1. Introduction

Ultrashort optical pulses are important light sources in recent years. Recently, we have successfully demonstrated the widely wavelength tunable ultrashort pulse generation using the compact fiber laser and optical fibers[1–4]. Using the nonlinearity of optical fibers, the wavelength tunable ultrashort pulses can be generated in the wavelength region from 1.3 to 2.0 µm. Since the whole system is very compact and the wavelengths of the generated pulses can be changed by merely varying the fiber input power, this system is the reliable and useful light source for practical applications. Since the wavelength shift is induced instantaneously by the nonlinear optical effect, the ultrahigh speed wavelength tuning can be demonstrated using the intensity modulator[5].

Using the dispersion shifted fibers and femtosecond fiber lasers, in addition to the wavelength tunable soliton pulse, the wavelength tunable anti-stokes pulse is generated[4]. The wavelength of the soliton pulse is shifted toward the longer wavelength side due to the soliton self-frequency shift[3,6–9]. However, the mechanism of the wavelength shift of anti-stokes pulse is not clarified yet. In order to analyze the nonlinear phenomena in ultrashort pulse propagation, it is important to observe the temporal relation among the spectral components in the pulse propagation.

In this paper, the characteristics of ultrashort pulse propagation at λ=1.55 µm in polarization maintaining dispersion shifted fiber (PM-DSF) is experimentally investigated using the frequency resolved optical gating (FROG)[10]. So far, the ultrashort pulse propagation near the zero-dispersion region in optical fibers have been investigated by several groups using FROG[11,12]. In those works, the variations of the phase or the temporal shape of the input pulse are mainly investigated and the intense ultrashort pulse propagation which accompanies the pulse breakup[4,8,9] has not been investigated yet. In this paper, the generated stokes pulse is picked out using the optical filter and is used as the probe pulse of the cross correlation FROG (X-FROG) [13]. The temporal distribution of the generated spectra are directly observed in the wide wavelength region. The initial process of the pulse breakup around the zero-dispersion region is observed directly for the first time. The observed X-FROG traces are in agreement with the observed optical spectra and the cross correlation traces.

2. Experimental Setup

Figure 1 shows the experimental setup. The passively mode-locked femtosecond fiber laser (IMRA Femtolight) is used as the laser source. It generates about 110 fs sech² like ultrashort pulse at the repetition frequency of 48 MHz. Figure 2 shows the observed optical spectrum and the autocorrelation trace of the output of the fiber laser. The width of the auto-correlation trace is 170 fs at full width at half maximum (FWHM) and the corresponding temporal width of the laser output is 110 fs under assumption of the sech² pulse. The spectral width is 20 nm at FWHM. The center wavelength is about 1556 nm.

 

Fig.1 Experimental setup of X-FROG measurement at the output of the optical fibers. The stokes pulse is picked out using the spectral filter and is used as the probe pulse

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Fig.2 Measured (a) optical spectrum and (b) auto-correlation trace of the laser output pulse.

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The output of the fiber laser is coupled into the polarization maintaining dispersion shifted fiber (PM-DSF, Fujikura DSM-15-P), in which the mode field diameter is 8 µm and the magnitude of dispersion is -0.1 ps²/km at 1.55 µm. The polarization direction of the output beam is adjusted along the birefringent axis of the fiber.

The output of the sample fiber is divided into two beams at the 1:1 beam splitter. The time difference is controlled with the delay line using the corner mirror and passed through the optical lens whose focus length is 150 mm. At the focus point of the lens, the 3mm thick KTP crystal is set to generate the wavelength converted correlation signals. The two beams are overlapped at the focus points and the generated sum frequency signals are injected into the monochromator. The output signals from the monochromator are detected using the photo multiplier tube (PMT, Hamamatsu R2658). The delay line, monochromator, and PMT are connected with the personal computer and the automatic measurement system is constructed.

When the ultrashort pulse is propagated along the PM-DSF, the several complex shaped spectra are generated and the observed trace of the usual second harmonic generation (SHG) FROG is very complicated. In order to observe the FROG trace directly, we used the low pass filter in one of the optical axes of the interferometer and the transmitted component of the stokes pulse is used as the probe pulse. Using this method, the X-FROG trace is observed directly and stably. The cutoff wavelength of the filter is 1600 nm. When the fiber length is enough long ~10 m, the soliton pulse is picked out and is used as the ideal probe pulse.

The optical spectra of the fiber output is observed with the optical spectrum analyzer (Anritsu 5210A). The temporal shape is measured with the two-photon absorption type autocorrelator (Femtochrome Research FR-103PD). Using the low pass filter inside the auto-correlator, the cross correlation trace is also observed.

3. Experimental Results

Figure 3 shows the observed optical spectra, cross-correlation trace, and the X-FROG traces at the output of the 4 m length of PM-DSF. The fiber input power is fixed at 24 mW. The measured delay time due to the chromatic dispersion in the PM-DSF is also shown in Fig.3(a). The inset in Fig.3(c) is the SHG-FROG trace of the probe pulse which is used in the X-FROG measurement. The temporal width is 120 fs and the spectral width is 13 nm at FWHM. The vertical axes in Fig.3(c) represent the wavelengths of the sum frequency generation (SFG) signals and the calculated wavelengths of the input pulse.

 

Fig.3 Observed (a) optical spectra, (b) cross-correlation trace, and (c) X-FROG trace for the output of 4 m length of PM-DSF. The inset in (c) shows the measured SHG-FROG trace of the probe pulse. The measured delay time in PM-DSF is also shown in (a).

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In Fig.3(a), we can see the optical spectra of the generated stokes and anti-stokes pulse at 1628 nm and 1420 nm. The temporal shape of the output pulses is clearly shown in the cross-correlation trace in Fig.3(b). However, the temporal relation among the spectral components can not be identified from Figs.3(a) and (b). From the X-FROG traces in Fig.3(c), we can observe the temporal distribution of the spectral components in the output pulse. When the X-FROG traces are observed, the wavelength sensitivity of the system is calibrated. The observed results of X-FROG traces are in agreement with the observed optical spectrum and the cross correlation trace.

Figure 4 is the movie of the measured X-FROG traces as the fiber length is changed from 2 to 5 m at interval of 1 m. The fiber input power is fixed at 24 mW. For the probe pulse, the temporal widths are 110–200 fs and the spectral widths are 6–13 nm at FWHM in this measurement. The temporal distribution of the spectral components in the initial process of pulse breakup[4,8,9] is observed clearly and stably in each figures. The measured X-FROG traces are in agreement with the corresponding optical spectra and the cross-correlation traces.

 

Fig.4 Movie of the observed X-FROG traces for initial process of pulse breakup when the fiber length is changed from 2 to 5 m at interval of 1 m. The fiber input power is fixed at 24 mW. (189K)

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In Fig.4, when the fiber length is 2 m, the optical spectrum is broadened from 1460 to 1640 nm owing to the self-phase modulation. The effect of chirping is clearly observed. In this fiber length, the temporal width of the autocorrelation trace is as narrow as 80 fs at FWHM and the pulse compression occurs.

When the fiber length is 3 m, the spectrum broadening is much advanced and the pulse breakup occurs due to the effects of four-wave mixing and stimulated Raman scattering[4,8,9]. The stokes and the anti-stokes components are generated at 1611 and 1430 nm, respectively. The anti-stokes pulse is separated from the pump pulse and it is almost overlapped temporally with the stokes pulse. Strictly speaking, the center of the anti-stokes pulse is slightly delayed from the soliton pulse and the anti-stokes pulse is overlapped at the trailing edge of the soliton pulse. In terms of the chromatic dispersion, the estimated group velocity of the anti-stokes pulse is slower than that of the stokes pulse.

Then the generated anti-stokes pulse and the stokes pulse is separated from the pump pulse and they are shifted toward the shorter and the longer wavelength sides. The stokes pulse suffers the soliton effect and the pulse and spectral shapes are gradually reached to be the sech² pulses. The anti-stokes pulse is divided into two parts and the pulse packet is constructed. The leading components of the anti-stokes pulses is almost overlapped with the soliton pulse and slightly delayed from the center of the soliton pulse. To our best knowledge, it is the first direct observation of the temporal distribution of the spectral components in the pulse breakup around the zero dispersion region.

Figure 5 shows the observed X-FROG traces, optical spectra, and the cross correlation traces for 10 m and 180 m lengths of PM-DSFs. For the 10 m fiber, the residual pump pulse propagates fast owing to the effect of chromatic dispersion and the soliton and the leading component of the anti-stokes pulses almost copropagate. The temporal width of the soliton pulse at the output of 10 m length of PM-DSF is measured to be 82 fs. The anti-stokes pulse is now separated into three parts and the temporal width of the pulse packet is about 2 ps.

When the fiber length is 180 m, the wavelengths of the soliton pulse and anti-stokes pulse are reached to 1700 and 1370 nm when the fiber input power is 20 mW. The wavelengths of the generated pulses can be shifted continuously by merely varying the fiber input power[4]. When the fiber input power is much increased up to 25 mW, the wavelength of the soliton pulse is shifted up to 1760 nm and that of the anti-stokes pulse is reached to 1320 nm. The temporal and spectral shapes of the soliton pulse are ideal sech² pulse. The temporal width of the soliton pulse is 200 fs at FWHM and the time-bandwidth product is 0.43 and it is slightly larger than that of the transform limited sech2 pulse.

 

Fig. 5 Observed X-FROG traces and the corresponding optical spectra and cross correlation traces. (a)–(c) fiber length is 10 m and input power is 24 mW, (d)–(f) fiber length is 180 m and fiber input power is 20 mW. In the X-FROG traces (d) for 180 m fiber, since the delay time is as large as 200 ps, only the observed traces of soliton and anti-stokes pulses are shown. The cross correlation trace in (f) corresponds to the bottom of the soliton pulse and the anti-stokes pulses.

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The leading component of the anti-stokes pulses almost copropagates with the soliton pulse and is slightly delayed from the center of the soliton pulse. In comparison with the results for 10 m fiber, the magnitude of the temporal separation between the components of the pulse packet of anti-stokes pulse is increased. Owing to the chromatic dispersion, the delay time between the pump pulse and the generated pulses is increased to be about 200 ps.

In ref. 4, we have also measured the delay times of the soliton and anti-stokes pulses from the pump pulse using the monochromator and pin photodiode. As the results, it has been observed that the soliton pulse and anti-stokes pulse come out from the fiber almost the same time. This result is in agreement with the observed ones using the X-FROG technique.

When only the effect of chromatic dispersion is considered, the estimated group velocity of anti-stokes pulse is slower than that of the soliton pulse for the short fiber less than 5 m. Howerver, it is observed that they almost copropagate along the fiber. The reason is explained by the effects of nonlinear phenomena induced by the propagating pulses. For the longer fiber such as 10 or 180 m, the estimated group velocities are almost equal for the soliton and anti-stokes pulses and they almost copropagate along the fiber. It is considered that after the pulse breakup, the wavelength of the soliton pulse is shifted toward the longer wavelength side due to the soliton self-frequency shift[3,6,7] and the group velocity is gradually decreased and reached to that of the anti-stokes pulse.

After a few meter propagation, the residual pump pulse separates from the soliton and anti-stokes pulse and it propagates faster than those generated pulses. The wavelength of the soliton pulse is increased owing to the soliton self-frequency shift. The wavelengths of the anti-stokes pulses are shifted toward the shorter wavelength side after the separation from the pump pulse. In this measurement, the soliton pulse and the anti-stokes pulse are partially overlapped and almost copropagate along the fiber. Thus it is considered that this wavelength shift is induced by the interaction between the soliton pulse and the anti-stokes pulse.

4. Conclusion

In this paper, the characteristics of the ultrashort pulse propagation at λ=1.55 µm in optical fibers around the zero dispersion region are analyzed experimentally. When the ultrashort pulses are inputted into the PM-DSF, the wavelength tunable soliton pulse and anti-stokes pulse are generated. The generated stokes pulse is picked out using the spectral filter and is used as the probe pulse in the X-FROG measurement. The output pulses are measured directly with the X-FROG method and the temporal and spectral relation of the output pulses are observed. The initial process of pulse breakup is observed for the first time. The measured FROG traces are in agreement with the observed optical spectra and the cross correlation traces.

In the initial process of pulse breakup, the optical spectrum is broadened and the soliton pulse and the anti-stokes pulse are separated from the broadened spectrum. Then the residual pump pulse propagates fast and the soliton pulse and anti-stokes pulse almost copropagate along the fiber. As the pulse propagation along the optical fiber, the soliton pulse is gradually constructed and the anti-stokes pulse separates into two- or three parts. The leading component of the anti-stokes pulses is temporally overlapped with the trailing edge of the soliton pulse. The group velocity of the soliton pulse which is estimated from the chromatic dispersion is faster than that of the anti-stokes pulse for the shorter fiber length and then they gradually approaches to that of the anti-stokes pulse. It is considered that after the pulse breakup, the wavelength shift of the anti-stokes pulse is induced by the interaction between the soliton pulse and the anti-stokes pulse.