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Coherence Degradation in the Process of Supercontinuum Generation in an Optical Fiber
OPTICAL FIBER TECHNOLOGY ARTICLE NO.
4, 215]223 Ž1998.
OF980253
Coherence Degradation in the Process of Supercontinuum Generation in an Optical Fiber Masataka Nakazawa, Kohichi Tamura, Hirokazu Kubota, and Eiji Yoshida Optical Lightwa¨ e Communication Laboratory, NTT Optical Network Systems Laboratories, Tokai, Ibaraki-ken 319-11, Japan E-mail: [email protected] Received January 7, 1998; revised January 15, 1998
Changes in coherence during the process of supercontinuum generation in a dispersion-shifted fiber ŽDSF., a dispersion-flattened fiber ŽDFF. and a dispersion-decreasing fiber ŽDDF. have been investigated in detail for the first time. It is shown that both time and frequency coherence are greatly degraded in DSF and DFF. This is due to the four wave mixing effect caused by self-phase modulation and group velocity dispersion in the presence of amplified spontaneous emission. Such a light pulse may be unsuitable for long-distance, high-speed transmission because it contains timing jitter and amplitude fluctuations. On the other hand, DDF can maintain its coherence as the spectral broadening occurs coherently through adiabatic N s 1 soliton compression. This fiber is useful for ultra-high-speed communication. Q 1998 Academic Press
Key Words: Supercontinuum; soliton; four wave mixing; coherence.
I. INTRODUCTION
With the advent of high-power pico-femtosecond lasers, a supercontinuum ŽSC., which occurs due to a combination of self-phase modulation, cross-phase modulation, four wave mixing, and the stimulated Raman effect, has been generated in many materials w1x. The SC, in other words ‘‘white light,’’ is very useful for the time-resolved spectroscopy of materials and multi-wavelength optical sources w1x. It is also well known that an SC has been used for the generation of femtosecond pulses with a pair of fiber gratings w2x. We used an SC in a multi-wavelength optical time domain reflectometer to measure not only fault locations but also the wavelength dependence of the fiber loss w3, 4x. 215 1068-5200r98 $25.00 Copyright Q 1998 by Academic Press All rights of reproduction in any form reserved.
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Recently there has been increasing interest in the application of the SC as a multi-wavelength optical source for high-speed WDM Žwavelength division multiplexed. optical communication w5]8x. However, the transmission distance is rather short Žof the order of 40]100 km. and it is not clear to what extent the SC source is suitable for long-distance, high-speed communication. It has also been reported that dispersion-decreasing fiber ŽDDF. can broaden the spectral width of the SC significantly more than dispersion-shifted fiber ŽDSF. or dispersion-flattened fiber ŽDFF. w9x. However, there has as yet been no investigation of the extent to which timing jitter and amplitude fluctuation exist, and hence how time and frequency coherence are maintained, during the process of SC generation. Such an investigation is of great importance if the SC technique is to be applied to high-speed, long-distance communication. In this paper, we report for the first time that SC generation causes a large coherence degradation due to the random excitation of high-order solitons initiated by amplified spontaneous emission ŽASE.. This process occurs mainly in DSF and DFF as we couple a high-intensity pulse to the low-dispersion fiber. However, we show that there is no such coherence degradation when a DDF is excited with fundamental or low-order solitons.
II. MEASUREMENT OF THE SC IN FIBERS
In order to measure the coherence degradation in an SC in fiber, we prepared three kinds of fiber ŽA, B, and C.. Fiber A was a dispersion-decreasing fiber which made it possible to shorten the input pulse width adiabatically via optical soliton compression. The length of fiber A was 0.91 km and the group velocity dispersion ŽGVD. was 9 psrkmrnm at the input end and nearly 0 psrkmrnm at the output end. Fiber B was a 1-km-long dispersion-shifted fiber with a zero GVD around 1539 nm. Fiber C was a 2-km-long dispersion-flattened fiber with a GVD of 0.2 psrkmrnm at 1.55 m m and a dispersion slope as small as q0.004 psrkmrnm2 in the 1.5-m m region. The input pulse into these fibers needed to produce the SC was generated by a regeneratively and harmonically mode-locked fiber laser w10x. This laser can emit a 3-ps transform-limited Gaussian pulse train at 10 GHz. Regenerative mode-locking was accomplished by feeding back the longitudinal self-beat signal which was detected with a high-speed photodetector and a high-Q filter. The phase between the pulse and the modulation signal was adjusted so that the pulses would always experience the maximum transmission when they passed through the modulator. Thus, complete mode-locking was achieved automatically because we used an ideal feedback signal as the modulation frequency. This reflected the instantaneous frequency change between the longitudinal beats even when perturbations were applied. This enabled us to realize a stable mechanism and long-term operation with neatly repetitive longitudinal modes. Here, it is important to use a pulse train with a high repetition rate in order to measure the longitudinal mode spacing clearly with a high-resolution Fabry]Perot resonator. It is generally difficult to measure coherence degradation using a
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femtosecond laser with a low repetition rate Ž10]100 MHz., as the longitudinal mode spacing cannot be resolved sufficiently without employing a monochromator with an ultrahigh resolution. However, if there is a longitudinal mode spacing of 10 GHz, it is easy to measure the change in the longitudinal mode. Therefore, this stable laser source made it possible for us to undertake a detailed study of the way in which the coherence is degraded for the first time. The finesse of the Fabry]Perot resonator we used was higher than 100 and the FSR was 170 GHz. The wavelength of the input pulse was 1542 nm. In order to generate spectral broadening due to nonlinear effects, the pulse was amplified with a high-power erbium-doped fiber amplifier ŽEDFA. and then the output pulse with a peak power of as high as a few watts was coupled into the test fibers. III. THE SC CHARACTERISTICS OF A DISPERSION-DECREASING FIBER
Figure 1 shows the spectral broadening generated by adiabatic soliton compression in fiber A ŽDDF.. The input power was approximately set at an N s 1 soliton to achieve adiabatic soliton compression. Figure 1a shows the broadened spectrum at around 1542 nm. The spectrum was broadened from 1500 to 1570 nm. The
FIG. 1. Supercontinuum characteristics of fiber A Ždispersion-decreasing fiber, DDF.: Ža. spectral broadening, Žb. change in the longitudinal modes Žcoherence degradation., and Žc. output pulse waveform measured with an autocorrelator.
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power of the SC in the longer wavelength region was higher than that in the shorter wavelength region, while the spectral broadening toward the shorter wavelength region was broader than that toward the longer wavelength region. Figure 1b shows the detailed structure of the spectra sliced every 10 nm between 1510 and 1570 nm. The longitudinal modes of the input pulse are clearly seen every 10 GHz in each spectrum, and the corresponding pulse shape in the time domain maintains a clean pulse waveform. The measured pulse width was approximately 16 ps and was the same in each spectrally sliced component. It is interesting to note that there are no continuous wave ŽCW. spectral components between the longitudinal modes in the spectral broadening in the longer wavelength region, while there is a gradual increase in the CW components between the modes toward the shorter wavelength region. This can be understood as follows. In the process of spectral broadening toward the longer wavelength region, the spectral components always experience anomalous GVD even though the GVD becomes gradually closer to zero. Here the nonlinear phase change can be balanced with the anomalous GVD due to the soliton effect and phase matching which occurs in the nonlinear process. This is the origin of soliton or modulational instability, in which the phase between the modes is conserved. In fiber A, an N s 1 soliton is excited and pulse spikes do not appear on the top of the soliton. On the other hand, when the spectrum is broadened into the shorter wavelength region, some of the spectral components experience small GVD or even normal GVD as the GVD at the output end is almost zero at 1542 nm. These shorter wavelength components, which experience small GVD, cause the excitation of high-order solitons. When there is ASE, the evolution of high-order solitons is disturbed and each pulse has a different waveform. This effect causes coherence degradation and eventually a CW spectral component appears between the longitudinal modes. The output pulse measured with an autocorrelator is shown in Fig. 1c. The pulse is compressed from 3 ps to 260 fs with this adiabatic process. This coherent SC has the same origin as pulse compression using DFF configurations w11, 12x. It should be noted that there is Gordon]Haus ŽG-H. jitter even when coherence is maintained throughout the SC process. If the ASE noise is large and the input power into the DDF is low, the G-H jitter becomes significant and this may limit the application rage of the SC to ultra-high-speed communication using femtosecond pulses. In addition, if the DFF is excited with a higher-order soliton pulse at the input, the coherence may deteriorate as described later. However, the order of the soliton number is relatively low compared with a DSF or a DFF with low GVD, and the contribution is smaller than those of the DSF or DFF. The other important factor is the nonuniformity in the adiabatic process. If the change in the GVD as a function of distance is very drastic and deviates from the adiabatic change, it also causes an incoherent SC. IV. THE SC CHARACTERISTICS OF A DISPERSION-SHIFTED FIBER
Figure 2 shows the spectral broadening generated by SC generation in fiber B ŽDSF.. Figure 2a shows the broadened spectrum at around 1542 nm, in which the
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FIG. 2. Supercontinuum characteristics of fiber B Ždispersion-shifted fiber, DSF.: Ža. spectral broadening, Žb. change in the longitudinal modes Žcoherence degradation., and Žc. output pulse waveform measured with an autocorrelator.
spectrum is broadened between 1510 and 1580 nm. Similar to Fig. 1a, the continuum in the longer wavelength region is higher than that in the shorter wavelength region. The spectral broadening toward the longer wavelength region is rather broader than that for fiber A ŽDDF.. This is due to the fact that the GVD of the DSF Žfiber B. is much smaller than that of the DDF Žfiber A. and therefore nonlinear interaction can be easily enhanced when the same power is coupled to the fiber. Figure 2b shows the detailed structure of the spectra sliced every 10 nm between 1510 and 1570 nm. There is a noticeable difference between Fig. 1b and Fig. 2b. In Fig. 2b, the longitudinal modes every 10 GHz have almost disappeared in each spectrum and CW components cover the whole spectral region. Such a spectral profile indicates that the output waveform has become incoherent. There is a slight indication of the longitudinal modes at 1550 nm, but it is already partially coherent. The degradation of the coherence is more rapid in the DSF than in the DDF. The reason for this degradation is that the evolution of very-high-order solitons is initiated by the ASE noise when optical amplifiers are used. It is important to note that the origin of this evolution is MI or FWM Žmodulational instability or four wave mixing. which occurs at the top of the soliton pulse w13x. When there is no ASE noise, the evolution of higher-order solitons is deterministic and the waveform varies repeatedly along the fiber w13x. Hence the coherence is
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not degraded. However, it is degraded when there is ASE noise. The output pulse width shown in Fig. 2c is 4.5 ps. It is important to note that the measured pulse width in each spectrally sliced component is almost the same but there is no coherence between the pulses. Moreover, when such a pulse train is measured with an autocorrelator, it is difficult to evaluate how much jitter and random amplitude fluctuation it contains. The nonlinear interaction can be reduced when the signal wavelength is set in the normal GVD region because phase matching to initiate MI process is not achieved. This may lead one to believe that, in terms of maintaining the coherence, it is better to use the normal GVD region. However, it is important to note that a broad SC is not obtained when the wavelength of the input pulse is set in the normal dispersion region. This is because the pulse is soon broadened thus halting the parametric process. This situation is different from the femtosecond pulse compression experiment described in Ref. w2x since there the fiber was as short as a few centimeters to a few tens of meters in length and the input power was extremely high. In such a case, a highly broadband SC can be obtained with relatively little pulse broadening Ža few picoseconds pulse width..
V. THE SC CHARACTERISTICS OF A DISPERSION-FLATTENED FIBER
Figure 3 shows the spectral broadening generated by SC generation in fiber C ŽDFF.. Figure 3a shows the SC broadened from 1470 to 1630 nm, which is the broadest among the three fibers. The continuum is broadened fairly symmetrically in both the longer and shorter wavelength regions compared with Figs. 1a and 2a. However, in the same way as with fiber B ŽDSF., the longitudinal modes soon disappear when the wavelength is detuned from the input wavelength. This result indicates that, although it is possible to generate a broader SC, the use of DFF is not effective for maintaining the coherence. This can be understood as follows. As with fiber B, high power excites a high-order soliton in the low GVD region, which is initiated with ASE noise. Hence the waveform and spectrum are different for each pulse, resulting in a degradation in the coherence. However, the spectrum is broadened greatly since the GVD is kept constant over a wide wavelength region. The output pulse is shown in Fig. 3c. This pulse is greatly distorted due to the group delay characteristic of fiber C.
VI. JITTER AND RANDOM EVOLUTION OF THE SC PULSES AND THEIR SUPPRESSION
In the next step, we measured the output pulse characteristics of the SC with an electrical sampling scope to see how much difference there is in the waveforms. We simultaneously investigated the RF spectrum to see how much noise appears around 10 GHz. The wavelength of the sliced spectrum was set at 1553 nm. The results are shown in Fig. 4, where fibers A, B, and C correspond to a, b, and c, respectively. In Fig. 4, the RF spectra are shown on the left and the output of the sampling scope is shown on the right. We used 0.25-nm optical filters to extract the
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FIG. 3. Supercontinuum characteristics of fiber C Ždispersion-flattened fiber, DFF.: Ža. spectral broadening, Žb. change in the longitudinal modes Žcoherence degradation., and Žc. output pulse waveform measured with an autocorrelator.
spectral component. With fiber A, a neatly repetitive 10 GHz component was clearly obtained as shown in Fig. 4a-1, which is also proven by the RF spectrum shown in Fig. 4a. A clean 10-GHz component appeared and there was no noise floor. These results indicate that there is no coherence degradation in fiber A. This means that a spectral slice using DDF can be used as an optical source for WDM w8x. However, with fibers B and C, the waveforms shown in Fig. 4b-2 and 4c-2 are very different from that in Fig. 4a-1 and have large amplitude fluctuations. This is due to randomly excited high-order solitons initiated by ASE. Although there is a pulse-like waveform, there is a very large amplitude fluctuation of almost 100%. Such pulses are not applicable for communication purposes since they even contain timing jitter. This is also confirmed with the RF spectra shown in Fig. 4b-1 and 4c-1, in which there is a uniform RF noise component over a broad frequency region. The line below y80 dBm is the noise level of the measurement system. Because of the amplitude fluctuation and timing jitter at the top of the pulse, the noise floor appears at y70 dBm. The integrated noise power becomes comparable to that of the 10 GHz components, which means that the amplitude fluctuation is almost 100%.
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FIG. 4. Output waveform characteristics of the SC measured with a high-speed electrical sampling scope and an RF spectrum analyzer. RF spectrum of the SC measured with a pin photo detector for Ža-1. DDF, Žb-1. DSF, and Žc-1. DFF. Output waveforms measured with a sampling scope for Ža-2. DDF, Žb-2. DSF, and Žc-2. DFF.
VII. SUMMARY
We have described for the first time changes in coherence during the SC generation in DSF, DFF, and DDF. It is shown that both time and frequency coherence are greatly degraded in DSF and DFF, when a higher-order soliton is excited in the presence of ASE noise. This can also be understood as a nonlinear pulse evolution in the presence of ASE noise through the MI effect. It should be noted that a high-order soliton does not evolve randomly even when there are perturbations such as the self-Raman effect or third-order dispersion. Although the waveform itself is greatly distorted due to the perturbations, each pulse of a pulse train is distorted to exactly the same degree. Thus there is no coherence degradation. When there is ASE noise at the beginning, however, it acts as a seed for the random evolution of high-order solitons, which degrades the coherence between the pulses. These pulses may not be suitable for long-distance, high-speed transmission.
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On the other hand, adiabatic N s 1 soliton compression in a DDF can maintain its longitudinal mode coherence. Therefore, such a fiber is very useful for producing a coherent SC and will be applicable to ultra-high-speed communication. It should be noted that the excitation of high-order solitons in a DDF also degrades the coherence in the presence of ASE.
ACKNOWLEDGMENTS The authors express their thanks to Drs. I. Yamashita and I. Kobayashi of NTT Optical Network Systems Laboratories for their continuing encouragement and fruitful comments.
REFERENCES w1x R. R. Alfano, Ed., ‘‘The Super Continuum Laser Sources,’’ Springer-Verlag, BerlinrNew York, 1989. w2xC. V Shank, R. L. Fork, R. Yen, and R. H. Stolen, ‘‘Compression of femtosecond optical pulses,’’ Appl. Phys. Lett., vol. 40, no. 9, 761 Ž1982.. w3x M. Nakazawa and M. Tokuda, ‘‘Continuum spectrum generation in a multimode fiber using two pump beams at 1.3 m m wavelength region,’’ Jap. J. Appl. Phys., vol. 22, no. 4, L239 Ž1983.. w4x M. Nakazawa and M. Tokuda, ‘‘Measurement of the fiber loss spectrum using fiber Raman optical-time-domain reflectometry,’’ Appl. Opt., vol. 22, no. 12, 1910 Ž1983.. w5x K. Mori, T. Morioka, H. Takara, and M. Saruwatari, ‘‘Continuum tunable optical pulse generation utilizing supercontinuum in an optical fiber pumped by an amplified gain-switched LD pulse,’’ in Proc. of Optical Amplifiers and Their Applications, OA & A’ 93, p. 190, MD11, 1993. w6x T. Morioka et al., ‘‘1 Tbitrs Ž100 Gbitrs = 10 channel . OTDMrWDM transmission using a single supercontinuum WDM source,’’ Electron. Lett., vol. 32, no. 10, 906, Ž1996.. w7x S. Kawanishi et al., ‘‘Single-channel 400 Gbitrs time-division-multiplexed transmission of 0.98 ps pulses over 40 km employing dispersion slope compensation,’’ Electron. Lett., vol. 32, no. 10, 916 Ž1996.. w8x K. Tamura, E. Yoshida, and M. Nakazawa, ‘‘Generation of 10 GHz pulse trains at 16 wavelengths by spectrally slicing a high power femtosecond source,’’ Electron. Lett., vol. 32, no. 18, 1691, Ž1996.. w9x T. Okuno, M. Onishi, and M. Nishimura, ‘‘Dispersion-flattened and decreasing fiber for ultrabroadband supercontinuum generation,’’ Proc. of ECOC’96, Edinburgh, UK, p. 80, PDP, 1997. w10x M. Nakazawa, E. Yoshida, and Y. Kimura, ‘‘Ultrastable harmonically and regeneratively modelocked polarisation-maintaining erbium fibre ring laser,’’ Electron. Lett., vol. 30, no. 19, 1603 Ž1994.. w11x S. V. Chernikov, D. J. Richardson, E. M. Dianov, and D. N. Payne, ‘‘Picosecond soliton pulse compressor based on dispersion decreasing fibre,’’ Electron. Lett., vol. 28, 1842 Ž1992.. w12x M. Nakazawa, E. Yoshida, H. Kubota, and Y. Kimura, ‘‘Generation of a 170 fs, 10 GHz transform-limited pulse train at 1.55 m m using a dispersion-decreasing, erbium-doped active soliton compressor,’’ Electron. Lett., vol. 30, no. 24, 2038 Ž1994.. w13x M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, ‘‘High-order solitons and the modulational instability,’’ Phys. Re¨ . A, vol. 39, no. 11, 5768 Ž1989..
4, 215]223 Ž1998.
OF980253
Coherence Degradation in the Process of Supercontinuum Generation in an Optical Fiber Masataka Nakazawa, Kohichi Tamura, Hirokazu Kubota, and Eiji Yoshida Optical Lightwa¨ e Communication Laboratory, NTT Optical Network Systems Laboratories, Tokai, Ibaraki-ken 319-11, Japan E-mail: [email protected] Received January 7, 1998; revised January 15, 1998
Changes in coherence during the process of supercontinuum generation in a dispersion-shifted fiber ŽDSF., a dispersion-flattened fiber ŽDFF. and a dispersion-decreasing fiber ŽDDF. have been investigated in detail for the first time. It is shown that both time and frequency coherence are greatly degraded in DSF and DFF. This is due to the four wave mixing effect caused by self-phase modulation and group velocity dispersion in the presence of amplified spontaneous emission. Such a light pulse may be unsuitable for long-distance, high-speed transmission because it contains timing jitter and amplitude fluctuations. On the other hand, DDF can maintain its coherence as the spectral broadening occurs coherently through adiabatic N s 1 soliton compression. This fiber is useful for ultra-high-speed communication. Q 1998 Academic Press
Key Words: Supercontinuum; soliton; four wave mixing; coherence.
I. INTRODUCTION
With the advent of high-power pico-femtosecond lasers, a supercontinuum ŽSC., which occurs due to a combination of self-phase modulation, cross-phase modulation, four wave mixing, and the stimulated Raman effect, has been generated in many materials w1x. The SC, in other words ‘‘white light,’’ is very useful for the time-resolved spectroscopy of materials and multi-wavelength optical sources w1x. It is also well known that an SC has been used for the generation of femtosecond pulses with a pair of fiber gratings w2x. We used an SC in a multi-wavelength optical time domain reflectometer to measure not only fault locations but also the wavelength dependence of the fiber loss w3, 4x. 215 1068-5200r98 $25.00 Copyright Q 1998 by Academic Press All rights of reproduction in any form reserved.
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Recently there has been increasing interest in the application of the SC as a multi-wavelength optical source for high-speed WDM Žwavelength division multiplexed. optical communication w5]8x. However, the transmission distance is rather short Žof the order of 40]100 km. and it is not clear to what extent the SC source is suitable for long-distance, high-speed communication. It has also been reported that dispersion-decreasing fiber ŽDDF. can broaden the spectral width of the SC significantly more than dispersion-shifted fiber ŽDSF. or dispersion-flattened fiber ŽDFF. w9x. However, there has as yet been no investigation of the extent to which timing jitter and amplitude fluctuation exist, and hence how time and frequency coherence are maintained, during the process of SC generation. Such an investigation is of great importance if the SC technique is to be applied to high-speed, long-distance communication. In this paper, we report for the first time that SC generation causes a large coherence degradation due to the random excitation of high-order solitons initiated by amplified spontaneous emission ŽASE.. This process occurs mainly in DSF and DFF as we couple a high-intensity pulse to the low-dispersion fiber. However, we show that there is no such coherence degradation when a DDF is excited with fundamental or low-order solitons.
II. MEASUREMENT OF THE SC IN FIBERS
In order to measure the coherence degradation in an SC in fiber, we prepared three kinds of fiber ŽA, B, and C.. Fiber A was a dispersion-decreasing fiber which made it possible to shorten the input pulse width adiabatically via optical soliton compression. The length of fiber A was 0.91 km and the group velocity dispersion ŽGVD. was 9 psrkmrnm at the input end and nearly 0 psrkmrnm at the output end. Fiber B was a 1-km-long dispersion-shifted fiber with a zero GVD around 1539 nm. Fiber C was a 2-km-long dispersion-flattened fiber with a GVD of 0.2 psrkmrnm at 1.55 m m and a dispersion slope as small as q0.004 psrkmrnm2 in the 1.5-m m region. The input pulse into these fibers needed to produce the SC was generated by a regeneratively and harmonically mode-locked fiber laser w10x. This laser can emit a 3-ps transform-limited Gaussian pulse train at 10 GHz. Regenerative mode-locking was accomplished by feeding back the longitudinal self-beat signal which was detected with a high-speed photodetector and a high-Q filter. The phase between the pulse and the modulation signal was adjusted so that the pulses would always experience the maximum transmission when they passed through the modulator. Thus, complete mode-locking was achieved automatically because we used an ideal feedback signal as the modulation frequency. This reflected the instantaneous frequency change between the longitudinal beats even when perturbations were applied. This enabled us to realize a stable mechanism and long-term operation with neatly repetitive longitudinal modes. Here, it is important to use a pulse train with a high repetition rate in order to measure the longitudinal mode spacing clearly with a high-resolution Fabry]Perot resonator. It is generally difficult to measure coherence degradation using a
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femtosecond laser with a low repetition rate Ž10]100 MHz., as the longitudinal mode spacing cannot be resolved sufficiently without employing a monochromator with an ultrahigh resolution. However, if there is a longitudinal mode spacing of 10 GHz, it is easy to measure the change in the longitudinal mode. Therefore, this stable laser source made it possible for us to undertake a detailed study of the way in which the coherence is degraded for the first time. The finesse of the Fabry]Perot resonator we used was higher than 100 and the FSR was 170 GHz. The wavelength of the input pulse was 1542 nm. In order to generate spectral broadening due to nonlinear effects, the pulse was amplified with a high-power erbium-doped fiber amplifier ŽEDFA. and then the output pulse with a peak power of as high as a few watts was coupled into the test fibers. III. THE SC CHARACTERISTICS OF A DISPERSION-DECREASING FIBER
Figure 1 shows the spectral broadening generated by adiabatic soliton compression in fiber A ŽDDF.. The input power was approximately set at an N s 1 soliton to achieve adiabatic soliton compression. Figure 1a shows the broadened spectrum at around 1542 nm. The spectrum was broadened from 1500 to 1570 nm. The
FIG. 1. Supercontinuum characteristics of fiber A Ždispersion-decreasing fiber, DDF.: Ža. spectral broadening, Žb. change in the longitudinal modes Žcoherence degradation., and Žc. output pulse waveform measured with an autocorrelator.
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power of the SC in the longer wavelength region was higher than that in the shorter wavelength region, while the spectral broadening toward the shorter wavelength region was broader than that toward the longer wavelength region. Figure 1b shows the detailed structure of the spectra sliced every 10 nm between 1510 and 1570 nm. The longitudinal modes of the input pulse are clearly seen every 10 GHz in each spectrum, and the corresponding pulse shape in the time domain maintains a clean pulse waveform. The measured pulse width was approximately 16 ps and was the same in each spectrally sliced component. It is interesting to note that there are no continuous wave ŽCW. spectral components between the longitudinal modes in the spectral broadening in the longer wavelength region, while there is a gradual increase in the CW components between the modes toward the shorter wavelength region. This can be understood as follows. In the process of spectral broadening toward the longer wavelength region, the spectral components always experience anomalous GVD even though the GVD becomes gradually closer to zero. Here the nonlinear phase change can be balanced with the anomalous GVD due to the soliton effect and phase matching which occurs in the nonlinear process. This is the origin of soliton or modulational instability, in which the phase between the modes is conserved. In fiber A, an N s 1 soliton is excited and pulse spikes do not appear on the top of the soliton. On the other hand, when the spectrum is broadened into the shorter wavelength region, some of the spectral components experience small GVD or even normal GVD as the GVD at the output end is almost zero at 1542 nm. These shorter wavelength components, which experience small GVD, cause the excitation of high-order solitons. When there is ASE, the evolution of high-order solitons is disturbed and each pulse has a different waveform. This effect causes coherence degradation and eventually a CW spectral component appears between the longitudinal modes. The output pulse measured with an autocorrelator is shown in Fig. 1c. The pulse is compressed from 3 ps to 260 fs with this adiabatic process. This coherent SC has the same origin as pulse compression using DFF configurations w11, 12x. It should be noted that there is Gordon]Haus ŽG-H. jitter even when coherence is maintained throughout the SC process. If the ASE noise is large and the input power into the DDF is low, the G-H jitter becomes significant and this may limit the application rage of the SC to ultra-high-speed communication using femtosecond pulses. In addition, if the DFF is excited with a higher-order soliton pulse at the input, the coherence may deteriorate as described later. However, the order of the soliton number is relatively low compared with a DSF or a DFF with low GVD, and the contribution is smaller than those of the DSF or DFF. The other important factor is the nonuniformity in the adiabatic process. If the change in the GVD as a function of distance is very drastic and deviates from the adiabatic change, it also causes an incoherent SC. IV. THE SC CHARACTERISTICS OF A DISPERSION-SHIFTED FIBER
Figure 2 shows the spectral broadening generated by SC generation in fiber B ŽDSF.. Figure 2a shows the broadened spectrum at around 1542 nm, in which the
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FIG. 2. Supercontinuum characteristics of fiber B Ždispersion-shifted fiber, DSF.: Ža. spectral broadening, Žb. change in the longitudinal modes Žcoherence degradation., and Žc. output pulse waveform measured with an autocorrelator.
spectrum is broadened between 1510 and 1580 nm. Similar to Fig. 1a, the continuum in the longer wavelength region is higher than that in the shorter wavelength region. The spectral broadening toward the longer wavelength region is rather broader than that for fiber A ŽDDF.. This is due to the fact that the GVD of the DSF Žfiber B. is much smaller than that of the DDF Žfiber A. and therefore nonlinear interaction can be easily enhanced when the same power is coupled to the fiber. Figure 2b shows the detailed structure of the spectra sliced every 10 nm between 1510 and 1570 nm. There is a noticeable difference between Fig. 1b and Fig. 2b. In Fig. 2b, the longitudinal modes every 10 GHz have almost disappeared in each spectrum and CW components cover the whole spectral region. Such a spectral profile indicates that the output waveform has become incoherent. There is a slight indication of the longitudinal modes at 1550 nm, but it is already partially coherent. The degradation of the coherence is more rapid in the DSF than in the DDF. The reason for this degradation is that the evolution of very-high-order solitons is initiated by the ASE noise when optical amplifiers are used. It is important to note that the origin of this evolution is MI or FWM Žmodulational instability or four wave mixing. which occurs at the top of the soliton pulse w13x. When there is no ASE noise, the evolution of higher-order solitons is deterministic and the waveform varies repeatedly along the fiber w13x. Hence the coherence is
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not degraded. However, it is degraded when there is ASE noise. The output pulse width shown in Fig. 2c is 4.5 ps. It is important to note that the measured pulse width in each spectrally sliced component is almost the same but there is no coherence between the pulses. Moreover, when such a pulse train is measured with an autocorrelator, it is difficult to evaluate how much jitter and random amplitude fluctuation it contains. The nonlinear interaction can be reduced when the signal wavelength is set in the normal GVD region because phase matching to initiate MI process is not achieved. This may lead one to believe that, in terms of maintaining the coherence, it is better to use the normal GVD region. However, it is important to note that a broad SC is not obtained when the wavelength of the input pulse is set in the normal dispersion region. This is because the pulse is soon broadened thus halting the parametric process. This situation is different from the femtosecond pulse compression experiment described in Ref. w2x since there the fiber was as short as a few centimeters to a few tens of meters in length and the input power was extremely high. In such a case, a highly broadband SC can be obtained with relatively little pulse broadening Ža few picoseconds pulse width..
V. THE SC CHARACTERISTICS OF A DISPERSION-FLATTENED FIBER
Figure 3 shows the spectral broadening generated by SC generation in fiber C ŽDFF.. Figure 3a shows the SC broadened from 1470 to 1630 nm, which is the broadest among the three fibers. The continuum is broadened fairly symmetrically in both the longer and shorter wavelength regions compared with Figs. 1a and 2a. However, in the same way as with fiber B ŽDSF., the longitudinal modes soon disappear when the wavelength is detuned from the input wavelength. This result indicates that, although it is possible to generate a broader SC, the use of DFF is not effective for maintaining the coherence. This can be understood as follows. As with fiber B, high power excites a high-order soliton in the low GVD region, which is initiated with ASE noise. Hence the waveform and spectrum are different for each pulse, resulting in a degradation in the coherence. However, the spectrum is broadened greatly since the GVD is kept constant over a wide wavelength region. The output pulse is shown in Fig. 3c. This pulse is greatly distorted due to the group delay characteristic of fiber C.
VI. JITTER AND RANDOM EVOLUTION OF THE SC PULSES AND THEIR SUPPRESSION
In the next step, we measured the output pulse characteristics of the SC with an electrical sampling scope to see how much difference there is in the waveforms. We simultaneously investigated the RF spectrum to see how much noise appears around 10 GHz. The wavelength of the sliced spectrum was set at 1553 nm. The results are shown in Fig. 4, where fibers A, B, and C correspond to a, b, and c, respectively. In Fig. 4, the RF spectra are shown on the left and the output of the sampling scope is shown on the right. We used 0.25-nm optical filters to extract the
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FIG. 3. Supercontinuum characteristics of fiber C Ždispersion-flattened fiber, DFF.: Ža. spectral broadening, Žb. change in the longitudinal modes Žcoherence degradation., and Žc. output pulse waveform measured with an autocorrelator.
spectral component. With fiber A, a neatly repetitive 10 GHz component was clearly obtained as shown in Fig. 4a-1, which is also proven by the RF spectrum shown in Fig. 4a. A clean 10-GHz component appeared and there was no noise floor. These results indicate that there is no coherence degradation in fiber A. This means that a spectral slice using DDF can be used as an optical source for WDM w8x. However, with fibers B and C, the waveforms shown in Fig. 4b-2 and 4c-2 are very different from that in Fig. 4a-1 and have large amplitude fluctuations. This is due to randomly excited high-order solitons initiated by ASE. Although there is a pulse-like waveform, there is a very large amplitude fluctuation of almost 100%. Such pulses are not applicable for communication purposes since they even contain timing jitter. This is also confirmed with the RF spectra shown in Fig. 4b-1 and 4c-1, in which there is a uniform RF noise component over a broad frequency region. The line below y80 dBm is the noise level of the measurement system. Because of the amplitude fluctuation and timing jitter at the top of the pulse, the noise floor appears at y70 dBm. The integrated noise power becomes comparable to that of the 10 GHz components, which means that the amplitude fluctuation is almost 100%.
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FIG. 4. Output waveform characteristics of the SC measured with a high-speed electrical sampling scope and an RF spectrum analyzer. RF spectrum of the SC measured with a pin photo detector for Ža-1. DDF, Žb-1. DSF, and Žc-1. DFF. Output waveforms measured with a sampling scope for Ža-2. DDF, Žb-2. DSF, and Žc-2. DFF.
VII. SUMMARY
We have described for the first time changes in coherence during the SC generation in DSF, DFF, and DDF. It is shown that both time and frequency coherence are greatly degraded in DSF and DFF, when a higher-order soliton is excited in the presence of ASE noise. This can also be understood as a nonlinear pulse evolution in the presence of ASE noise through the MI effect. It should be noted that a high-order soliton does not evolve randomly even when there are perturbations such as the self-Raman effect or third-order dispersion. Although the waveform itself is greatly distorted due to the perturbations, each pulse of a pulse train is distorted to exactly the same degree. Thus there is no coherence degradation. When there is ASE noise at the beginning, however, it acts as a seed for the random evolution of high-order solitons, which degrades the coherence between the pulses. These pulses may not be suitable for long-distance, high-speed transmission.
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On the other hand, adiabatic N s 1 soliton compression in a DDF can maintain its longitudinal mode coherence. Therefore, such a fiber is very useful for producing a coherent SC and will be applicable to ultra-high-speed communication. It should be noted that the excitation of high-order solitons in a DDF also degrades the coherence in the presence of ASE.
ACKNOWLEDGMENTS The authors express their thanks to Drs. I. Yamashita and I. Kobayashi of NTT Optical Network Systems Laboratories for their continuing encouragement and fruitful comments.
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