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Optics Express

  • Editor: Michael Duncan
  • Vol. 10, Iss. 5 — Mar. 11, 2002
  • pp: 256–261
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Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers

Norihiko Nishizawa and Toshio Goto  »View Author Affiliations


Optics Express, Vol. 10, Issue 5, pp. 256-261 (2002)
http://dx.doi.org/10.1364/OE.10.000256


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Abstract

A novel phenomenon of trapped pulse generation by orthogonally polarized femtosecond soliton pulse is discovered in low birefringent optical fiber. As pulse propagation, wavelengths of soliton pulse and trapped pulse are shifted toward longer wavelength side due to effects of soliton self-frequency shift and pulse trapping. The energy of trapped pulse is increased exponentially through Raman gain of soliton pulse and orthogonally polarized and temporally overlapped two colored femtosecond twin pulses are generated. The spectrogram of output pulses is observed using cross-correlation frequency resolved optical gating technique. The characteristics of this phenomenon are also analyzed numerically and numerical results are almost in agreement with experimental ones.

© 2002 Optical Society of America

1. Introduction

Nonlinear optical effects can be obtained effectively using optical fibers and ultrashort pulses. So far, the wavelength tunable ultrashort pulses and super continuum have been generated [1–4

1. N. Nishizawa and T. Goto, “Compact system of wavelength tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11, 325–327 (1999). [CrossRef]

]. These light sources are useful for optical communications, spectroscopy, etc.

When the optical pulses collide in a fiber, the interaction between the pulses is induced through the nonlinear optical effects [5

5. G. P. Agrawal, Nonlinear fiber optics, third ed. (Academic, San Diego, Calif. 2001).

]. In 1989, Islam et al discovered the phenomenon of soliton trapping in low birefringent optical fibers, in which two orthogonally polarized equal intensity soliton pulses trap each other and copropagate along the fiber [6

6. M. N. Islam, C. D. Poole, and J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett. 14, 1011–1013 (1989). [CrossRef] [PubMed]

]. This phenomenon is observed at the low power level in which the effect of Raman scattering is negligible.

Recently, we have discovered a new phenomenon, pulse trapping by a femtosecond soliton pulse across the zero-dispersion wavelength [7

7. N. Nishizawa and T. Goto, “Pulse trapping by ultrashort soliton pulses in optical fibers across zero-dispersion wavelength,” Opt. Lett. 27, 152–154 (2002). [CrossRef]

]. In this phenomenon, optical pulse at normal dispersion region is trapped by a femtosecond soliton pulse at anomalous dispersion region and the trapped pulse and soliton pulse copropagate along the fiber. As the fiber input power of the soliton pulse is increased, the wavelength of the soliton pulse is shifted toward the longer wavelength side due to the soliton self-frequency shift (SSFS) [8

8. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986). [CrossRef] [PubMed]

] and that of the trapped pulse is shifted toward the shorter wavelength side.

In this paper, a novel phenomenon of trapped pulse generation by orthogonally polarized femtosecond soliton pulse is discovered in low birefringent fiber. In ref. 9

9. N. Nishizawa and T. Goto, “Widely wavelength-tunable ultrashort pulse generation using polarization maintaining fibers,” IEEE J. Select. Topics in Quantum Electron. 7, 325–327 (2001). [CrossRef]

, we have observed a phenomenon that the orthogonally polarized small pulse spectrum is trapped by a soliton pulse in low birefringent fiber. In this paper, it is observed, to the best of our knowledge, for the first time that the orthogonally polarized pulse is trapped by the soliton pulse and the trapped pulse is amplified through the Raman gain of the soliton pulse. The energy of the trapped pulse is finally increased above that of the soliton pulse. The temporal relation of the spectrum components for the pulse trapping is observed using the technique of cross-correlation frequency resolved optical gating (X-FROG) [10

10. S. Linden, H. Giessen, and J. Kuhl, “XFROG-a new method for amplitude and phase characterization of weak ultrashort pulses,” Phys. Stat. Sol. (b) 206, 119–124 (1998). [CrossRef]

,11

11. N. Nishizawa and T. Goto, “Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlated frequency resolved optical gating,” Opt. Express 8, 328–335 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328. [CrossRef] [PubMed]

] and the pulse trapping by the soliton pulse is directly observed.

So far, the co-propagation of two optical pulses have been investigated numerically for the non-birefringent fiber with the effect of Raman scattering and for the birefringent fiber without Raman scattering [12

12. S. Kumar, A. Selvarajan, and G. V. Anand, “Influence of Raman scattering on the cross phase modulation in optical fibers,” Opt. Commun. 102, 329–335 (2002). [CrossRef]

,13

13. S. Kumar, A. Selvarajan, and G. V. Anand, “Nonlinear copropagation of two optical pulses of different frequencies in birefringent fibers,” J. Opt. Soc. Am. B 11, 810–817 (1994). [CrossRef]

]. In this paper, in addition to the experiments, the co-propagation of two ultrashort pulses in birefringent optical fibers are analyzed numerically considering the effects of Raman scattering, corss-phase modulation, Raman gain, etc. The characteristics of the trapped pulse generation are analyzed using the strict coupled nonlinear Schrödinger equations.

2. Experimental

In the experiment, the passively mode-locked Er-doped fiber laser (IMRA femtolight) is used as the laser source. It generates non-transform limited 110 fs sech2 like ultrashort pulse at wavelength of 1.55 μm. The repetition frequency is 48 MHz and the pulse energy is 1.2 nJ. The spectral width of the output pulse is 20 nm at full width at half maximum (FWHM) and the pulse spectrum is broadened from 1515 to 1600 nm at -30 dB level from the spectral peak.

Fig.1 Observed optical spectra of soliton pulse and trapped pulse when the polarization direction of the input pulse is inclined from the slow axis of LB-PMF by 19 degree. The fiber length is 140 m and fiber input power is 30 mW. The spectra around 1556 nm are the pump pulse at fast axis and the residual components of the pump pulse at slow axis which are not converted into the soliton pulse.

The laser output is passed through a half-wave plate and polarization beam splitter and the throughput power is controlled. Then the polarization direction of the pulse from the fiber laser is rotated by the half-wave plate and the output pulses are coupled into the optical fibers.

As the optical fiber, a low birefringent polarization maintaining fiber (LB-PMF, 3M CG-5811) is used. The magnitude of the second-order dispersion is -19 ps2/km at a wavelength of 1.55 μm and the diameter of the core is 8 μm. The magnitude of birefringence is 3×10-4.

When the polarization direction of the input pulse is aligned along the fast axis, the mono-colored femtosecond soliton pulse is generated at the longer wavelength side of the pump pulse due to the effect of SSFS [1

1. N. Nishizawa and T. Goto, “Compact system of wavelength tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11, 325–327 (1999). [CrossRef]

,9

9. N. Nishizawa and T. Goto, “Widely wavelength-tunable ultrashort pulse generation using polarization maintaining fibers,” IEEE J. Select. Topics in Quantum Electron. 7, 325–327 (2001). [CrossRef]

,14

14. N. Nishizawa, R. Okamura, and T. Goto, “Analysis of widely wavelength tunable femtosecond soliton pulse generation using optical fibers,” Jpn. J. Appl. Phys. 38, 4768–4771 (1999). [CrossRef]

]. When the polarization direction of the input pulse is aligned along near the slow axis, in addition to the soliton pulse, the trapped pulse spectrum is observed at the longer wavelength side of the soliton pulse. Figure 1 shows the observed optical spectra at the output of 140-m-long LB-PMF. The fiber input power is 30 mW and the polarization direction of the fiber input pulse is inclined from the slow axis of LB-PMF by 19 degree. In this case, the spectral intensity of the trapped pulse is slightly increased beyond that of the soliton pulse and the maximum power of the trapped pulse is obtained. This trapped pulse is polarized along the fast axis and the center wavelength is 40 nm at the longer wavelength side of the soliton pulse. The group velocity mismatch due to birefringence is compensated by the chromatic dispersion and the soliton pulse and trapped pulse copropagate along the fiber. The soliton pulse and trapped pulse can be separated by using the polarizer [9

9. N. Nishizawa and T. Goto, “Widely wavelength-tunable ultrashort pulse generation using polarization maintaining fibers,” IEEE J. Select. Topics in Quantum Electron. 7, 325–327 (2001). [CrossRef]

].

Fig. 2 Characteristics of wavelength shift of output pulses and the intensity variation of the trapped pulse as a function of fiber length. The red line shows the spectral intensity of trapped pulse. The green and blue lines are center wavelengths of the soliton pulse and trapped pulse, respectively.

Figure 2 shows the characteristics of the wavelength shift of output pulses and the intensity variation of the trapped pulse in terms of the fiber length. Since the spectral width and shape of the trapped pulse are not changed, the peak intensity of the pulse spectrum is in proportion to the pulse energy. As the fiber length is increased, the wavelength of the soliton pulse is increased monotonously due to SSFS [8

8. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986). [CrossRef] [PubMed]

,14

14. N. Nishizawa, R. Okamura, and T. Goto, “Analysis of widely wavelength tunable femtosecond soliton pulse generation using optical fibers,” Jpn. J. Appl. Phys. 38, 4768–4771 (1999). [CrossRef]

]. The wavelength of the trapped pulse is also shifted toward the longer wavelength side keeping the wavelength separation between the two pulses. The magnitude of the wavelength separation is about 40–50 nm and it is slightly decreased as the magnitudes of the wavelength shifts of two pulses are increased [9

9. N. Nishizawa and T. Goto, “Widely wavelength-tunable ultrashort pulse generation using polarization maintaining fibers,” IEEE J. Select. Topics in Quantum Electron. 7, 325–327 (2001). [CrossRef]

]. Since the wavelength separation between the soliton pulse and trapped pulse is within the bandwidth of the Raman gain in silica fiber, the trapped pulse suffers the Raman gain of the soliton pulse. The intensity of the trapped pulse is increased exponentially as the fiber length is increased. Since the longer wavelength side of the pulse spectra of pump pulse is broadened up to 1600 nm, it is considered that a part of the spectral components at the longer wavelength side of the pump pulse at fast axis are initially trapped by the soliton pulse at slow axis and acts as the seed pulse of the generated trapped pulse. In terms of power dependence, the energy of the trapped pulse is also increased monotonously as the fiber input power is increased.

Next, in order to observe the precise temporal relation of the soliton pulse and trapped pulse, we have observed the spectrogram of the output pulses from the fiber using the technique of X-FROG [10

10. S. Linden, H. Giessen, and J. Kuhl, “XFROG-a new method for amplitude and phase characterization of weak ultrashort pulses,” Phys. Stat. Sol. (b) 206, 119–124 (1998). [CrossRef]

,11

11. N. Nishizawa and T. Goto, “Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlated frequency resolved optical gating,” Opt. Express 8, 328–335 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328. [CrossRef] [PubMed]

]. Figure 3 shows the scheme of X-FROG measurement. The output pulses are divided into two optical axes at 1:1 beam splitter. At the optical axis of the reference beam, the polarization beam splitter (PBS) is used and only the soliton pulse is selected and is used as the probe pulse. Then the temporal difference between the two pulse components are adjusted using the corner mirror and the two beams are focused into the 0.3 mm thick BBO crystal using the optical lens whose focus length is 150 mm. In the optical axis of the signal pulses, the λ/2 plate is used to adjust the polarization direction of the pulses to generate the sum frequency signals of both the soliton pulse and orthogonally polarized trapped pulse. The generated sum frequency signals are passed through the monochromator and the output beam is detected using the photo multiplier tube (PMT). In order to increase the detection sensitivity, the lock-in amplifier system is used for signal amplification. The lock-in amplifier, monochromator, and delay line are all connected with the personal computer and the automatic measurement system is constructed.

Fig.3 Experimental setup of X-FROG measurement for observation of the soliton pulse and trapped pulse.

Figure 4 shows the observed spectrogram of the output pulses from 140-m-long LB-PMF using the X-FROG measurement system in Fig.3. The elliptical component at 842 nm is the SHG signal of soliton pulse and those at 852 nm are sum frequency signal of trapped pulse. The spectrogram of soliton pulse and trapped pulse are clearly observed. From this figure, it is confirmed that the soliton pulse and trapped pulse are temporally overlapped each other. The trapped pulse has two peaks and the intense peak component is slightly delayed from the center of the soliton pulse. For the soliton pulse, a pedestal free clear trace is observed. The temporal width of the soliton pulse is estimated to be 220 fs at FWHM. Owing to the effect of chromatic dispersion, the residual components of the pump pulse which are not converted into the soliton pulse are much advanced from the soliton pulses temporally [11

11. N. Nishizawa and T. Goto, “Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlated frequency resolved optical gating,” Opt. Express 8, 328–335 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328. [CrossRef] [PubMed]

]. The observed results of the X-FROG are almost in agreement with those using the auto-correlator and optical spectrum analyzer.

Fig.4 Observed spectrogram of soliton and trapped pulses at the output of 140-m-long LB-PMF.

3. Numerical analysis and discussion

Next, the characteristics of the pulse trapping are numerically analyzed using the strict coupled nonlinear Schrödinger equations [5

5. G. P. Agrawal, Nonlinear fiber optics, third ed. (Academic, San Diego, Calif. 2001).

],

Az+2A22AT2β3A63AT3=(A2A+23B2A+iω0AA2ATTRAA2T)gA2B2A
(1)
BzdBT+2B22BT2β3B63BT3=(B2B+23A2B+iω0BB2BTTRBB2T)+gB2A2B
(2)

where A is the pulse envelope in the fast axis and B is that in the slow axis of LB-PMF. In this case, A is the envelope of the soliton pulse and B is that of the trapped pulse. The symbol z is the distance and T=t1 z, where t is the time and β1 is the first-order dispersion. The left-hand side represents the linear effects; the effects of the chromatic dispersion and birefringence of are included, where d is the parameter corresponds to the birefringence, β2A, and β3A are the second- and third-order dispersions for the pulse envelope A and β2B and β3B are those for the pulse envelope B. The magnitudes of dispersion parameters are measured experimentally. The right hand sides represent the nonlinear effects; the self phase modulation, cross-phase modulation, self-steepening, Raman scattering, and the effect of Raman gain are included, where γ is the magnitude of nonlinearity, ω0A and ω0B are the center angular frequencies of the pulse envelopes A and B, T R is the parameter corresponding to the Raman response time, and gA and gB are Raman gain coefficients for the pulse envelopes of A and B. Since the fiber length is not so long, the effect of attenuation loss is neglected.

The parameters in the numerical simulation are set to be consistent with those in the experiment. As the soliton pulse, 100 fs sech2 pulse whose peak power is 2 kW is assumed. As the seed pulse of the trapped pulse, 100 fs sech2 pulse whose peak power is 2 W is assumed and injected into the fiber simultaneously with the soliton pulse. At the fiber input, the center wavelengths of the soliton pulse and seed pulse are assumed to be 1.55 and 1.65 μm, respectively.

Fig. 5 Numerical results of the characteristics of wavelength shift and variation of pulse energy for the soliton pulse and trapped pulse as a function of fiber length. Red and blue lines correspond to the characteristics of soliton pulse and trapped pulse, respectively.
Fig.6 Numerical results of trapped pulse generation at the propagation length of 140 m , (a) temporal and (b) spectral change. Red lines are slow axis components and blue ones are fast axis ones.

Figure 5 shows the characteristics of the wavelength shift and variation of pulse energy for the soliton pulse and trapped pulse as a function of fiber length. As the fiber length is increased, the center wavelength of the soliton pulse is shifted toward the longer wavelength side due to the effect of SSFS [8

8. F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986). [CrossRef] [PubMed]

,14

14. N. Nishizawa, R. Okamura, and T. Goto, “Analysis of widely wavelength tunable femtosecond soliton pulse generation using optical fibers,” Jpn. J. Appl. Phys. 38, 4768–4771 (1999). [CrossRef]

]. The center wavelength of the trapped pulse is at the longer wavelength side of the soliton pulse and is shifted toward the longer wavelength side. The wavelength separation between the soliton pulse and trapped pulse is about 30–50 nm and the group velocity matching is always satisfied. Strictly speaking, the magnitude of the wavelength separation is gradually decreased as the wavelength shift is increased due to the effect of chromatic dispersion [9

9. N. Nishizawa and T. Goto, “Widely wavelength-tunable ultrashort pulse generation using polarization maintaining fibers,” IEEE J. Select. Topics in Quantum Electron. 7, 325–327 (2001). [CrossRef]

]. As the fiber length is increased, the trapped pulse suffers the Raman gain from the soliton pulse and the energy of the soliton pulse is gradually converted into the trapped pulse. Thus the energy of the trapped pulse is increased exponentially in the propagation along the fiber and finally almost all of the energy of the soliton pulse is converted into the trapped pulse.

Figure 6 shows the spectral and temporal change for the trapped pulse generation at the propagation length of 140 m. In the numerical simulation, since the input pulse is an ideal sech2 pulse, almost all the part of the pump pulse is converted into the wavelength shifted soliton pulse and trapped pulse. In this fiber length, the trapped pulse which has almost the same temporal shape as that of the soliton pulse is generated. The trapped pulse and soliton pulse perfectly overlap each other temporally and the temporal shapes are pedestal free sech2. In the spectral domain, the soliton pulse and trapped pulse are generated at 1.690 and 1.725 μm and the spectral shapes are also clear sech2. In Fig.6(b), the small spectral components around 1.55 μm at fiber output are the residual pump pulse which are not converted into the soliton pulse. These numerical results are almost in agreement with the experimental ones.

4. Conclusion

In this paper, we have discovered a novel phenomenon of trapped pulse generation by the orthogonally polarized femtosecond soliton pulse in low birefringent optical fibers. The trapped pulse by the soliton pulse is amplified through the Raman gain of the soliton pulse in the propagation along the fiber. As the wavelength of the soliton pulse is shifted toward the longer wavelength side, the wavelength of the trapped pulse is also shifted toward the longer wavelength to satisfy the condition of group velocity matching. The spectrogram of the output pulses is observed using the X-FROG technique and it is confirmed that the soliton pulse and trapped pulse are overlapped temporally and copropagate along the fiber. The characteristics of the trapped pulse generation are analyzed numerically using the strict coupled nonlinear Schrödinger equations and the numerical results are almost in agreement with the experimental ones. Using this phenomenon, we can generate the orthogonally polarized and temporally overlapped two colored femtosecond twin pulses.

References and links

1.

N. Nishizawa and T. Goto, “Compact system of wavelength tunable femtosecond soliton pulse generation using optical fibers,” IEEE Photon. Technol. Lett. 11, 325–327 (1999). [CrossRef]

2.

N. Nishizawa, R. Okamura, and T. Goto, “Widely wavelength tunable ultrashort soliton pulse and anti-stokes pulse generation for wavelengths of 1.32–1.75 μm,” Jpn. J. Appl. Phys. 39, L409–L411 (2000). [CrossRef]

3.

T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, “Transform-limited femtosecond WDM pulse generation by spectral filtering of gigahertz supercotinuum,” Electron. Lett. 30, 1166–1168 (1994). [CrossRef]

4.

N. Nishizawa and T. Goto, “Widely broadened super continuum generation using highly nonlinear dispersion shifted fibers and femtosecond fiber laser,” Jpn. J. Appl. Phys. 40, L365–L367 (2001). [CrossRef]

5.

G. P. Agrawal, Nonlinear fiber optics, third ed. (Academic, San Diego, Calif. 2001).

6.

M. N. Islam, C. D. Poole, and J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett. 14, 1011–1013 (1989). [CrossRef] [PubMed]

7.

N. Nishizawa and T. Goto, “Pulse trapping by ultrashort soliton pulses in optical fibers across zero-dispersion wavelength,” Opt. Lett. 27, 152–154 (2002). [CrossRef]

8.

F. M. Mitschke and L. F. Mollenauer, “Discovery of the soliton self-frequency shift,” Opt. Lett. 11, 659–661 (1986). [CrossRef] [PubMed]

9.

N. Nishizawa and T. Goto, “Widely wavelength-tunable ultrashort pulse generation using polarization maintaining fibers,” IEEE J. Select. Topics in Quantum Electron. 7, 325–327 (2001). [CrossRef]

10.

S. Linden, H. Giessen, and J. Kuhl, “XFROG-a new method for amplitude and phase characterization of weak ultrashort pulses,” Phys. Stat. Sol. (b) 206, 119–124 (1998). [CrossRef]

11.

N. Nishizawa and T. Goto, “Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlated frequency resolved optical gating,” Opt. Express 8, 328–335 (2001) http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328. [CrossRef] [PubMed]

12.

S. Kumar, A. Selvarajan, and G. V. Anand, “Influence of Raman scattering on the cross phase modulation in optical fibers,” Opt. Commun. 102, 329–335 (2002). [CrossRef]

13.

S. Kumar, A. Selvarajan, and G. V. Anand, “Nonlinear copropagation of two optical pulses of different frequencies in birefringent fibers,” J. Opt. Soc. Am. B 11, 810–817 (1994). [CrossRef]

14.

N. Nishizawa, R. Okamura, and T. Goto, “Analysis of widely wavelength tunable femtosecond soliton pulse generation using optical fibers,” Jpn. J. Appl. Phys. 38, 4768–4771 (1999). [CrossRef]

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(320.7100) Ultrafast optics : Ultrafast measurements
(320.7140) Ultrafast optics : Ultrafast processes in fibers

ToC Category:
Research Papers

History
Original Manuscript: January 17, 2002
Revised Manuscript: March 5, 2002
Published: March 11, 2002

Citation
Norihiko Nishizawa and Toshio Goto, "Trapped pulse generation by femtosecond soliton pulse in birefringent optical fibers," Opt. Express 10, 256-261 (2002)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-10-5-256


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References

  1. N. Nishizawa and T. Goto, ?Compact system of wavelength tunable femtosecond soliton pulse generation using optical fibers,? IEEE Photon. Technol. Lett. 11, 325-327 (1999). [CrossRef]
  2. N. Nishizawa, R. Okamura, and T. Goto, ?Widely wavelength tunable ultrashort soliton pulse and antistokes pulse generation for wavelengths of 1.32-1.75 <font face="Symbol">m</font>m,? Jpn. J. Appl. Phys. 39, L409-L411 (2000). [CrossRef]
  3. T. Morioka, S. Kawanishi, K. Mori, and M. Saruwatari, ?Transform-limited femtosecondWDM pulse generation by spectral filtering of gigahertz supercotinuum,? Electron. Lett. 30, 1166-1168 (1994). [CrossRef]
  4. N. Nishizawa and T. Goto, ?Widely broadened super continuum generation using highly nonlinear dispersion shifted fibers and femtosecond fiber laser,? Jpn. J. Appl. Phys. 40, L365-L367 (2001). [CrossRef]
  5. G. P. Agrawal, Nonlinear fiber optics, third ed. (Academic, San Diego, Calif. 2001).
  6. M. N. Islam, C. D. Poole, and J. P. Gordon, ?Soliton trapping in birefringent optical fibers,? Opt. Lett. 14, 1011-1013 (1989). [CrossRef] [PubMed]
  7. N. Nishizawa and T. Goto, ?Pulse trapping by ultrashort soliton pulses in optical fibers across zerodispersion wavelength,? Opt. Lett. 27, 152-154 (2002). [CrossRef]
  8. F. M. Mitschke and L. F. Mollenauer, ?Discovery of the soliton self-frequency shift,? Opt. Lett. 11, 659-661 (1986). [CrossRef] [PubMed]
  9. N. Nishizawa and T. Goto, ?Widely wavelength-tunable ultrashort pulse generation using polarization maintaining fibers,? IEEE J. Select. Topics in Quantum Electron. 7, 325-327 (2001). [CrossRef]
  10. S. Linden, H. Giessen, and J. Kuhl, ?XFROG-a new method for amplitude and phase characterization of weak ultrashort pulses,? Phys. Stat. Sol. (b) 206, 119-124 (1998). [CrossRef]
  11. N. Nishizawa and T. Goto, ?Experimental analysis of ultrashort pulse propagation in optical fibers around zero-dispersion region using cross-correlated frequency resolved optical gating,? Opt. Express 8, 328-335 (2001) <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-8-6-328</a>. [CrossRef] [PubMed]
  12. S. Kumar, A. Selvarajan, and G. V. Anand, ?Influence of Raman scattering on the cross phase modulation in optical fibers,? Opt. Commun. 102, 329-335 (2002). [CrossRef]
  13. S. Kumar, A. Selvarajan, and G. V. Anand, ?Nonlinear copropagation of two optical pulses of different frequencies in birefringent fibers,? J. Opt. Soc. Am. B 11, 810-817 (1994). [CrossRef]
  14. N. Nishizawa, R. Okamura, and T. Goto, ?Analysis of widely wavelength tunable femtosecond soliton pulse generation using optical fibers,? Jpn. J. Appl. Phys. 38, 4768-4771 (1999). [CrossRef]

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