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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 11 — May. 24, 2010
  • pp: 11700–11706
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Wideband spectral compression of wavelength-tunable ultrashort soliton pulse using comb-profile fiber

N. Nishizawa, K. Takahashi, Y. Ozeki, and K. Itoh  »View Author Affiliations


Optics Express, Vol. 18, Issue 11, pp. 11700-11706 (2010)
http://dx.doi.org/10.1364/OE.18.011700


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Abstract

We demonstrated spectral compression of ultrashort soliton pulses in a wide wavelength region based on an adiabatic soliton spectral compression technique using a comb-profile fiber. The comb-profile fiber was carefully designed using numerical analysis and fabricated using a conventional single-mode fiber and a dispersion-shifted fiber. The spectral width of a 200 fs soliton pulse was compressed from 12 to 15 nm to 0.54–0.71 nm in the wavelength region 1620–1850 nm, giving a spectral compression factor of up to 19.8–25.9. Owing to the soliton effect, the side lobe level was suppressed to –19.2 to –9.7 dB.

© 2010 OSA

1. Introduction

Wavelength-tunable, narrow-linewidth light sources are important for spectroscopy, nonlinear microscopy, metrology, optical communication, and swept-source optical coherence tomography (SS-OCT). In the field of SS-OCT, rapidly swept sources have been developed and used for high-speed OCT imaging [1

1. S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, “High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter,” Opt. Lett. 28(20), 1981–1983 (2003). [CrossRef] [PubMed]

3

3. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14(8), 3225–3237 (2006). [CrossRef] [PubMed]

]. Rapidly wavelength-tunable laser sources using semiconductor optical amplifiers (SOAs) have been developed using polygon mirrors and galvanometer mirrors [1

1. S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, “High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter,” Opt. Lett. 28(20), 1981–1983 (2003). [CrossRef] [PubMed]

,2

2. R. Huber, M. Wojtkowski, J. G. Fujimoto, J. Y. Jiang, and A. E. Cable, “Three-dimensional and C-mode OCT imaging with a compact, frequency swept laser source at 1300 nm,” Opt. Express 13(26), 10523–10538 (2005). [CrossRef] [PubMed]

]. Also, a Fourier-domain mode-locked laser (FD-MLL) has been developed as a new high-speed wavelength-tunable narrow-linewidth laser [3

3. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14(8), 3225–3237 (2006). [CrossRef] [PubMed]

]. The wavelength tuning bandwidths of these light sources are, however, limited by the gain bandwidth of the SOA used, and suitable wideband wavelength-tunable light sources, which are necessary for ultrahigh-resolution (UHR) OCT, have not yet been demonstrated.

Using ultrashort pulses and anomalous dispersive fibers, it is possible to generate widely wavelength-tunable ultrashort pulse sources [4

4. N. Nishizawa and T. Goto, “Compact system of wavelength tunable femtosecond soliton pulse generation system,” IEEE Photon. Technol. Lett. 11, 325 (1999). [CrossRef]

6

6. J. H. Lee, J. van Howe, C. Xu, and X. Liu, “Soliton self-frequency shift: Experimental demonstrations and applications,” IEEE J. Sel. Top. Quantum Electron. 14(3), 713–723 (2008). [CrossRef]

]. Since the wavelength is continuously shifted as a function of the fiber input power, electronically controlled rapid and arbitrary wavelength tuning can be demonstrated [7

7. T. Hori, N. Nishizawa, H. Nagai, M. Yoshida, and T. Goto, “Electronically controlled high-speed wavelength-tunable femtosecond soliton pulse generation using acoustooptic modulator,” IEEE Photon. Technol. Lett. 13(1), 13–15 (2001). [CrossRef]

,8

8. K. Sumimura, T. Ohta, and N. Nishizawa, “Quasi-super-continuum generation using ultrahigh-speed wavelength-tunable soliton pulses,” Opt. Lett. 33(24), 2892–2894 (2008). [CrossRef] [PubMed]

]. If we can compress the optical spectra of the generated soliton pulses, it will be possible to demonstrate wideband and ultrafast wavelength-tunable narrow-linewidth light sources.

So far, there have been few studies of spectral compression of ultrashort pulses [9

9. M. Oberthaler and R. A. Hopfel, “Spectral narrowing of ultrashort laser pulses by self-phase modulation in optical fibers,” Appl. Phys. Lett. 63(8), 1017 (1993). [CrossRef]

12

12. E. R. Andresen, J. Thøgersen, and S. R. Keiding, “Spectral compression of femtosecond pulses in photonic crystal fibers,” Opt. Lett. 30(15), 2025–2027 (2005). [CrossRef] [PubMed]

]. Pre-chirping using a prism pair and self-phase modulation in optical fiber have been used for spectrum narrowing. With this approach, a spectral compression factor of 16 was obtained at a wavelength of 1060 nm [11

11. J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tunnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B 74(2), 191–195 (2002). [CrossRef]

]. Also, a compression factor of 21 was achieved at a wavelength of 800 nm using a photonic crystal fiber [12

12. E. R. Andresen, J. Thøgersen, and S. R. Keiding, “Spectral compression of femtosecond pulses in photonic crystal fibers,” Opt. Lett. 30(15), 2025–2027 (2005). [CrossRef] [PubMed]

]. However, a side lobe component generally arises with this approach, and it is difficult to obtain a high-quality narrow spectrum. In addition, spectrum narrowing in a wide wavelength band has also not been demonstrated yet.

In the work described here, we demonstrated wideband spectral compression of wavelength-tunable soliton pulses based on an adiabatic soliton spectral compression technique in dispersion-increasing fiber. A comb-like dispersion profiled fiber (CPF), which has been developed for pulse compression and high-repetition-rate pulse generation [13

13. S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Comblike dispersion-profiled fiber for soliton pulse train generation,” Opt. Lett. 19(8), 539–541 (1994). [CrossRef] [PubMed]

,14

14. K. Igarashi, J. Hiroishi, T. Yagi, and S. Namiki, “Comb-like profiled fiber for efficient generation of high quality 160 GHz sub-picosecond soliton train,” Electron. Lett. 41(12), 688 (2005). [CrossRef]

], was employed to realize the dispersion-increasing fiber. The CPF was carefully designed by numerical analysis and fabricated by fusion splicing a conventional single-mode fiber and a dispersion-shifted fiber. High-quality spectral compression was successfully demonstrated in a wide wavelength region using this technique.

2. Numerical analysis of adiabatic soliton spectral compression in comb-like dispersion profiled fiber

First we explain the principle of adiabatic soliton spectral compression. The soliton order, N, is given by
N2=γP0TFWHM23.11|β2|,
(1)
where γ is the nonlinear coefficient, P 0 is the peak power, TFWHM is the temporal pulse width at full-width at half-maximum (FWHM), and β2 is the second-order dispersion [15

15. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

]. When an optical pulse whose soliton order is between 0.5 and 1.5 propagates along a fiber, the pulse automatically changes its shape and gradually becomes a fundamental soliton, whose soliton order N = 1, by the soliton effect. Thus, from Eq. (1), if |β2| is continuously increased along the propagation length, the propagating pulse is gradually temporally broadened, and the pulse spectrum is gradually compressed to preserve the fundamental soliton condition. The propagating soliton pulse keeps a sech2 shape so that the spectral shape is preserved and the pedestal component is suppressed. Since there is no energy dissipation in this process, we call this spectral compression technique adiabatic soliton spectral compression.

A special fabrication process is required to realize a dispersion-increasing fiber. We employed the CPF technique, which was developed for pulse compression [13

13. S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Comblike dispersion-profiled fiber for soliton pulse train generation,” Opt. Lett. 19(8), 539–541 (1994). [CrossRef] [PubMed]

,14

14. K. Igarashi, J. Hiroishi, T. Yagi, and S. Namiki, “Comb-like profiled fiber for efficient generation of high quality 160 GHz sub-picosecond soliton train,” Electron. Lett. 41(12), 688 (2005). [CrossRef]

]. Recently, CPF has also been used for parabolic pulse generation [16

16. B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fiber,” Electron. Lett. 42(17), 965 (2006). [CrossRef]

]. In those studies, CPF has been used to realize a dispersion-decreasing profile. In this work, the dispersion-increasing fiber was demonstrated with the CPF technique using only a commercially available conventional single-mode fiber (SMF) and dispersion-shifted fiber (DSF).

Figure 1
Fig. 1 (a) Profile of actual and averaged second-order dispersion of comb-profile fiber at each segment, and variation of (b) spectral width at FWHM and (c) soliton order, N, as a function of propagation length.
shows the dispersion profile and variation of the pulse characteristics for the CPF as a function of propagation length. The comb-profile fiber was designed to exhibit the narrowest ideal pulse spectrum at a wavelength of 1.62 μm using numerical analysis based on the strict nonlinear Schrödinger equation [15

15. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

]. The effect of splice loss, chromatic dispersion, and wavelength dependence of propagation loss and mode field diameter were considered. The magnitude of β2 was gradually decreased from –5 to –28 ps2/km. The CPF was made starting with a short piece of SMF having a β2 value of –28 ps2/km at 1.62 μm. Then the SMF was spliced with DSF having a β2 value of –5 ps2/km at 1.62 μm. As the fiber length was increased, the ratio of SMF was gradually increased, and average dispersion finally reached –28 ps2/km after a propagation length of 740 m. In this work, the average splice loss was 0.13 dB. As the number of splicing points increases, the variation of the average dispersion becomes gentle, but the total splicing loss increases. Therefore, the CPF was designed to obtain the ideal spectrum with the minimum number of splicing points. In this work, the total number of fusion splices was 19, and total splice loss was about 2.5 dB.

Figure 1(b) shows the variation of the spectral width in the CPF for the wavelengths of 1620 and 1770 nm. As the parameters of the input pulse, the temporal width was 200 fs, and the peak power was 150 W for 1620 nm. For 1770 nm, the temporal width was 200 fs, and the peak power was 700 W. The pulse spectrum was initially compressed and then gradually narrowed along the fiber. The soliton order varied between 0.25 and 2.75 and then gradually reached 1.0, as shown in Fig. 1(c). It is interesting to note that we can see some small fluctuations on the curve for 1620 nm wavelength in Fig. 1(b) around the breathing point in Fig. 1(c).

Figure 2
Fig. 2 (a) Spectra (Media 1) and (b) temporal shapes of input and output pulses for the CPF at wavelength of 1620 nm. The instantaneous wavelength of the output pulse is also shown in (b).
shows the temporal and spectral shapes of the CPF input and output pulses at a wavelength of 1620 nm, for which the CPF was designed. The variation of the pulse spectrum as a function of propagation length is also shown as a movie in Media 1. The spectral width was compressed from 12.3 nm to 0.72 nm. The compression factor was as large as 17. The side lobe was also well-suppressed, generating a high-quality narrow line spectrum. The brightness at the center of the spectrum was increased by a factor of 10. Regarding the temporal shape, a clear sech2-shaped pulse was obtained at the output. The temporal width was 4.3 ps at 1620 nm, which is an almost transform-limited pulse. In practice, there were negligibly small sub-pulses before and after the main pulse. They correspond to the small sidelobe components in the pulse spectrum. For the wavelength of 1770 nm, a 0.78 nm compressed spectrum with low side lobes was also obtained. In the numerical analysis, the performance of spectral compression was almost the same as that for an ideal dispersion increasing fiber, except for power attenuation. For the spectral width, the narrower the input pulse spectrum was, the narrower the compressed pulse spectrum was.

3. Experimental

Figure 3
Fig. 3 Experimental setup for spectral compression of wavelength-tunable soliton pulses using CPF. PBS: polarization beam splitter, PM-SMF: polarization-maintaining single mode fiber, VA: variable attenuator, CPF: comb-like dispersion profile fiber.
shows the experimental setup for spectral compression of wavelength-tunable soliton pulses. A passively mode-locked Er-doped fiber laser (IMRA, femtolite B-35) was used as the seed pulse source. It generated ~200 fs sech2-like ultrashort pulses, which were introduced into a custom-made Er-doped fiber amplifier system, and the amplified pulses were coupled into polarization maintaining SMF to generate wavelength-tunable soliton pulses [4

4. N. Nishizawa and T. Goto, “Compact system of wavelength tunable femtosecond soliton pulse generation system,” IEEE Photon. Technol. Lett. 11, 325 (1999). [CrossRef]

,5

5. N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron. 45(11), 1446–1455 (2009). [CrossRef]

]. The wavelength of the soliton pulses was varied by controlling the fiber input power. The output pulses were passed through a long-pass filter to pick out only the soliton pulses. The observed temporal width of the soliton pulses was almost constant at ~215 fs FWHM for the whole wavelength region. Then, the power of the soliton pulses was controlled using a variable attenuator, and then the attenuated pulses were coupled into the CPF. The output pulses were observed using an optical spectrum analyzer and a power meter.

Figure 4
Fig. 4 Optical spectra of spectrum-compressed pulse at 1620 nm, showing (a) experimental and (b) numerical results.
shows the experimental and numerical optical spectra of the spectrum-compressed pulse at 1620 nm. Experimentally, the spectral width was 0.62 nm FWHM, and the side lobe level was –19.2 dB from the spectral peak. Numerically, the spectral width was 0.724 nm FWHM, and the side lobe level was –18.0 dB. The numerical results were almost in agreement with the experimental ones for the whole wavelength region.

Figure 5
Fig. 5 Optical spectra of (a) wavelength-tunable soliton pulses and (b) spectrum-compressed pulses in the wavelength region 1620–1850 nm.
shows the optical spectra of the generated wavelength-tunable soliton pulses and spectrum-compressed pulses. The sharp spikes in the soliton pulse spectra in the 1800–1900 nm region in Fig. 5(a) were due to the effect of H2O absorption in the optical spectrum analyzer. For the spectral compression, the input power into the comb-profile fiber was optimized at each wavelength. Large spectral compression was obtained in a wide wavelength region from 1620 to 1850 nm. The original pulse spectrum with a width of 12.3–15.1 nm was compressed to 0.54–0.71 nm.

Figure 6
Fig. 6 Wavelength dependence of the spectral compression showing (a) compressed spectral width at FWHM, compression ratio (CR), and side lobe suppression ratio (SLSR) and (b) output power and power of soliton pulse.
shows the wavelength dependence of the spectral compression and output power. Here we defined the side lobe suppression ratio (SLSR) as the ratio the spectral peak level to side lobe level. The compressed spectral width was below 0.71 nm, giving a spectral compression ratio larger than 20, for the whole wavelength region. The observed maximum compression factor was up to 25.9. The SLSR was also larger than 9.7 dB for the whole wavelength region. As the center wavelength was increased, the SLSR gradually decreased. The maximum SRSL was 19.2 dB at 1620 nm, and the minimum was 9.7 dB at 1850 nm. The output power almost linearly increased from 1.2 to 5.4 mW as the wavelength was increased.

In order to obtain the optimum spectral compression, the coupling ratio into the CPF has to be controlled as a function of the wavelength. In this work, we used the chromatic aberration of the coupling lens to demonstrate the wavelength dependence of the fiber coupling ratio. Figure 7
Fig. 7 Optical spectra of spectrum-compressed wavelength-tunable soliton pulses using CPF and chromatic ablation of coupling lens.
shows the optical spectra of the spectrum-compressed pulses when only the wavelength of the soliton pulse was shifted. Although the narrowest spectra were not obtained at some wavelengths, well-compressed pulse spectra were obtained in the 1620–1840 nm region without a variable attenuator. Using a specially designed wavelength filter, it is expected that we can optimize the spectral compression performance for a wide wavelength region. If we use the photonic crystal fibers, although the output power is attenuated by the effect of splice loss, it is expected that we can demonstrate this technique of spectral compression at the shorter wavelength range.

4. Conclusion

We demonstrated spectral compression of wavelength-tunable ultrashort soliton pulses using a comb-like dispersion profile fiber (CPF). The CPF, using only commercially available single mode fiber and dispersion-shifted fiber, was designed to realize a dispersion-increasing fiber, bringing about an adiabatic soliton spectral compression phenomenon. Sech2-shaped spectra of 12–15 nm were compressed down to 0.54–0.71 nm over a wide wavelength range of 1620–1850 nm. The observed maximum compression factor was up to 25.9. To the best of our knowledge, this is the largest spectral compression factor observed to date. Owing to the soliton effect, the side lobe components were well-suppressed at the level of –9.7 to –19.2 dB. It is expected that we can demonstrate rapid and arbitrary wavelength sweeping motion by using an intensity modulator. This system consists mostly of all-fiber devices and is useful for practical applications, such as spectroscopy and swept-source optical coherence tomography.

References and links

1.

S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, “High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter,” Opt. Lett. 28(20), 1981–1983 (2003). [CrossRef] [PubMed]

2.

R. Huber, M. Wojtkowski, J. G. Fujimoto, J. Y. Jiang, and A. E. Cable, “Three-dimensional and C-mode OCT imaging with a compact, frequency swept laser source at 1300 nm,” Opt. Express 13(26), 10523–10538 (2005). [CrossRef] [PubMed]

3.

R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14(8), 3225–3237 (2006). [CrossRef] [PubMed]

4.

N. Nishizawa and T. Goto, “Compact system of wavelength tunable femtosecond soliton pulse generation system,” IEEE Photon. Technol. Lett. 11, 325 (1999). [CrossRef]

5.

N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron. 45(11), 1446–1455 (2009). [CrossRef]

6.

J. H. Lee, J. van Howe, C. Xu, and X. Liu, “Soliton self-frequency shift: Experimental demonstrations and applications,” IEEE J. Sel. Top. Quantum Electron. 14(3), 713–723 (2008). [CrossRef]

7.

T. Hori, N. Nishizawa, H. Nagai, M. Yoshida, and T. Goto, “Electronically controlled high-speed wavelength-tunable femtosecond soliton pulse generation using acoustooptic modulator,” IEEE Photon. Technol. Lett. 13(1), 13–15 (2001). [CrossRef]

8.

K. Sumimura, T. Ohta, and N. Nishizawa, “Quasi-super-continuum generation using ultrahigh-speed wavelength-tunable soliton pulses,” Opt. Lett. 33(24), 2892–2894 (2008). [CrossRef] [PubMed]

9.

M. Oberthaler and R. A. Hopfel, “Spectral narrowing of ultrashort laser pulses by self-phase modulation in optical fibers,” Appl. Phys. Lett. 63(8), 1017 (1993). [CrossRef]

10.

B. R. Washburn, J. A. Buck, and S. E. Ralph, “Transform-limited spectral compression due to self-phase modulation in fibers,” Opt. Lett. 25(7), 445–447 (2000). [CrossRef]

11.

J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tunnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B 74(2), 191–195 (2002). [CrossRef]

12.

E. R. Andresen, J. Thøgersen, and S. R. Keiding, “Spectral compression of femtosecond pulses in photonic crystal fibers,” Opt. Lett. 30(15), 2025–2027 (2005). [CrossRef] [PubMed]

13.

S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Comblike dispersion-profiled fiber for soliton pulse train generation,” Opt. Lett. 19(8), 539–541 (1994). [CrossRef] [PubMed]

14.

K. Igarashi, J. Hiroishi, T. Yagi, and S. Namiki, “Comb-like profiled fiber for efficient generation of high quality 160 GHz sub-picosecond soliton train,” Electron. Lett. 41(12), 688 (2005). [CrossRef]

15.

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).

16.

B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fiber,” Electron. Lett. 42(17), 965 (2006). [CrossRef]

OCIS Codes
(060.5530) Fiber optics and optical communications : Pulse propagation and temporal solitons
(320.5540) Ultrafast optics : Pulse shaping

ToC Category:
Ultrafast Optics

History
Original Manuscript: April 2, 2010
Revised Manuscript: May 15, 2010
Manuscript Accepted: May 15, 2010
Published: May 18, 2010

Citation
N. Nishizawa, K. Takahashi, Y. Ozeki, and K. Itoh, "Wideband spectral compression of wavelength-tunable ultrashort soliton pulse using comb-profile fiber," Opt. Express 18, 11700-11706 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-11-11700


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References

  1. S. H. Yun, C. Boudoux, G. J. Tearney, and B. E. Bouma, “High-speed wavelength-swept semiconductor laser with a polygon-scanner-based wavelength filter,” Opt. Lett. 28(20), 1981–1983 (2003). [CrossRef] [PubMed]
  2. R. Huber, M. Wojtkowski, J. G. Fujimoto, J. Y. Jiang, and A. E. Cable, “Three-dimensional and C-mode OCT imaging with a compact, frequency swept laser source at 1300 nm,” Opt. Express 13(26), 10523–10538 (2005). [CrossRef] [PubMed]
  3. R. Huber, M. Wojtkowski, and J. G. Fujimoto, “Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography,” Opt. Express 14(8), 3225–3237 (2006). [CrossRef] [PubMed]
  4. N. Nishizawa and T. Goto, “Compact system of wavelength tunable femtosecond soliton pulse generation system,” IEEE Photon. Technol. Lett. 11, 325 (1999). [CrossRef]
  5. N. Nishizawa, “Highly functional all-optical control using ultrafast nonlinear effects in optical fibers,” IEEE J. Quantum Electron. 45(11), 1446–1455 (2009). [CrossRef]
  6. J. H. Lee, J. van Howe, C. Xu, and X. Liu, “Soliton self-frequency shift: Experimental demonstrations and applications,” IEEE J. Sel. Top. Quantum Electron. 14(3), 713–723 (2008). [CrossRef]
  7. T. Hori, N. Nishizawa, H. Nagai, M. Yoshida, and T. Goto, “Electronically controlled high-speed wavelength-tunable femtosecond soliton pulse generation using acoustooptic modulator,” IEEE Photon. Technol. Lett. 13(1), 13–15 (2001). [CrossRef]
  8. K. Sumimura, T. Ohta, and N. Nishizawa, “Quasi-super-continuum generation using ultrahigh-speed wavelength-tunable soliton pulses,” Opt. Lett. 33(24), 2892–2894 (2008). [CrossRef] [PubMed]
  9. M. Oberthaler and R. A. Hopfel, “Spectral narrowing of ultrashort laser pulses by self-phase modulation in optical fibers,” Appl. Phys. Lett. 63(8), 1017 (1993). [CrossRef]
  10. B. R. Washburn, J. A. Buck, and S. E. Ralph, “Transform-limited spectral compression due to self-phase modulation in fibers,” Opt. Lett. 25(7), 445–447 (2000). [CrossRef]
  11. J. Limpert, T. Gabler, A. Liem, H. Zellmer, and A. Tunnermann, “SPM-induced spectral compression of picosecond pulses in a single-mode Yb-doped fiber amplifier,” Appl. Phys. B 74(2), 191–195 (2002). [CrossRef]
  12. E. R. Andresen, J. Thøgersen, and S. R. Keiding, “Spectral compression of femtosecond pulses in photonic crystal fibers,” Opt. Lett. 30(15), 2025–2027 (2005). [CrossRef] [PubMed]
  13. S. V. Chernikov, J. R. Taylor, and R. Kashyap, “Comblike dispersion-profiled fiber for soliton pulse train generation,” Opt. Lett. 19(8), 539–541 (1994). [CrossRef] [PubMed]
  14. K. Igarashi, J. Hiroishi, T. Yagi, and S. Namiki, “Comb-like profiled fiber for efficient generation of high quality 160 GHz sub-picosecond soliton train,” Electron. Lett. 41(12), 688 (2005). [CrossRef]
  15. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic Press, 2007).
  16. B. Kibler, C. Billet, P.-A. Lacourt, R. Ferriere, L. Larger, and J. M. Dudley, “Parabolic pulse generation in comb-like profiled dispersion decreasing fiber,” Electron. Lett. 42(17), 965 (2006). [CrossRef]

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