two explanations are complementary for explaining long-tail statistical distributions usually observed at the SC long-wavelength edge [21

21. M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, “Third-order dispersion for generating optical rogue solitons,” Phys. Lett. A 374, 691–695 (2010). [CrossRef]

].

Fig. 4 Simulated SC spectrograms representing the temporal and spectral dynamics for three propagation distances z of 2.5, 3 and 7 m, respectively from (a) to (c). The full movie of the spectrogram evolution from 0 to 8 m is available online. ( Media 1)

In the case of the present experiments however, this dynamics is strongly affected by the SSFS cancellation occurring near the PBG edge [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

, 15

15. O. Vanvincq, A. Kudlinski, A. Bétourné, Y. Quiquempois, and G. Bouwmans, “Extreme deceleration of the soliton self-frequency shift by the third-order dispersion in solid-core photonic bandgap fibers,” J. Opt. Soc. Am. B 27, 2328–2335 (2010). [CrossRef]

], as can be seen from Figs. 4(b) and (c). Firstly, these figures show that, as long as solitons are frequency-locked around 1562 nm, they all have very close group velocities at this location in the spectrum, as confirmed by the movie of Fig. 4. Consequently, once they have reached the PBG edge, they cannot collide anymore, which prevents the formation of brief spikes [5

5. 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, 17010–17015 (2009). [CrossRef] [PubMed]

] and leads to an enhanced pulse-to-pulse stability at the SC edge. Secondly, since all solitons whose SSFS has been cancelled near the PBG edge have very close characteristics, as can be seen from the spectrogram movie of Fig. 4, power fluctuations are reduced in this spectral region as compared to the usual case in which only a few solitons with slightly higher peak power are rare at the long-wavelength edge [3

3. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1058 (2007). [CrossRef]

, 4

4. J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008). [CrossRef] [PubMed]

].

As a consequence, the reduction of pulse-to-pulse fluctuations at the long-wavelength edge as a function of propagation distance is intimately linked to the cancellation of the SFSS recently reported [11

11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

, 15

15. O. Vanvincq, A. Kudlinski, A. Bétourné, Y. Quiquempois, and G. Bouwmans, “Extreme deceleration of the soliton self-frequency shift by the third-order dispersion in solid-core photonic bandgap fibers,” J. Opt. Soc. Am. B 27, 2328–2335 (2010). [CrossRef]

]. It is thus in fact due to the specific linear properties inherent to solid-core PBG fibers, and in particular to the strong third-order dispersion near the PBG edge [15

15. O. Vanvincq, A. Kudlinski, A. Bétourné, Y. Quiquempois, and G. Bouwmans, “Extreme deceleration of the soliton self-frequency shift by the third-order dispersion in solid-core photonic bandgap fibers,” J. Opt. Soc. Am. B 27, 2328–2335 (2010). [CrossRef]

].

5. Conclusions

Acknowledgments

We acknowledge Remi Habert for experimental assistance, and Karen Delplace for assistance in fiber fabrication. This work was partly supported by the Agence Nationale de la Recherche through the IMFINI ANR-09-BLAN-0065 project, by French Ministry of Higher Education and Research, the Nord-Pas de Calais Regional Council and FEDER through the “Contrat de Projets Etat Région (CPER) 2007–2013” and the “Campus Intelligence Ambiante” (CIA).

References and links

1.

J. M. Dudley and S. Coen, “Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers,” Opt. Lett. 27, 1180–1182 (2002). [CrossRef]

2.

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

3.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1058 (2007). [CrossRef]

4.

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008). [CrossRef] [PubMed]

5.

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, 17010–17015 (2009). [CrossRef] [PubMed]

6.

G. Genty, C.M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J.M. Dudley, “Collisions and turbulence in optical rogue wave formation,” Phys. Lett. A 374, 989–996 (2010). [CrossRef]

7.

F. Vanholsbeeck, S. Martin-Lopez, M. González-Herráez, and S. Coen, “The role of pump incoherence in continuous-wave supercontinuum generation,” Opt. Express 13, 6615–6625 (2005). [CrossRef] [PubMed]

8.

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

9.

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

10.

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

11.

A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, “Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers,” Opt. Lett. 34, 3083–3085 (2009). [CrossRef] [PubMed]

12.

B. Kibler, T. Martynkien, M. Szpulak, C. Finot, J. Fatome, J. Wojcik, W. Urbanczyk, and S. Wabnitz, “Nonlinear femtosecond pulse propagation in an all-solid photonic bandgap fiber,” Opt. Express 17, 10393–10398 (2009). [CrossRef] [PubMed]

13.

A. Bétourné, G. Bouwmans, Y. Quiquempois, M. Perrin, and M. Douay, “Improvements of solid-core photonic bandgap fibers by means of interstitial air holes,” Opt. Lett. 32, 1719–1721 (2007). [CrossRef] [PubMed]

14.

V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, “Overview on solid core photonic bandgap fibers,” Fiber and Integrated Optics 28, 27–50 (2009). [CrossRef]

15.

O. Vanvincq, A. Kudlinski, A. Bétourné, Y. Quiquempois, and G. Bouwmans, “Extreme deceleration of the soliton self-frequency shift by the third-order dispersion in solid-core photonic bandgap fibers,” J. Opt. Soc. Am. B 27, 2328–2335 (2010). [CrossRef]

16.

C. Lafargue, J. Bolger, G. Genty, F. Dias, J. M. Dudley, and B. J. Eggleton, “Direct detection of optical rogue wave energy statistics in supercontinuum generation,” Electron. Lett. 45, 217–219 (2009). [CrossRef]

17.

H. Kubota, K. R. Tamura, and M. Nakazawa, “Analyses of coherence-maintained ultrashort optical pulse trains and supercontinuum generation in the presence of soliton-amplified spontaneous-emission interaction,” J. Opt. Soc. Am. B 16, 2223–2232 (1999). [CrossRef]

18.

J. Laegsgaard, “Mode profile dispersion in the generalized nonlinear Schrödinger equation,” Opt. Express 15, 16110–16123 (2007). [CrossRef] [PubMed]

19.

M. Erkintalo, G. Genty, and J.M. Dudley, “On the statistical interpretation of optical rogue waves,” Eur. Phys. J. Special Topics 185, 135–144 (2010). [CrossRef]

20.

K. Hammani, B. Kibler, C. Finot, and A. Picozzi, “Emergence of rogue waves from optical turbulence,” Phys. Lett. A 374, 3585–3589 (2010). [CrossRef]

21.

M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, “Third-order dispersion for generating optical rogue solitons,” Phys. Lett. A 374, 691–695 (2010). [CrossRef]

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(060.5295) Fiber optics and optical communications : Photonic crystal fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: September 14, 2010
Revised Manuscript: October 21, 2010
Manuscript Accepted: October 23, 2010
Published: November 5, 2010

Citation
O. Vanvincq, B. Barviau, A. Mussot, G. Bouwmans, Y. Quiquempois, and A. Kudlinski, "Significant reduction of power fluctuations at the long-wavelength edge of a supercontinuum generated in solid-core photonic bandgap fibers," Opt. Express 18, 24352-24360 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-23-24352


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. M. Dudley, and S. Coen, "Coherence properties of supercontinuum spectra generated in photonic crystal and tapered optical fibers," Opt. Lett. 27, 1180-1182 (2002). [CrossRef]
  2. J. M. Dudley, G. Genty, and S. Coen, "Supercontinuum generation in photonic crystal fiber," Rev. Mod. Phys. 78, 1135-1184 (2006). [CrossRef]
  3. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054-1058 (2007). [CrossRef]
  4. J. M. Dudley, G. Genty, and B. J. Eggleton, "Harnessing and control of optical rogue waves in supercontinuum generation," Opt. Express 16, 3644-3651 (2008). [CrossRef] [PubMed]
  5. 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, 17010-17015 (2009). [CrossRef] [PubMed]
  6. G. Genty, C. M. de Sterke, O. Bang, F. Dias, N. Akhmediev, and J. M. Dudley, "Collisions and turbulence in optical rogue wave formation," Phys. Lett. A 374, 989-996 (2010). [CrossRef]
  7. F. Vanholsbeeck, S. Martin-Lopez, M. González-Herráez, and S. Coen, "The role of pump incoherence in continuous-wave supercontinuum generation," Opt. Express 13, 6615-6625 (2005). [CrossRef] [PubMed]
  8. G. Genty, and J. M. Dudley, "Route to coherent supercontinuum generation in the long pulse regime," IEEE J. Quantum Electron. 45, 1331-1335 (2009). [CrossRef]
  9. G. Genty, J. M. Dudley, and B. J. Eggleton, "Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime," Appl. Phys. B 94, 187-194 (2009). [CrossRef]
  10. D. R. Solli, C. Ropers, and B. Jalali, "Active control of rogue waves for stimulated supercontinuum generation," Phys. Rev. Lett. 101, 233902 (2008). [CrossRef] [PubMed]
  11. A. Bétourné, A. Kudlinski, G. Bouwmans, O. Vanvincq, A. Mussot, and Y. Quiquempois, "Control of supercontinuum generation and soliton self-frequency shift in solid core photonic bandgap fibers," Opt. Lett. 34, 3083-3085 (2009). [CrossRef] [PubMed]
  12. B. Kibler, T. Martynkien, M. Szpulak, C. Finot, J. Fatome, J. Wojcik, W. Urbanczyk, and S. Wabnitz, "Nonlinear femtosecond pulse propagation in an all-solid photonic bandgap fiber," Opt. Express 17, 10393-10398 (2009). [CrossRef] [PubMed]
  13. A. Bétourné, G. Bouwmans, Y. Quiquempois, M. Perrin, and M. Douay, "Improvements of solid-core photonic bandgap fibers by means of interstitial air holes," Opt. Lett. 32, 1719-1721 (2007). [CrossRef] [PubMed]
  14. V. Pureur, A. Bétourné, G. Bouwmans, L. Bigot, A. Kudlinski, K. Delplace, A. Le Rouge, Y. Quiquempois, and M. Douay, "Overview on solid core photonic bandgap fibers," Fiber and Integrated Optics 28, 27-50 (2009). [CrossRef]
  15. O. Vanvincq, A. Kudlinski, A. Bétourné, Y. Quiquempois, and G. Bouwmans, "Extreme deceleration of the soliton self-frequency shift by the third-order dispersion in solid-core photonic bandgap fibers," J. Opt. Soc. Am. B 27, 2328-2335 (2010). [CrossRef]
  16. C. Lafargue, J. Bolger, G. Genty, F. Dias, J. M. Dudley, and B. J. Eggleton, "Direct detection of optical rogue wave energy statistics in supercontinuum generation," Electron. Lett. 45, 217-219 (2009). [CrossRef]
  17. H. Kubota, K. R. Tamura, and M. Nakazawa, "Analyses of coherence-maintained ultrashort optical pulse trains and supercontinuum generation in the presence of soliton-amplified spontaneous-emission interaction," J. Opt. Soc. Am. B 16, 2223-2232 (1999). [CrossRef]
  18. J. Laegsgaard, "Mode profile dispersion in the generalized nonlinear Schrödinger equation," Opt. Express 15, 16110-16123 (2007). [CrossRef] [PubMed]
  19. M. Erkintalo, G. Genty, and J. M. Dudley, "On the statistical interpretation of optical rogue waves," Eur. Phys. J. Spec. Top. 185, 135-144 (2010). [CrossRef]
  20. K. Hammani, B. Kibler, C. Finot, and A. Picozzi, "Emergence of rogue waves from optical turbulence," Phys. Lett. A 374, 3585-3589 (2010). [CrossRef]
  21. M. Taki, A. Mussot, A. Kudlinski, E. Louvergneaux, M. Kolobov, and M. Douay, "Third-order dispersion for generating optical rogue solitons," Phys. Lett. A 374, 691-695 (2010). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

Multimedia

Multimedia FilesRecommended Software
» Media 1: AVI (7782 KB)      QuickTime

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited