OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 16, Iss. 21 — Oct. 13, 2008
  • pp: 16467–16474
« Show journal navigation

Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers

Kamal Hammani, Christophe Finot, John. M. Dudley, and Guy Millot  »View Author Affiliations


Optics Express, Vol. 16, Issue 21, pp. 16467-16474 (2008)
http://dx.doi.org/10.1364/OE.16.016467


View Full Text Article

Acrobat PDF (695 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We report experimental observation and characterization of rogue wave-like extreme value statistics arising from pump-signal noise transfer in a fiber Raman amplifier. Specifically, by exploiting Raman amplification with an incoherent pump, the amplified signal is shown to develop a series of temporal intensity spikes whose peak power follows a power-law probability distribution. The results are interpreted using a numerical model of the Raman gain process using coupled nonlinear Schrödinger equations, and the numerical model predicts results in good agreement with experiment.

© 2008 Optical Society of America

1. Introduction

Optical fiber systems are well-known to provide convenient platforms with which to investigate fundamental non-linear phenomena such as modulation instability [1

1. K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986). [CrossRef] [PubMed]

], soliton dynamics [2

2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980). [CrossRef]

, 3

3. A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent solitons in instantaneous response nonlinear media,” Phys. Rev. Lett. 92, 143906 (2004). [CrossRef] [PubMed]

], and self-similarity [4

4. J. M. Dudley, C. Finot, G. Millot, and D. J. Richardson, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007). [CrossRef]

]. As well as these studies focusing on dynamical aspects of nonlinear propagation, recent work has also considered the associated statistical properties, and there has been particular interest in the observation of statistically-rare high power solitons observed during fiber supercontinuum generation [5

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

, 6

6. 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]

]. Significantly, because these experiments were carried out in a regime where modulation instability played a key role in the dynamics, it has been possible to propose an important correspondence with the infamous oceanic rogue waves whose origin has been discussed in terms of similar modulation instabilities that occur in a hydrodynamic context.

The observation of “optical rogue waves” in supercontinuum generation is significant in itself, and has indeed motivated additional work investigating how such instabilities can be harnessed and controlled [6

6. 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]

]. But the results are also of much general interest, as such statistically-rare events form part of a general and important class of phenomena that exhibit “extreme-value” statistics, typically characterized by heavy-tailed or L-shaped probability distributions. In this paper, we demonstrate that such extreme-value events are not restricted only to supercontinuum generation in optics, but can also be observed in the nonlinear process of fiber Raman amplification. Specifically, by exploiting Raman amplification with a partially coherent pump, we show that noise transfer from the pump to a coherent signal results in intensity spikes that also exhibit optical “rogue wave-like” extreme value statistics.

2. Experimental set-up

Figure 1(a) shows our experimental set-up, which is all fiber-format and uses only commercially available components at telecommunications wavelengths. We study Raman amplification in two readily-available fibers: a 500 m length of highly nonlinear fiber (HNLF) with dispersion β2=7×10-4 ps2 m-1 and nonlinearity γ=10 W-1.km-1; and a 3.5 km length of non-zero dispersion shifted fiber (DSF) with β2=3.2×10-3 ps2 m-1 and γ=2.4 W-1 km-1 at 1550 nm. Note that both fibers exhibit similar integrated Raman gain and cumulative nonlinearity γ L. Both fibers are also normally dispersive so that neither the pump nor the amplified signal experience solitonic or modulation instability effects [1

1. K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986). [CrossRef] [PubMed]

, 2

2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980). [CrossRef]

]. This is an important feature of our set up that ensures that the effects stimulating the emergence of rare events does not overlap with the processes involved in supercontinuum generation [5

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

, 6

6. 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]

].

The fibers under investigation are codirectionally pumped by an unpolarized Raman fiber laser delivering up to 2 W average power at 1455 nm. The pump delivers a partially coherent quasi-continuous wave (CW) output whose spectral linewidth varies over 20-100 GHz as the pump output power increased from 100-1100 mW [12

12. C. Headley and G. P. Agrawal, Raman amplification in fiber optical communications (Academic Press, 2005).

]. The pump temporal coherence was characterized experimentally via non-collinear intensity autocorrelation, and the solid blue line in Fig. 1(b) shows the results obtained at a power level of 300 mW. Similar results were obtained for higher pump powers. The figure shows the expected 2:1 contrast ratio of a partially incoherent source, and the experimental results are in good agreement with the calculated autocorrelation function (circles) based on a numerical model of the pump assuming chaotic statistical fluctuations with a Gaussian amplitude distribution and a 25 ps coherence time [14

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

]. To illustrate the pump fluctuations explicitly, Fig. 1(c) shows a 1 ns section of the temporal intensity distribution calculated from the numerical model.

Fig. 1. (a) Experimental set-up (b) Autocorrelation of the pump at 1455 nm, experimental results (solid blue line) compared to a Gaussian distribution with a coherence time of 25 ps (circles). (c) Corresponding intensity fluctuations normalized according to the median value.

We have studied the statistical properties of Raman amplification at 1550 nm which is close to the Raman gain peak for a 1455 nm pump. Different aspects of the amplified signal properties were examined using CW and pulsed signal sources. The CW source was an external cavity laser having a MHz spectral linewidth with 0.35 mW average power. The pulsed source was a 22 MHz repetition rate passively-modelocked erbium-doped fiber laser delivering 1 ps pulses (FWHM) and with average power of a few µW.

3. Temporal evolution

3.1 Experimental results

Experiments were first carried to characterize an amplified CW signal for on-off integrated gains in the range of 3-16 dB corresponding to pump powers in the range of 300-900 mW for the HNLF and 350-1700 mW for the DSF. The temporal properties of the amplified signal were studied using both a 1 GHz bandwidth oscilloscope detection system as well as intensity autocorrelation. Figure 2(a) shows a typical single-shot oscilloscope trace spanning 500 ns using the HNLF fiber at 12 dB gain (700 mW pump power). This time series illustrates clearly that the amplified signal exhibits distinct intensity spikes generated without any temporal periodicity. Note that a spectral filter was used to remove possible contributions to the trace arising from spontaneous Raman emission outside the signal bandwidth. The amplified signal characteristics were then examined with higher temporal resolution using intensity autocorrelation as shown in Fig. 2(b). The measured autocorrelation for the HNLF amplifier (black, gray) is compared with that of the pump (blue) and a DSF amplifier (red).

Fig. 2. (a). Amplified CW signal in a HNLF amplifier at 12 dB gain. The intensity is normalized relative to the median value. (b). Autocorrelation of pump and amplified signal in HNLF and DSF amplifiers at gains indicated.

The autocorrelation measurements clearly show the very different characteristics of the pump and the HNLF-amplified signal. Specifically, although the autocorrelation width of the pump and HNLF-amplified signal are comparable, the background level of the signal autocorrelation decreases to near zero, highlighting significant differences between the pump and amplified signal statistics. In addition, the low background level indicates the presence of high contrast pulses in the amplified signal time series, and the similar autocorrelation halfwidths allow us to infer a characteristic temporal pulse width comparable to the 25 ps pump coherence time. In contrast to these measurements of the HNLF-amplified signal, the signal amplified in the DSF yields an autocorrelation signal that decreases only slightly (~10%) over the 120 ps scan range. This indicates that the pump fluctuations transferred to the amplified signal are averaged over a significant timespan due (as we discuss below), to the non-negligible group velocity mismatch between the pump and the signal.

Fig. 3. (a). Eye-diagrams of: (a1) the initial ps pulse train compared with (a2-a5) amplified signals in DSF and HNLF for 3-dB and 12-dB on-off gains (b) Probability of the peak powers for both fibers and different gains. Peak-power values are normalized compared to the median value. Experimental results on a log-scale (lines) are compared with an exponential-decreasing fit (grey and black circles for HNLF amplifier) or with a linear fit (red circles).

3.2 Numerical simulations

To interpret our results, we have developed numerical simulations based on a standard coupled nonlinear equation model of the Raman amplifier :

{ψsz=gr2ψp2ψsα2ψs+iγ[ψs2+2ψp2]ψsψpz=gr2ψs2ψpα2ψp+iγ[ψp2+2ψs2]ψpδψpT
(1)

We used this model to simulate the experimental results (with no free parameters) in the case of a CW signal, and the numerical results obtained are shown in Fig. 4. In Fig. 4(a) we show results illustrating the generation and the longitudinal exponential growth of a particular rogue-wave event that occurs for an HNLF amplifier. The time series simulated on a longer time scale [Fig. 4(b)] reproduces qualitatively the fluctuations in the amplified signal seen in the experimental measurements in Fig. 2(a) as well as the characteristics of the experimentally measured autocorrelation function in Fig. 2(b). The calculated peak-power probability distribution is also in good qualitative agreement with the experimental trends, with linear and exponential decreasing evolutions on a log scale for DSF and HNLF, respectively.

Simulations carried out over a wider parameter range allow us to identify the physical origin of the rogue wave statistics as the transfer of intensity noise from the pump to the signal via the exponential Raman gain. Similar extreme nonlinear shaping of the statistical distribution of the pulse energy under the influence of Raman gain has already been mentioned for nanosecond pump pulses delivered by Q-switched lasers [10

10. A. Betlej, P. Schmitt, P. Sidereas, R. Tracy, C. G. Goedde, and J. R. Thompson, “Increased Stokes pulse energy variation from amplified classical noise in a fiber Raman generator,” Opt. Express 13, 2948–2960 (2005). [CrossRef] [PubMed]

] or dye lasers [13

13. A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, “Pulse-energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump,” Phys. Rev. A 56, 1666–1669 (1997). [CrossRef]

]. Our study considering optical fluctuations in the picosecond range gives further insight and illustrates that this transfer only occurs efficiently for a weak pump-signal walk-off. This is the case for the HNLF used here with an integrated walk-off (δL=29 ps) which is comparable with the coherence time of the pump. Under these conditions, the temporal fluctuations of the pump are directly translated into signal variations as confirmed experimentally and numerically by the similar autocorrelation widths for the pump and the amplified signals. However, the intensity noise transfer is not linear but exponential, leading to different autocorrelation contrasts.

On the contrary, for the DSF the integrated walk-off is much higher (δL=1.8 ns) so that the pump fluctuations are averaged over a longer timescale. As a consequence the amplifier signal does not exhibit such extreme temporal statistics. Another direct manifestation of the walk-off impact is the influence of the pumping scheme : no rogue wave structure has been experimentally observed in the HNLF when pumping in a counterpropagating scheme where the walk off parameter is nearly twice the speed of light [15

15. C. Fludger, V. Handerek, and R. J. Mears, “Pump to signal RIN transfer in Raman fiber amplifiers,” J. Lightwave Technol. 19, 1140–1148 (2001). [CrossRef]

].

Fig. 4. Numerical results based on the integration of Eq. (1). (a) 3D representation of the longitudinal evolution of the temporal intensity profile of a rogue intensity spike. (b) Amplified continuous signal observed at the amplifier output (c) Autocorrelation signal of the pump and output amplified signal after propagation in HNLF and DSF for gain values as indicated (d) Statistics of the peak powers for DSF and HNLF-based amplifiers (subplots (d1) and (d2) respectively) and for different gains. Results on a logarithmic scale are compared with a linear fit (red dots) or an exponential decreasing fit (grey and black circles).

4. Spectral evolution and control of the rare events

Fig. 5. (a). Optical spectra of the amplified signal at different gains. Results for the HNLF amplifier are compared with the intial seed and the DSF results. Experimental and simulated results are plotted in (a1) and (a2), respectively. (b). Spectro-temporal plot of a rogue wave-type fluctuation (c). Experimental temporal signal obtained after spectral slicing by a 9 GHz filter and for different spectral offsets of (c1) 0 GHz, (c2) 150 GHz and (c3) 350 GHz.

The observation that the highest amplitude rogue events are associated with increased spectral broadening suggests that an offset filtering technique can be used to isolate their occurrence within the amplified signal time series. In our experiments, by using a bandpass fiber-Bragg filter having a spectral bandwidth of 9 GHz, we have experimentally recorded the output temporal sequence for different values of signal-filter frequency detuning. On the central part of the spectrum, as can also be seen in Fig. 5(b), both moderate and high peak powers structures are present (Fig. 5(c1)). But (similar to XPM-based regeneration and wavelength conversion techniques [17

17. B. E. Olsson, P. Öhlen, L. Rau, and D. J. Blumenthal, “A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering,” IEEE Photon. Technol. Lett. 12, 846–848 (2000). [CrossRef]

]) progressively increasing the spectral offset (Fig. 5(c2)) enables the discrimination of the highest peak powers structures from residual noise. This is because the effect of XPM is to lead to preferential spectral broadening for events with higher amplitude and thus spectral filtering can be used to efficiently isolate the rarest and most intense events (Fig. 5(c3)). Although this technique appears at first sight similar to the spectral filtering technique used to isolate the optical rogue waves in supercontinuum generation [5

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

, 6

6. 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]

], we stress again that the extreme event generation mechanisms are very different. In fact, a significant practical difference is that in contrast to the detection of red-shifted rogue solitons, the technique for detecting rogue Raman events can use both low and high wavelength filtering.

5. Conclusion

Acknowledgments

We would like to thank S. Pitois and J. Fatome for illuminating discussions and for experimental assistance. This work was supported by the Agence Nationale de la Recherche (ANR SUPERCODE and SOFICARS projects: ANR-06-BLAN-0401-01 and ANR-07-RIB-013-03), by the Conseil Régional de Bourgogne, and was carried out within the framework of the Research Networks GDR Phonomi2, COST action 299 FIDES and PRES UFC-UB.

References and links

1.

K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986). [CrossRef] [PubMed]

2.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond pulse narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980). [CrossRef]

3.

A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, “Incoherent solitons in instantaneous response nonlinear media,” Phys. Rev. Lett. 92, 143906 (2004). [CrossRef] [PubMed]

4.

J. M. Dudley, C. Finot, G. Millot, and D. J. Richardson, “Self-similarity in ultrafast nonlinear optics,” Nat. Phys. 3, 597–603 (2007). [CrossRef]

5.

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

6.

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]

7.

J. R. Thompson and R. Roy, “Statistical fluctuations in multiple four-wave mixing in a single-mode optical fiber,” Phys. Rev. A 44, 7605–7614 (1991). [CrossRef] [PubMed]

8.

E. Huynh, E. Manzano, A. Medrano, T. Thorn, A. Zavala, C. G. Goedde, and J. R. Thompson, “The interplay of thermal and pump fluctuations in stimulated Brillouin scattering,” Opt. Commun. 281, 836–845 (2008). [CrossRef]

9.

L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, “Influence of classical pump noise on long-pulse multiorder stimulated Raman scattering in optical fiber,” J. Opt. Soc. Am. B 19, 2727–2736 (2002). [CrossRef]

10.

A. Betlej, P. Schmitt, P. Sidereas, R. Tracy, C. G. Goedde, and J. R. Thompson, “Increased Stokes pulse energy variation from amplified classical noise in a fiber Raman generator,” Opt. Express 13, 2948–2960 (2005). [CrossRef] [PubMed]

11.

E. Landahl, D. Baiocchi, and J. R. Thompson, “A simple analytic model for noise shaping by an optical fiber Raman generator,” Opt. Commun. 150, 339–347 (1998). [CrossRef]

12.

C. Headley and G. P. Agrawal, Raman amplification in fiber optical communications (Academic Press, 2005).

13.

A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, “Pulse-energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump,” Phys. Rev. A 56, 1666–1669 (1997). [CrossRef]

14.

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

15.

C. Fludger, V. Handerek, and R. J. Mears, “Pump to signal RIN transfer in Raman fiber amplifiers,” J. Lightwave Technol. 19, 1140–1148 (2001). [CrossRef]

16.

G. Ravet, A. A. Fotidai, and P. Mégret, “Spectral broadening in Raman fiber amplifier pumped by partially coherent wave,” in CLEO Europe , (2007),

17.

B. E. Olsson, P. Öhlen, L. Rau, and D. J. Blumenthal, “A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering,” IEEE Photon. Technol. Lett. 12, 846–848 (2000). [CrossRef]

18.

D. Borlaug and B. Jalali, “Extreme value statistics in silicon photonics,” to be presented at the 21st Annual Meeting of The IEEE Lasers & Electro-Optics Society, Newport Beach, United-States, 9–13 Nov. 2008. http://arxiv.org/abs/0809.0152v1

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(060.7140) Fiber optics and optical communications : Ultrafast processes in fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: July 29, 2008
Revised Manuscript: September 17, 2008
Manuscript Accepted: September 17, 2008
Published: October 1, 2008

Citation
Kamal Hammani, Christophe Finot, John M. Dudley, and Guy Millot, "Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers," Opt. Express 16, 16467-16474 (2008)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-21-16467


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. K. Tai, A. Hasegawa, and A. Tomita, "Observation of modulational instability in optical fibers," Phys. Rev. Lett. 56, 135-138 (1986). [CrossRef] [PubMed]
  2. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, "Experimental observation of picosecond pulse narrowing and solitons in optical fibers," Phys. Rev. Lett. 45, 1095-1098 (1980). [CrossRef]
  3. A. Picozzi, M. Haelterman, S. Pitois, and G. Millot, "Incoherent solitons in instantaneous response nonlinear media," Phys. Rev. Lett. 92, 143906 (2004). [CrossRef] [PubMed]
  4. J. M. Dudley, C. Finot, G. Millot, and D. J. Richardson, "Self-similarity in ultrafast nonlinear optics," Nat. Phys. 3, 597-603 (2007). [CrossRef]
  5. D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, "Optical rogue waves," Nature 450, 1054 (2007). [CrossRef] [PubMed]
  6. 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]
  7. J. R. Thompson and R. Roy, "Statistical fluctuations in multiple four-wave mixing in a single-mode optical fiber," Phys. Rev. A 44, 7605-7614 (1991). [CrossRef] [PubMed]
  8. E. Huynh, E. Manzano, A. Medrano, T. Thorn, A. Zavala, C. G. Goedde, and J. R. Thompson, "The interplay of thermal and pump fluctuations in stimulated Brillouin scattering," Opt. Commun. 281, 836-845 (2008). [CrossRef]
  9. L. Garcia, J. Jenkins, Y. Lee, N. Poole, K. Salit, P. Sidereas, C. G. Goedde, and J. R. Thompson, "Influence of classical pump noise on long-pulse multiorder stimulated Raman scattering in optical fiber," J. Opt. Soc. Am. B 19, 2727-2736 (2002). [CrossRef]
  10. A. Betlej, P. Schmitt, P. Sidereas, R. Tracy, C. G. Goedde, and J. R. Thompson, "Increased Stokes pulse energy variation from amplified classical noise in a fiber Raman generator," Opt. Express 13, 2948-2960 (2005). [CrossRef] [PubMed]
  11. E. Landahl, D. Baiocchi, and J. R. Thompson, "A simple analytic model for noise shaping by an optical fiber Raman generator," Opt. Commun. 150, 339-347 (1998). [CrossRef]
  12. C. Headley and G. P. Agrawal, Raman amplification in fiber optical communications (Academic Press, 2005).
  13. A. S. Grabtchikov, A. I. Vodtchits, and V. A. Orlovich, "Pulse-energy statistics in the linear regime of stimulated Raman scattering with a broad-band pump," Phys. Rev. A 56, 1666-1669 (1997). [CrossRef]
  14. F. Vanholsbeeck, S. Martin-Lopez, M. Gonzalez-Herraez, and S. Coen, "The role of pump incoherence in continuous-wvae supercontinuum generation," Opt. Express 13, 6615-6625 (2005). [CrossRef] [PubMed]
  15. C. Fludger, V. Handerek, and R. J. Mears, "Pump to signal RIN transfer in Raman fiber amplifiers," J. Lightwave Technol. 19, 1140-1148 (2001). [CrossRef]
  16. G. Ravet, A. A. Fotidai, and P. Mégret, "Spectral broadening in Raman fiber amplifier pumped by partially coherent wave," in CLEO Europe, (2007).
  17. B. E. Olsson, P. �?hlen, L. Rau, and D. J. Blumenthal, "A simple and robust 40-Gb/s wavelength converter using fiber cross-phase modulation and optical filtering," IEEE Photon. Technol. Lett. 12, 846-848 (2000). [CrossRef]
  18. D. Borlaug and B. Jalali, "Extreme value statistics in silicon photonics," to be presented at the 21st Annual Meeting of The IEEE Lasers & Electro-Optics Society, Newport Beach, United-States, 9-13 Nov. 2008. http://arxiv.org/abs/0809.0152v1

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited