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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 13 — Jun. 27, 2005
  • pp: 4848–4853
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Experimental performance comparison for various continuous-wave supercontinuum schemes: ring cavity and single pass structures

Ju Han Lee and Kazuro Kikuchi  »View Author Affiliations


Optics Express, Vol. 13, Issue 13, pp. 4848-4853 (2005)
http://dx.doi.org/10.1364/OPEX.13.004848


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Abstract

We experimentally perform a comparative study on performance of three different schemes for generation of continuous-wave (CW) supercontinuum by use of nonlinear optical fiber, i.e. our proposed erbium-doped fiber (EDF)-based ring laser scheme incorporating a highly-nonlinear dispersion-shifted fiber (HNL-DSF), the Raman gain-based ring laser scheme incorporating an HNL-DSF, and the conventional scheme based on pump beam single propagation through an HNL-DSF. The three schemes show different physical mechanisms of supercontinuum evolution from a CW pump beam. In particular, our proposed EDF-based ring laser configuration is found to have a better relative intensity noise performance than the other two schemes.

© 2005 Optical Society of America

1. Introduction

Optical fiber-based supercontinuum sources have been of extensive research focus in recent years due to the fact that such ultra-broad band light sources possess enormous potential applications in a variety of areas such as optical communication [1

1. K. Mori, K. Sato, H. Takara, and T. Ohara, “Supercontinuum lightwave source generating 50 GHz spaced optical ITU grid seamlessly over S-, C- and L-bands,” Electronics Lett. 39, 544–546 (2003). [CrossRef]

], optical coherent tomography [2

2. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001). [CrossRef]

], metrology [3

3. K. Kim, B. R. Washburn, G. Wilpers, C. W. Oates, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser,” Opt. Lett. 30, 932–934 (2005) [CrossRef] [PubMed]

], and optical sensing [4

4. H. Kano and H. Hamaguchi, “Characterization of a supercontinuum generated from a photonic crystal fiber and its application to coherent Raman spectroscopy,” Opt. Lett. 28, 2360–2362 (2003). [CrossRef] [PubMed]

]. A number of researches have thus been performed to understand the phenomenon as well as to implement the corresponding stable and practical devices. Moreover, the recent technological advance in fabricating high-quality nonlinear optical fibers such as the holey fiber [5

5. S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001). [CrossRef]

] and the highly-nonlinear dispersion-shifted fiber (HNL-DSF) [6

6. P. S. Westbrook, J. W. Nicholson, K. S. Feder, and A. D. Yablon, “Improved supercontinuum generation through UV processing of highly nonlinear fibers,” J. Lightwave Technol. 23, 13–18 (2005). [CrossRef]

] allows us to readily implement stable and practical supercontinuum sources. The rapid progress of the high-peak power fiber laser technology, on the other hand, enables us to sort out the compactness issue associated with the supercontinuum source using bulky Ti:Sapphire laser systems.

Supercontinuum generation in optical fibers is mainly based on the combined use of a high peak-power sub-picosecond pulse laser and an adequate nonlinear optical fiber. The generated supercontinuum also exhibits short pulse characteristics in the time domain [1

1. K. Mori, K. Sato, H. Takara, and T. Ohara, “Supercontinuum lightwave source generating 50 GHz spaced optical ITU grid seamlessly over S-, C- and L-bands,” Electronics Lett. 39, 544–546 (2003). [CrossRef]

]. Although a spatial- and phase-coherent spectral continuum can be easily obtained by injecting sub-picosecond pulses into a highly-nonlinear fiber, the considerable intensity noise in the time domain that could be caused by the nonlinear amplification of quantum fluctuations both in the input laser light and in the Raman scattering process, might be a limiting factor for some applications [7

7. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90, 113904 (2003). [CrossRef] [PubMed]

].

An alternative approach for generation of high quality of optical supercontinuum in both of the spectral and temporal domains would be the use of a pure continuous-wave (CW) pump beam within a highly-nonlinear fiber. Prabhu et al. first demonstrated that CW supercontinuum could be generated in optical fibers by using a strong CW Raman fiber laser pump [8

8. M. Prabhu, N. S. Kim, and K. Ueda, “Ultra-broadband CW supercontinuum generation centered at 1483.4 nm from Brillouin/Raman fiber laser,” Jpn. J. Appl. Phys. 39, L291–L293 (2000). [CrossRef]

]. Further researches by other groups have been subsequently performed to understand the physical origin of CW supercontinuum phenomenon and have resulted in a range of demonstrations of novel CW supercontinuum sources [9

9. A. V. Avdokhin, S. V. Popov, and J. R. Taylor, “Continuous-wave, high-power, Raman continuum generation in holey fibers,” Opt. Lett. 28, 1353–1355 (2003). [CrossRef] [PubMed]

,10

10. W. Zhang, Y. Wang, J. Peng, and X. Liu, “Broadband high power continuous wave fiber Raman source and its applications,” Opt. Comm. 231, 371–374 (2004). [CrossRef]

,11

11. A. K. Abeeluck, C. Headley, and C. G. JØrgensen, “High-power supercontinuum generation in highly nonlinear dispersion-shifted fibers by use of a continuous-wave Raman fiber laser,” Opt. Lett. 29, 2163–2165 (2004). [CrossRef] [PubMed]

,12

12. A. K. Abeeluck and C. Headley, “Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation,” Opt. Lett. 30, 61–63 (2005). [CrossRef] [PubMed]

].

Recently, we experimentally demonstrated a new concept of the rare earth-doped fiber-based CW supercontinuum laser [13

13. J. H. Lee, Y. Takushima, and K. Kikuchi, “Continuous-wave supercontinuum laser based on erbium-doped fiber ring cavity incorporating highly-nonlinear optical fiber,” to be published in Opt. Lett. (2005).

]. The laser had a simple ring cavity structure incorporating an erbium-doped fiber (EDF) and an HNL-DSF. Erbium gain inside the cavity generates a seed light oscillation and the oscillated light subsequently evolved into supercontinuum by interplay between MI and SRS in the HNL-DSF. Using the laser high quality of the depolarized supercontinuum laser output with a spectral bandwidth larger than 200 nm was readily achieved.

In this paper, we experimentally carry out further research on our proposed EDF-based CW supercontinuum laser. In particular, the performance of our proposed supercontinuum laser is compared with that of two other CW supercontinuum generating schemes, i.e. the Raman gain-based ring cavity supercontinuum laser and the conventional CW supercontinuum generating source based on single propagation of the pump beam through a highly-nonlinear fiber.

2. Experimental setup

Experimental schematics of the three different configurations for generation of CW supercontinuum are shown in Fig. 1, together with that of a conventional EDF-based ring laser. Type I is our proposed EDF-based supercontinuum ring laser incorporating an HNL-DSF. The laser of Type I had a simple ring cavity structure based on EDF gain. The EDF used inside the cavity had a peak absorption of 16.7 dB/m at 1530 nm and a length of 5 m. Different from the conventional EDF-based ring cavity lasers, a 2-km-long HNL-DSF with a nonlinearity parameter γ of 15.5 W-1.km-1 was inserted into the cavity. The zero group velocity dispersion (GVD) wavelength of the HNL-DSF was 1554 nm and the dispersion slope was 0.027 ps/nm2/km. The fiber propagation loss was ~1.3 dB/km. As an EDF pump source we used a commercially-available high-power 1480-nm Raman fiber laser and the pump power up to ~2.2 W was coupled into the cavity via a 1480/1550-nm wavelength division multiplexer (WDM) of filter type. The laser output power was extracted from the ring cavity using an 80:20 fiber coupler, with which 80 % of the oscillated light was fed back into the EDF. An optical isolator was placed after the coupler within the cavity to ensure the directional light oscillation

Fig. 1. Experimental schematics. (a) Type I: EDF-based supercontinuum laser incorporating an HNL-DSF. (b) Type II: Raman-based supercontinuum laser incorporating an HNL-DSF. (c) Type III: Conventional single-pass supercontinuum source. (d) Conventional EDF-based ring laser

Type II is a Raman gain-based supercontinuum ring laser where the 5-m-long EDF was not employed. The pump beam was directly launched into the 2-km-long HNL-DSF within the cavity by the WDM to generate SRS. Type II was composed of the same optical components to those of Type I as shown in Fig. 1(b). Type III in Fig. 1(c) is a conventional CW supercontinuum generating structure where a strong pump beam simply propagates through the 2-km HNL-DSF. Figure 1(d) illustrates a conventional EDF-based ring laser incorporating only the 5-m-long EDF within the cavity.

3. Experimental results

Fig. 2. Measured spectral evolution of the optical output as a function of pump power. (a) Type I: EDF-based supercontinuum laser incorporating an HNL-DSF. (b) Type II: Raman-based supercontinuum laser incorporating an HNL-DSF. (c) Type III: Conventional singl-pass supercontinuum source. (d) Conventional EDF-based ring laser

First, we performed the measurement of spectral evolution for the output beams from the four configurations described in Fig.1 as a function of pump power. These results are summarized in Fig. 2. In case of our proposed EDF-based supercontinuum laser of Type I, a seed light oscillation was generated at a wavelength of 1562 nm due to the strong EDF gain as shown in Fig. 2(a). At a pump power of 0.185 W we observed a single spectral peak output with an extremely broad linewidth of 9 nm, which is unusual in case of conventional erbium-doped fiber ring lasers. This linewidth broadening can be attributed to MI within the laser cavity [14

14. V. Roy and P. A.-Vachon, “Modulation instability in cw erbium-doped fiber ring lasers,” in Proc. Quantum Electronics and Laser Science Conference, Baltimore USA, May 2001, paper QThF5.

]. Even the second spectral peak started growing at a pump power of 0.48 W and a broadband double peak spectrum was clearly observed at a pump power level of 0.762 W. The double peak phenomenon could be explained by using Raman pulse generation phenomenon [12

12. A. K. Abeeluck and C. Headley, “Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation,” Opt. Lett. 30, 61–63 (2005). [CrossRef] [PubMed]

] as follows: The weak temporal perturbations appear as a noisy, feeble, ultra-short pulse train in the time domain and the shorter wavelength components of the pulses experience intraband SRS to transfer their energy into longer wavelength bands. Further increase in the pump power was found to lead to the generation of double first-order Raman Stokes lines at 1690 and 1730 nm, which were pumped by the double erbium oscillation peaks. Then, the output spectrum evolved into a flat continuum at a 1.37-W pump level. The physical mechanism of such a conversion from Raman Stokes generation into supercontinuum generation needs to be further investigated although it might be attributed to strong MI gain generation over the broad bandwidth. The high quality of CW supercontinuum was clearly observed at a pump power of more than 1.9 W. The measured 20-dB spectral bandwidth was ~250 nm, which was limited by the maximum measurable wavelength of our optical spectrum analyzer (OSA).

In case of the Raman gain-based supercontinuum ring laser of Type II as shown in Fig. 2(b) a seed light oscillation at 1580 nm grew owing to the lasing effect based on strong Raman gain within the ring cavity, different from Type I since no EDF was employed within the cavity. However, no evolution of two spectral peaks induced by Raman pulse generation was observed. The strong single Raman oscillation peak was found to transfer its energy into the second-order Stokes at ~1700 nm and subsequently to evolve into a spectral continuum as the pump power was further increased.

Different from the configurations of Type I, II, and III, the conventional EDF-based ring laser was constructed without using any HNL-DSF inside the cavity as shown in Fig. 2(d). No significant spectral broadening of the laser output was observed when the pump power was increased up to 2.18 W although some degree of MI associated linewidth broadening was observed as predicted in Ref. [14

14. V. Roy and P. A.-Vachon, “Modulation instability in cw erbium-doped fiber ring lasers,” in Proc. Quantum Electronics and Laser Science Conference, Baltimore USA, May 2001, paper QThF5.

].

Fig. 3. Measured output optical power versus pump power for the four different configurations.

Next, we characterized the four configurations in terms of output optical power. Figure 3 shows measured output optical power versus pump power for the four different configurations. Our proposed supercontinuum ring lasers of Type I exhibited some degree of output power saturation. In particular, a critical pump power turning from the linear regime into the saturating regime was observed to exist at 1.06 W. The maximum saturation output power was 83 mW at a 2.2-W pump power. Interestingly, the critical pump power of 1.06 W corresponds to the point at which SRS comes into play as shown in Fig. 2(a). The output power saturation is believed to be associated with the fact that the broadened spectral components stretch into the higher-loss wavelength bands larger than 1700nm.

In case of the Raman gain-based supercontinuum ring laser of Type II the output power saturation was also observed. Furthermore, the output power started declining when the launched pump power was enlarged to be more than 1.5 W. The measured maximum output power was 105 mW at a 1.5-W pump power. In case of the conventional single pass structure of Type III, the critical pump power was found to be only ~0.45 W and the highest power conversion efficiency was observed among the three supercontinuum generating schemes. The maximum output power was 537 mW at a 2.2-W pump power. However, the output power of the conventional erbium fiber ring lasers without the HNL-DSF was observed to be in linear proportion to pump power as expected.

Fig. 4. Measured relative intensity noise (RIN) of the output beams from the four different configurations together with that of the 1480-nm pump beam.

Finally, we measured relative-intensity noise (RIN) of the output beams from the four configurations. The outputs beams from the four configurations were passed through a 15-nm bandpass filter centered at 1570 nm, and subsequently coupled onto a low-noise photodetector with a bandwidth of 150 MHz. The detected electrical signals were then ac-coupled into an electrical spectrum analyzer. Fig. 4 shows the measured RIN spectra for the four configurations. Note that the high RIN levels of Type I, II, and III were mainly due to the fact that the commercial 1480-nm pump source used in this experiment possessed a substantially high RIN as shown in Fig. 4. One interesting point in this measurement was that Type I was found to have a lower RIN level than Type II and III by ~10 dB in a frequency range of 0~150 MHz. This means that our proposed EDF-based supercontinuum laser of Type I would not suffer from MI-induced nonlinear amplification of pump noise [15

15. S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995). [CrossRef] [PubMed]

] due to the conversion process of pump-to-laser through Er3+ ions, which have a slow response time.

4. Conclusion

We have experimentally compared performance and physical features of three different schemes for generating CW optical supercontinuum by use of nonlinear optical fiber, i.e. our proposed EDF-based supercontinuum ring laser incorporating an HNL-DSF, the Raman gain-based supercontinuum ring laser incorporating an HNL-DSF, and the conventional supercontinuum generating structure where a strong pump beam simply propagates through a an HNL-DSF. The three schemes showed different physical mechanisms of supercontinuum evolution from a pump beam although the main nonlinear process was SRS in all the three cases. In terms of RIN, our proposed EDF-based supercontinuum ring laser was found to have superior performance compared to the other two schemes owing to the slow response time of Er3+ ions in the pump-to-laser conversion. Further investigation needs to be performed for fully understanding the physical mechanism of the EDF-based supercontinuum laser.

Acknowledgments

The authors thank Y. Takushima for helpful discussion.

References and links

1.

K. Mori, K. Sato, H. Takara, and T. Ohara, “Supercontinuum lightwave source generating 50 GHz spaced optical ITU grid seamlessly over S-, C- and L-bands,” Electronics Lett. 39, 544–546 (2003). [CrossRef]

2.

I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, “Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,” Opt. Lett. 26, 608–610 (2001). [CrossRef]

3.

K. Kim, B. R. Washburn, G. Wilpers, C. W. Oates, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, and M. F. Yan, “Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser,” Opt. Lett. 30, 932–934 (2005) [CrossRef] [PubMed]

4.

H. Kano and H. Hamaguchi, “Characterization of a supercontinuum generated from a photonic crystal fiber and its application to coherent Raman spectroscopy,” Opt. Lett. 28, 2360–2362 (2003). [CrossRef] [PubMed]

5.

S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, “White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,” Opt. Lett. 26, 1356–1358 (2001). [CrossRef]

6.

P. S. Westbrook, J. W. Nicholson, K. S. Feder, and A. D. Yablon, “Improved supercontinuum generation through UV processing of highly nonlinear fibers,” J. Lightwave Technol. 23, 13–18 (2005). [CrossRef]

7.

K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, “Fundamental noise limitations to supercontinuum generation in microstructure fiber,” Phys. Rev. Lett. 90, 113904 (2003). [CrossRef] [PubMed]

8.

M. Prabhu, N. S. Kim, and K. Ueda, “Ultra-broadband CW supercontinuum generation centered at 1483.4 nm from Brillouin/Raman fiber laser,” Jpn. J. Appl. Phys. 39, L291–L293 (2000). [CrossRef]

9.

A. V. Avdokhin, S. V. Popov, and J. R. Taylor, “Continuous-wave, high-power, Raman continuum generation in holey fibers,” Opt. Lett. 28, 1353–1355 (2003). [CrossRef] [PubMed]

10.

W. Zhang, Y. Wang, J. Peng, and X. Liu, “Broadband high power continuous wave fiber Raman source and its applications,” Opt. Comm. 231, 371–374 (2004). [CrossRef]

11.

A. K. Abeeluck, C. Headley, and C. G. JØrgensen, “High-power supercontinuum generation in highly nonlinear dispersion-shifted fibers by use of a continuous-wave Raman fiber laser,” Opt. Lett. 29, 2163–2165 (2004). [CrossRef] [PubMed]

12.

A. K. Abeeluck and C. Headley, “Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation,” Opt. Lett. 30, 61–63 (2005). [CrossRef] [PubMed]

13.

J. H. Lee, Y. Takushima, and K. Kikuchi, “Continuous-wave supercontinuum laser based on erbium-doped fiber ring cavity incorporating highly-nonlinear optical fiber,” to be published in Opt. Lett. (2005).

14.

V. Roy and P. A.-Vachon, “Modulation instability in cw erbium-doped fiber ring lasers,” in Proc. Quantum Electronics and Laser Science Conference, Baltimore USA, May 2001, paper QThF5.

15.

S. B. Cavalcanti, G. P. Agrawal, and M. Yu, “Noise amplification in dispersive nonlinear media,” Phys. Rev. A 51, 4086–4092 (1995). [CrossRef] [PubMed]

OCIS Codes
(140.3500) Lasers and laser optics : Lasers, erbium
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.5650) Nonlinear optics : Raman effect

ToC Category:
Research Papers

History
Original Manuscript: May 20, 2005
Revised Manuscript: June 9, 2005
Published: June 27, 2005

Citation
Ju Han Lee and Kazuro Kikuchi, "Experimental performance comparison for various continuous-wave supercontinuum schemes: ring cavity and single pass structures," Opt. Express 13, 4848-4853 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-13-4848


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References

  1. K. Mori, K. Sato, H. Takara, and T. Ohara, �??Supercontinuum lightwave source generating 50 GHz spaced optical ITU grid seamlessly over S-, C- and L-bands,�?? Electronics Lett. 39, 544-546 (2003) [CrossRef]
  2. I. Hartl, X. D. Li, C. Chudoba, R. K. Ghanta, T. H. Ko, J. G. Fujimoto, J. K. Ranka, and R. S. Windeler, �??Ultrahigh-resolution optical coherence tomography using continuum generation in an air-silica microstructure optical fiber,�?? Opt. Lett. 26, 608-610 (2001). [CrossRef]
  3. K. Kim, B. R. Washburn, G. Wilpers, C. W. Oates, L. Hollberg, N. R. Newbury, S. A. Diddams, J. W. Nicholson, M. F. Yan, �??Stabilized frequency comb with a self-referenced femtosecond Cr:forsterite laser,�?? Opt. Lett. 30, 932-934 (2005) [CrossRef] [PubMed]
  4. H. Kano and H. Hamaguchi, �??Characterization of a supercontinuum generated from a photonic crystal fiber and its application to coherent Raman spectroscopy,�?? Opt. Lett. 28, 2360-2362 (2003). [CrossRef] [PubMed]
  5. S. Coen, A. H. L. Chau, R. Leonhardt, J. D. Harvey, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, �??White-light supercontinuum generation with 60-ps pump pulses in a photonic crystal fiber,�?? Opt. Lett. 26, 1356-1358 (2001). [CrossRef]
  6. P. S. Westbrook, J. W. Nicholson, K. S. Feder, and A. D. Yablon, �??Improved supercontinuum generation through UV processing of highly nonlinear fibers,�?? J. Lightwave Technol. 23, 13-18 (2005). [CrossRef]
  7. K. L. Corwin, N. R. Newbury, J. M. Dudley, S. Coen, S. A. Diddams, K. Weber, and R. S. Windeler, �??Fundamental noise limitations to supercontinuum generation in microstructure fiber,�?? Phys. Rev. Lett. 90, 113904 (2003). [CrossRef] [PubMed]
  8. M. Prabhu, N. S. Kim, and K. Ueda, �?? Ultra-broadband CW supercontinuum generation centered at 1483.4 nm from Brillouin/Raman fiber laser,�?? Jpn. J. Appl. Phys. 39, L291-L293 (2000). [CrossRef]
  9. A. V. Avdokhin, S. V. Popov, and J. R. Taylor, �??Continuous-wave, high-power, Raman continuum generation in holey fibers,�?? Opt. Lett. 28, 1353-1355 (2003). [CrossRef] [PubMed]
  10. W. Zhang, Y. Wang, J. Peng, and X. Liu, �??Broadband high power continuous wave fiber Raman source and its applications,�?? Opt. Comm. 231, 371-374 (2004). [CrossRef]
  11. A. K. Abeeluck, C. Headley, and C. G. J�?rgensen, �??High-power supercontinuum generation in highly nonlinear dispersion-shifted fibers by use of a continuous-wave Raman fiber laser,�?? Opt. Lett. 29, 2163-2165 (2004). [CrossRef] [PubMed]
  12. A. K. Abeeluck and C. Headley, �??Continuous-wave pumping in the anomalous- and normal-dispersion regimes of nonlinear fibers for supercontinuum generation,�?? Opt. Lett. 30, 61-63 (2005). [CrossRef] [PubMed]
  13. J. H. Lee, Y. Takushima, and K. Kikuchi, �??Continuous-wave supercontinuum laser based on erbium-doped fiber ring cavity incorporating highly-nonlinear optical fiber,�?? to be published in Opt. Lett. (2005).
  14. V. Roy and P. A.-Vachon, �??Modulation instability in cw erbium-doped fiber ring lasers,�?? in Proc. Quantum Electronics and Laser Science Conference, Baltimore USA, May 2001, paper QThF5.
  15. S. B. Cavalcanti, G. P. Agrawal, and M. Yu, �??Noise amplification in dispersive nonlinear media,�?? Phys. Rev. A 51, 4086-4092 (1995). [CrossRef] [PubMed]

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