1. Introduction

Super-continuum (SC) generation from optical fibers by using ultrashort pulse mode-locked lasers is an attractive way to realize broadband optical sources, and so far, compact SC sources have been demonstrated by using Er-doped/Yb-doped fiber lasers and semiconductor lasers [1–5]. However, it is not straightforward to increase their output power because nonlinear effects and dispersion in high power amplifiers oppose severe obstacles to obtaining clean ultrashort pulses with high average power. In addition, the continuum light might have significant ripples in its spectrum depending on the pulse distortion [6–8]. Although the SC generation has potential applications in optical sensing and device characterizations, these features are disadvantages in comparison with legacy incoherent light sources such as light-emitting diodes.

On the contrary, SC generation by using incoherent light or continuous wave (CW) light has been examined, and it was shown that high power continua with small spectrum ripples could be obtained [9–14]. When a CW incoherent light such as amplified spontaneous emission noise (ASE) was used as a seed light, the spectrum broadened due to soliton-Raman effect and four-wave mixing[9, 10]. Even when a low-noise CW light was used, the spectrum broadens initially due to the noise enhancement through modulation instability gain and then broadband continuum was generated in a similar way [9–13]. Also, the broadband SC generation by using incoherent noise bursts has been reported recently in refs. [14] and [15], in which a stretched-pulse Er-doped fiber laser was operated in noise-like mode and incoherent noise bursts were generated [16]. Although the envelope of noise bursts was relatively wide (>several tens of pico-seconds) as a seed pulse for SC generation, the spectrum generated had a bandwidth of over 900 nm and the spectral ripples were also small. These results suggest that the incoherent light might be suitable for flat, broadband SC spectrum.

In this paper, we investigate the nonlinear propagation of incoherent pulse trains (noiselike pulse), and examine SC generation by using ASE noise burst from an Er-doped fiber amplifier (EDFA) instead of ultrashort pulses. The temporal waveform of the incoherent noise has a fine temporal structure with a duration of the inverse of the bandwidth, and can be used as a bunch of ultrashort pulses. Therefore, if the peak power is high, it can induce nonlinear effects enough to broaden the spectrum. In addition, it is straightforward to obtain high average power because the pulse distortion and the deterioration of the signal-to-noise ratio during the amplification are not harmful. Thus, this method is expected to provide a high-power broadband source with simple configuration. In the following, we discuss the propagation of noise burst. Then, we demonstrate SC generation with a bandwidth of over 950 nm by using a highly nonlinear (HNL) fiber and an ASE noise source.

2. Propagation of broadband noise burst in optical fibers

In order to grasp the difference from conventional SC generation, we numerically calculate the propagation of an ASE noise burst and compare it with that of an ultrashort pulse train. We assume that the fiber for SC generation is an HNL fiber. The nonlinear coefficient is 20.0 km^-1W^-1. In order to express the chromatic dispersion in a wide wavelength range, we consider the fiber dispersion β_n = dⁿβ/dωⁿ up to fifth order, where β is a propagation constant. The dispersion values at a center wavelength of the input light (1550 nm) are: β ₂ = -0.74 ps²/km (anomalous), β ₃ = 0.05 ps³/km,/β ₄ = -0.64×10^-3 ps⁴/km, and β ₅ = 1.57×10^-6 ps⁵/km. These values are chosen in such a way that the dispersion profile of the fiber fits well with that used in the experiment. The zero dispersion wavelength λ₀ is 1531 nm and the fiber has anomalous dispersion at a wavelength longer than λ₀. For numerical calculation, we use the generalized nonlinear Schrödinger equation which includes the instantaneous and delayed Raman response, and ignore the stochastic process originating from the spontaneous Raman scattering [7, 17,18].

Figures 1(a) show evolutions of the waveform and the spectrum when a 300-fs Gaussian pulse with a peak power of 300 W is launched into the fiber. The pulse is compressed by the interaction of the self-phase modulation (SPM) and the anomalous dispersion of the fiber, and the spectrum broadens drastically in the first few meters. However, due to higher-order dispersion and nonlinear effects, the pulse generates dispersive waves while the main pulse component loses its energy [19]. As a result, the spectrum broadening stops after propagation of around 4 m, and many ripples remains in its spectrum.

 

Fig. 1. Evolutions of the intensity waveforms and the spectra when (a) an ultrashort pulse and (b) an ASE noise burst are used. All waveforms and spectra are offset vertically for clarity.

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On the other hand, when the noise burst is used as a seed pulse, the behavior of the spectrum broadening becomes different. Figures 1(b) show evolutions of the waveform and the spectrum when a noise burst is launched into the fiber. The 3-dB bandwidth of the noise burst is 20 nm and the duration of the envelope is 33 ps. As shown by the waveform at the input end (the distance L=0) in Fig. 1(b), the noise has a fine temporal structure and can be considered as a bunch of short pulses with a duration of around 300 fs. In this calculation, the energy of the burst noise is set to 1.5 nJ in such a way that the peak power of the noise component becomes as high as that of the pulse in the previous calculation shown in Fig. 1(a).

Similarly to the case of the ultrashort pulse propagation, the spectrum broadens drastically in the first few meters, and the waveform also changes. The difference from the ultrashort pulse propagation is that the noise burst still has a fine temporal structure with high intensity even when the waveform is distorted. Therefore, the noise burst can still induce the fiber nonlinearity until the envelope of the noise burst is spread out. In fact, the spectrum gradually broadens even after the propagation of over 10 m as shown in Fig. 1(b). Thus, when the ASE noise is used, the nonlinear interaction length becomes effectively long, resulting in the broad SC spectrum.

 

Fig. 2. Contour maps of the spectrogram of the continuum generated from noise burst.

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For further investigation of the nonlinear propagation of the noise burst, we calculate the time-frequency distribution of the continuum spectra shown in Fig. 1(b). Figures 2 show the contour maps of the spectrogram (the intensity as functions of time and wavelength) calculated with a time window of 300 fs for different propagation distance L. As shown in Fig. 2(a), the noise burst has a bandwidth of 20 nm and the duration of 33 ps at the input end. After the nonlinear propagation of 1.5 m, the peaks of the noise burst are compressed and the spectrum broadens partially as shown in Fig. 2(b), and then the noise burst breaks into lots of short pulses and some of them forms solitons in longer wavelength region (Fig. 2(c)) [10, 20]. After that, these pulses move toward longer wavelength region mainly due to Raman self frequency shift, and simultaneously the dispersive wave spread out toward shorter wavelength as shown in Fig. 2(d). Consequently, the majority of the launched energy go to longer wavelength region, and interestingly, relatively uniform continuum is formed at shorter wavelength region.

The formation of uniform continuum in shorter wavelength region can be observed for different input noise bursts. Figure 2(e) shows the spectrogram generated from a different noise burst. Similar to Fig. 2(d), the continuum in the region from 1200 nm to 1500 nm are relatively uniform. Thus, the continuum in this wavelength range is less sensitive to the initial pulse and the continuum has a property similar to broadband white noise. On the other hand, the short pulse components formed in longer wavelength region varies with the input noise bursts. That is, the spectrum has a strong dependence on initial pulse like the SC generation from ultrashort pulses. From these results, we can estimate that the noise properties such as the relative intensity noise (RIN) are entirely different in shorter and longer wavelength regions. However, this point is out of the scope of this paper, and will be discussed elsewhere.

Anyway, the fluctuation of the spectrum is averaged out when repetitive noise bursts are launched and detected by a slow detector (compared with the repetition frequency). As a result, the observed spectrum becomes smooth. In fact, thick curves in the left figure of Fig. 1(b) show the spectra averaged over a number of noise bursts. As can be seen, the average spectrum is relatively smooth in the whole wavelength range. In addition, since the pulse-to-pulse coherence of the noise burst does not exist unlike ultrashort pulse trains, the output pulse becomes incoherent.

 

Fig. 3. Experimental setup

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Fig. 4. Continuum spectra for different average input powers measured by the optical spectrum analyzer.

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3. Generation of broadband super-continuum by using ASE noise from an EDFA

Figure 3 shows a schematic diagram of the experimental setup. In order to generate a broadband noise burst having short duration, we used an ASE noise source and modulated the intensity by an electro-absorption (EA) modulator driven with short electrical pulse trains. The repetition rate was 500 MHz. The duration of the ASE noise burst generated was 33 ps. Then it was amplified by a high-power EDFA, and launched into a 60-m HNL fiber. The dispersion values and the nonlinear coefficient are the same to those used in the numerical simulation. Both ends of the HNL fiber are fusion-spliced to standard single-mode fibers (SMF’s) with low coupling loss. The output spectrum was measured by an optical spectrum analyzer (1000nm-1700 nm) and a monochromator with a temperature-controlled InP detector (longer than 1700 nm). In this setup, all optical components were connected by SMF’s with conventional FC connectors. Unlike the case when femtosecond pulse trains are used, careful management of the fiber dispersion is not needed for handling the ASE noise burst before launching it into the HNL fiber. In fact, even when we added a 10-m SMF before the HNL fiber, the change in the continuum spectrum was negligible. This point is a great advantage from an engineering point of view.

 

Fig. 5. Input spectrum (dotted curve) and continuum spectra (solid curves) for different input average powers measured by the optical spectrum analyzer (1000 nm - 1700 nm) and the monochromator (1700nm - 2300 nm).

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Figure 4 shows the SC spectra measured by the optical spectrum analyzer for different input powers. The resolution is 1 nm. As the input power increases, the spectrum broadens gradually and the very flat continuum is generated especially in a shorter wavelength region. The sharp fluctuations observed at around 1400 nm originate from the absorption of the humidity in the optical spectrum analyzer. The peak component at 1550 nm is attributed mainly to background noise in between ASE noise bursts.

Figure 5 shows the whole SC spectra measured by the optical spectrum analyzer and the monochromator. The dotted curve (a) shows the spectrum of the input ASE noise burst and solid curves show output SC spectra for various input average power. As the launched power increases, the output spectrum initially broadens toward longer wavelength, and then the spectral density in shorter wavelength region gradually increases. This tendency is very similar to that when femtosecond pulses are used [2]. In this experiment, the SC spectrum of 956 nm was achieved (1178 nm to 2134 nm) when the launched power was 1.64 W. In this wavelength range, the spectral density exceeds -10 dBm/nm. The drift of the spectral density of the continuum is less than 0.1 dB per hour measured with a wavelength resolution of 1 nm, and this stability is much better than that when an ultrashort pulse laser is used as a seed pulse source [21]. It should be noted that the ASE noise burst as well as the output continuum is depolarized because the EA modulator is polarization-insensitive. In fact, the degree of polarization of the spectrum slice of the continuum was much less than the measurement limit (<0.05).

In comparison with the SC generation with CW pumping [11, 12], the broader continuum was generated with low average power sources and short HNL fibers in this experiment. However, the difference of the required power and the fiber length might simply originate from the difference of the peak power, and the basic mechanism of the spectrum broadening should not be so different between noise burst pumping and CW pumping. Further discussion can be carried out by investigating the dependence of the initial bandwidth and the duration of the noise burst/CW light on the continuum spectrum, but this point is out of the scope of this paper. It will be discussed elsewhere.

4. Conclusions

We have investigated SC generation by using the incoherent noise burst. It was shown that the fine temporal structure of the broadband noise could play the role of a bunch of ultrashort pulses and enabled us to generate flat continuum with high average power. In the experiment, we successfully generated SC spectra whose spectral density was over -10dBm/nm in the wavelength range of 956 nm by using ASE noise of the EDFA.