Real-time experimental measurements of the spectrally-resolved noise properties of supercontinuum (SC) have been challenging because of the lack of ultrafast optical spectrometer technologies. Understanding the SC noise is increasingly important because it not only can gain new insight of the complex spectral dynamics of SC generation, but also provides clues to search for stable SC source. Driven by the intense interest in the active seeding mechanism for SC generation, we experimentally demonstrate real-time spectrally-resolved, broadband, statistical characterization of minute continuous-wave (CW) seeded SC, enabled by an ultrahigh-speed spectral acquisition technique called optical time-stretch (OTS). The shot-to-shot statistical analysis shows that the seeded SC exhibits a general compromise between SC bandwidth and spectral stability. OTS also allows us to experimentally identify the seeding condition for SC suppression, in which the spectral broadening is mainly contributed by the cascaded parametric process that delays Akhmediev Breather breakup process and subsequent soliton self-frequency shift. Additionally, the characteristic spectral signature of the Raman solitons, which are becalmed by the minute CW seed, can be clearly captured in real-time by OTS operated at a spectral acquisition rate as high as 20 MHz. We anticipate the OTS technique could provide further new insights for understanding more complex mechanisms of seeded-SC generation which can be examined experimentally.
© 2014 Optical Society of America
The complex spectral dynamics of supercontinuum (SC), which are the result of a multitude of intertwined optical nonlinear and dispersive processes, are well-known to be highly sensitive to noise . The lack of real-time ultrafast spectrometers has made it challenging to study the impact of noise on the spectral dynamics of SC in the shot-to-shot time scale (~MHz to GHz), except resorting to numerical simulation. To date, SC measurements using conventional spectrometers only allow time-average spectral analysis. This explains why shot-to-shot spectral noise performance is essentially omitted in the specifications of all the commercial SC sources. Understanding the SC noise properties becomes increasingly important because it not only can gain new insight of the complex spectral dynamics of SC generation, but also provides clues to search for stable SC sources. Following the work by Solli et. al.  in which the small input noise seed is reported to play an overriding role in governing the spectral broadening and the subsequent rogue events in SC generation, different seeding approaches (either pulse or continuous-wave(CW)) introducing a minute modulation across the pump pulse envelope [3–11] have been found to counteract the noise in the modulation instability (MI) process and consequently influences the SC power, bandwidth, rare event possibilities or the overall spectral stability – providing a new way to actively control the SC source.
Optical time-stretch (OTS) was recently found to be a viable approach, not only for imaging and spectroscopy [12–20], but also to experimentally investigate the shot-to-shot spectral dynamics of SC in real-time [2, 21–25]. This technique maps the spectrum of each SC pulse into a temporal waveform via group velocity dispersion (GVD). The waveform, which is the replica of the spectrum in time, can be acquired by a high-speed photodetector (PD) at a speed not achievable by the conventional optical spectrum analyzer (OSA). Driven by the intense interest in the aforementioned active seeding mechanism for SC generation, we here apply OTS to perform comprehensive real-time analysis of the complex spectral statistics of the SC influenced by a weak CW. Using this ultrafast technique, we are able to retrieve a number of useful statistical parameters, which are otherwise missing in the measurements by OSA, such as the spectrally-resolved power histograms, higher-order moment statistics (coefficient of variation , skewness and kurtosis ), as well as the spectral intensity correlation map (SICM). Overall speaking, we observe that the minute CW seed can actively broaden, suppress and reshape the SC spectra depending upon different seeding conditions. The seeded SC bandwidth is generally anti-correlated with the spectral stability, i.e. bandwidth enhancement is achieved at the expense of shot-to-shot spectral stability, and vice versa. Another key observation is that OTS allows us to identify the experimental seeding scenario for SC suppression, in which the less spectral broadening is mainly contributed by the cascaded coherent parametric process (namely four-wave mixing (FWM)) that delays the pulse breakup during the Akhmediev Breather (AB) dynamics. Here we refer the SC suppression observed in our experiments to that the spectral broadening is delayed and thus make the SC generation “less vigorous”. Similar suppression effect has recently been observed in MI  as well as unseeded SC generation . The competition (essentially interference) among the MI modes or pre-solitonic features within the MI gain bandwidth is found to play an important role in delaying the substantial spectral broadening in SC generation [21–25]. While this could be one of the possible routes to seeded SC suppression, our experimental results suggest that coherent FWM processes predominantly contribute the effect as the suppression is generally at its strongest when the seed experiences largest MI gain. More interestingly, we observe that the Raman soliton can be “stagnated” and even suppressed by the weak seed. While it has been demonstrated that the red-edge of the SC spectra (mostly corresponding to the Raman solitons) can be stabilized in the presence of the seed , this is the first time, to the best of our knowledge, that the stabilized Raman solitons generated in SC is spectrally resolved experimentally in real-time by OTS. This allows us to investigate the shot-to-shot spectral variations of these Raman solitons. Presenting the comprehensive experimental statistical characterizations of both seeded SC suppression and enhancement, this study provide a more complete understanding of the seeding mechanism of SC generation, which can be evaluated experimentally in real-time, thanks to the OTS technique.
2. Experimental setup
A 20-meter long photonic crystal fiber (PCF), with a zero dispersion wavelength of 1040 nm, is used in our experiment for SC generation. A pulsed pump beam from a mode-locked laser (center-wavelength = 1064 nm, full-width at half-maximum (FWHM) 7 ps, repetition rate = 20 MHz) is launched into the PCF together with a weak CW trigger, which is from a wavelength tunable laser (1035-1081 nm). Note that we in this paper focus on picosecond anomalous dispersion pumping scenario in which the initial dynamics of the SC generation is primarily influenced by the noise-driven MI . Thus the presence of the weak seed is expected to perturb noise-competing MI gain process. The output SC pulses subsequently undergo OTS process in one branch by a dispersive fiber (Nufern’s 1060-XP) with a total GVD ≅ 0.18 ns/nm, which gives rise to a spectral resolution of ~0.2 nm . The time-stretched SC pulses are then captured by a PD (bandwidth: 8GHz, sensitivity: −19dBm) and a real-time oscilloscope (bandwidth: 16 GHz, sampling frequency: 80 GSa/s). Note that the GVD is chosen to be large enough such that the spectral resolution is determined by OTS according to the definitions set by either stationary phase approximation  or uncertainty principle , not by the sampling rate of the oscilloscope, thus all the OTS-captured spectra satisfy the Nyquist’s sampling criterion. In the other branch after the SC generation, the time-averaged spectra of the SC pulses are recorded by an OSA in order to validate the time-to-wavelength mapping of the OTS process. As the spectral acquisition rate of the OSA is only 2 Hz, ~6 orders-of-magnitude slower than that achieved by the OTS, the spectral comparison between the two branches is meaningful only in a time-average sense. Operating at an ultrafast spectral acquisition of 20 MHz, the total measurable bandwidth can be as wide as 280 nm, based on 1/ = GVD × . The nonlinear wavelength-time mapping due to higher-order GVD becomes more obvious for broadband spectral analysis and thus has already been taken into account in the wavelength calibration. All the spectrally-resolved statistical analyses are evaluated by 2000 OTS-captured spectra (the total number of spectra is limited by the available memory of the oscilloscope).
3. Experimental real-time statistical analysis of seeded SC
3.1 Effects of the seed wavelengths: spectrally-resolved power histograms
In order to demonstrate the unique strength of OTS for ultrafast real-time SC spectral analysis, we present 2000 overlapped SC spectra for each seed wavelength in the color-coded spectrally-resolved histograms shown in Fig. 1. In this experiment, the launched pump peak power is fixed at 80 W which gives rise to the anti-Stokes and Stokes MI gain peaks at ~1049 nm and ~1079 nm, respectively . Note that the MI gain profile is subject to pump power depletion along propagation. The CW seed power is ~80,000 times weaker than the pump peak power and the seed wavelength is tuned from 1035 nm to 1081 nm, covering the two conjugate MI gain bands.
First of all, we compare the spectrally-resolved histograms among the cases of the unseeded SC, seeded SC at seed wavelength of 1073 nm (about half of the MI peak shift), 1081nm (the Stokes MI peak shift), and 1079 nm, as illustrated in Fig. 1(a). The spectrally-resolved histograms can reveal clearly not only the overall spectral features (e.g. overall bandwidth, solitonic features), but also the subtle variation in the shot-to-shot stability across the whole SC bandwidth, both of which are strongly influenced by the CW seed. Specifically, when the CW seed is at the MI peak, the SC bandwidth is effectively suppressed and even narrower than that of the unseeded SC. We here define the SC bandwidth as the 15 dB level below the spectral peak power. This definition is used throughput the paper. It can be understood by that the seed experiences maximum MI gain and promotes more efficiently the cascaded four wave mixing (FWM), which counteracts the noise-driven MI process.
However, the efficient FWM components deplete the pump greatly and thus MI gain profile shrinks along the fiber. As a result, the energetic higher order FWM components outside the MI gain profile delay AB dynamics and thus SC broadening (further elaborated in the later sections). Another noteworthy feature is that the suppressed SC exhibits the highly undulated features, which are in general more stable than the enhanced SC when the seed is detuned from the MI peak to 1073 nm. For example, the higher-order FWM components in the SC suppression case are clearly distinguishable (refer to the histograms S1 and S2 respectively in Fig. 1(b)). In contrast, when the seed is tuned to about half of the MI peak shift, the seeded SC spectra are broadened because the cascaded FWM components locate well within the effective MI gain profile along the fiber and promote the earlier onset of AB pulse breakup. These broken up solitons will undergo SSFS, and their resultant peak powers and frequency shifts varies in a statistical-like manner . Thus the shot-to-shot spectral stability tends to be worsen across the SC spectra. Except the range close to the pump, i.e. ~1060 – 1080 nm where the undulated features are obvious, the fine spectral features of such enhanced SC in other spectral ranges are essentially washed out. Only two solitonic features are barely visible as indicated by the arrows in Fig. 1(a) (see also the histograms E1 and E2 in Fig. 1(b)). The shot-to-shot spectral stability in this SC enhancement case has no obvious improvement compared to the case of unseeded SC (see the solitonic features indicated by the arrows in Fig. 1(a) and the corresponding histograms U1 and U2 in Fig. 1(b)). Interestingly, we observe that a well-defined spectral feature signifying Raman soliton in red-edge (~1150 nm) of the reshaped SC spectrum (refer to R2 in Fig. 1(a)). This feature shows a Gaussian-like statisticaldistribution (with mild left-skewness), as shown in the histogram R2 (Fig. 1(b)), in clear contrast to the case of CW-enhanced SC, which shows a general right-skewed statistical distribution, albeit the presence of seed (histogram E2). Similar right-skewed distribution can also be observed in the red-edge (histogram U2) unseeded SC. This is the first time, to the best of our knowledge that the Raman solitons are found experimentally to be shot-to-shot spectrally resolved and stabilized in the seeded SC. From the above observations, there is an apparent compromise between the SC bandwidth enhancement and the shot-to-shot spectral stability (especially the SC’s red-edge), which has not been discussed in detail in the prior work. The general trend of such phenomenon with respect to seed wavelengths can be observed in Fig. 2. Again, the seeded SC’s bandwidth is enhanced when the seed is detuned from the pump, with no obvious improvement in stability across the whole spectrum. But, the seeded SC becomes increasingly undulated with a suppressed bandwidth when the seed is close to the MI peaks.
3.2 Effects of the seed wavelengths: higher-order moment statistics
OTS also allows us to further quantify the temporal fluctuation across the seeded-SC by the higher-order moment statistics: (i) coefficient of variation Cυ, which reflects the shot-to-shot spectral stability; (ii) skewness γ, which shows distribution asymmetry; (iii) kurtosis κ, which indicates the degree of long tail distribution [23,29] (Fig. 3). As mentioned earlier that the SC suppression is attributed to that the pump is preferentially depleted to generate cascaded FWM. While it might not be obvious to observe directly the FWM components in the SC spectra, they could be visualized more clearly in the plots of coefficient of variation as well as skewness. These FWM components, generated coherently from the seed and the pump, appear as the dips in these plots (V1, S1 in Fig. 3), thus are generally more stable. Hence, coefficient of variation and skewness, both derived from OTS-captured SC spectra, further verify experimentally the role of cascaded FWM in the seeded SC suppression scenarios. As the associated higher values of skewness and kurtosis essentially imply the presence of rare events, these higher moment parameters can provide insights on how the seed promotes or delays AB break-up and the subsequent SSFS as well as the rogue events in SC generation. Notably, we can observe both the skewness and kurtosis are greatly suppressed, particularly at the red-edge, when the seed is near the MI peaks (1051 nm & 1081 nm) – indicating the spectral stability is improved in such seeded SC suppression scenario, at the expense of bandwidth. Moreover, the becalmed soliton feature induced by 1079/1053 nm seeding can be evident by the clear low-value gaps (S2, S3 in Fig. 3) in skewness. In comparison, the skewness and kurtosis increase, particularly in the red-edge of the bandwidth-enhanced SC, when the seed is detuned away from the MI peak.
3.3 Effects of the seed wavelengths: spectral intensity correlation map (SICM)
Another unique strength of OTS for SC analysis is its ability to experimentally extract a broadband SICM, which provides statistical information of how the energy of the spectral components is transferred across the SC spectra. Detailed definition and interpretation of SICM can be referred to ref [21,23,24]. In brief, the SICM shows the relationships between shot-to-shot intensity fluctuations at any two wavelengths and in the SC. It is represented by a spectral correlation matrix function ρ(,), bounded between the upper limit of + 1 and the lower limit of –1. Positive correlation (ρ > 0) means that the intensity variations at the two wavelengths follow the same increasing or decreasing trend, i.e. intensities at λ1 increase or decrease together with that at λ2. Negative correlation (also called anti-correlation, ρ < 0) means that the intensity variations at the two wavelengths follow an opposite trend. SICM derived from OTS-captured SC spectra has been recently applied to study the spectral correlation of the unseeded SC [21,23,24]. Here, we investigate how the SICM is influenced by the seed.
As it is well-known that SC generation pumped by long pulse (picoseconds or longer) is in general dominated by the noise-driven MI in the initial stage, the subsequent breakup of AB into sub-pulses is evolved in a random fashion due to higher order dispersion and Raman perturbation. Thus, in the unseeded SC, the SICM shows almost no obvious correlation across the SC spectra (except along the diagonal line in the SICM) as expected (Fig. 4(a)). However, the correlation becomes more pronounced near the red-edge, i.e. the upper right corner region of the SICM (Fig. 4(a)) – showing the energy exchange from shorter to longer wavelengths within this spectral band. This indicates that the wavelength components within this spectral window exhibit significant spectral jitter . Note that this spectral jitter feature is skewed toward longer wavelength (see the high correlation region diverges toward the upper right corner of the SICM in Fig. 4(a)). This signifies the stochastic nature of soliton fission which results in significant bandwidth enhancement in the red-tail of the SC . We note that this characteristic SCIM of the picosecond-pumped SC is in clear contrast to that of the femtosecond-pumped SC, in which better spectral correlation can generally be observed .
In the case of seeded SC enhancement, i.e. when the seed is at about half of the MI gain peak shift, the spectral positive correlation region is slightly narrowed particularly near the soliton peak (featured as E2 in Fig. 1(a)) as shown in Fig. 4(b)). It shows that the random AB breakup is moderately stabilized in the presence of the seed and thus the solitonic spectral feature is more well-defined with less spectral jitter – rendering the narrowing effect in the SICM. Furthermore, the enhancement effect due to the seed in this case can be verified by that the solitonic feature in the SICM has more red-shift and broader (more outspread) than the unseeded case. The similar, but stronger narrowing effect can also be observed in the Raman soliton feature appeared in the SICM of the SC reshaping case, indicating that the spectral jitter is smaller (Fig. 4(c)). Such high-correlation region is relatively more confined and has less red-shift than the SC enhancement. This once again proves that the weak CW seed becalms the Raman solitons in the SC reshaping scenario (seed at 1079 nm, i.e. at the MI peak). Moreover, the spectral correlation is also improved near the pump region (~1040 - 1080 nm). This can be attributed to the more deterministic spectral broadening driven by the seeded MI and the subsequent cascaded FWM processes. Note that in this case, the weak CW seed experiences the largest MI gain and thus the initial spectral broadening is preferentially dominated by the cascaded FWM processes. The significant spectral broadening process is in other word delayed but has higher correlation with this early dynamics. This can be verifiedby that the pump region (~1040-1080 nm) shows better correlation with the Raman solitons (~1150 nm) (Fig. 4(c)) – implying the Raman SSFS generated from the pump and the seed is relatively more deterministic. When SC is seeded at 1081 nm (near the MI peak), the coherent and cascaded FWM processes dominate the spectral broadening process and delay the subsequent solitonic dynamics. This is signified by that the high-correlation red-edge in Fig. 4(d) is even smaller compared with Fig. 4(c) – suggesting less energy exchange appeared on the red edge.
3.4 Effects of the pump powers: spectrally-resolved power histograms and higher-order moment statistics
We discussed earlier that the seed tends to delay the initial AB breakup dynamics and its subsequent SSFS, which lead to SC suppression when the seed experiences the large MI gain. This can be further verified by investigating how the seeded SC evolves as a function of pump power. In this study, the pump peak power is tuned from 20 W up to 108 W. The CW seed wavelength is fixed at 1078 nm. In the low pump power regime (~20-36 W), the seed is essentially outside the MI gain spectrum and thus has no noticeable influence on the output spectra. Thus, the seeded spectra are similar to the unseeded ones, which show the typical MI sidelobes (Fig. 5). When the pump power goes beyond ~52 W, the unseeded spectra starts showing the characteristic triangular shapes (on a logarithmic scale) which can be described by AB dynamics - indicating the onset of pulse breaking into sub-pulses due to higher order dispersion and Raman perturbation and thus SC generation . However, in the seeded case at the pump power ~52 W, the spectra are clearly featured with the cascaded FWM components (i.e. the discrete peaks) generated from the seed and the pump. The pre-solitonic AB feature is not obvious until the pump power is increased up to 68 W. Thus, the seed apparently delays the AB pulse breakup and delays SC generation. As the seed is near the MI peak at such pump power, this observation is consistent with the SC suppression scenarios discussed in the previous sections.
By studying the higher-order statistical moments as shown in Fig. 6, we can observe that the SC suppression effect is particularly obvious when the pump power is around 68-84 W. The effect of the seed on the SC vanishes when the pump is boosted over 100 W. In this regime, the seeded SC is roughly similar to the unseeded counterpart, except a distinct soliton peak appearing at around 1120 nm in the seeded SC (the arrow in Fig. 5). Such vanishing seeding effect is consistent with the recent experimental  and numerical studies  that progressively higher pump power tends to introduce turbulent solitonic dynamics which could overwhelm the seeding effect.
In summary, we have performed a comprehensive experimental characterization of the minute seeding effect on the picosecond-pumped SC generation by an ultrafast real-time spectral acquisition technique called OTS. This technique is able to access of shot-to-shot broadband (>200 nm) spectral information of the SC at a spectral acquisition rate as high as tens of MHz – not achievable with any existing spectrometers. Having this unique capability, OTS allows us to experimentally evaluate the spectral statistical properties of SC under the influence of the seed, which has only been possible with numerical simulation. Based on the OTS-captured SC spectral data, we have investigated their spectrally-resolved power histograms, higher-order moment statistics (coefficient of variation Cυ, skewness γ and kurtosis κ), and SICM. We have observed that SC can be enhanced, suppressed or reshaped by the seed depending upon the seed wavelength within the MI gain spectrum. More importantly, there is a general tradeoff between the seeded SC bandwidth and the spectral stability, i.e. the overall SC is generally more temporally stable when the SC is suppressed by the seed. The key mechanism behind is that when the seed experiences significant MI gain, the initial spectral broadening tends to be routed through coherent cascaded FWM processes and depletes the pump more efficiently. Consequently, adding the seed delays the AB pulse breakup, the subsequent SSFS and thus SC generation. More importantly, in this seeding scenario, the generated Raman solitons appeared to be more temporally stable. This is the first time, to the best of our knowledge, the becalmed Raman solitons, stagnated by the seed, is spectrally-resolved shot-to-shot in real-time. The present work showed that OTS is a handy approach to experimentally identify the favorable active-control scenarios for generating SC with the desired performance metrics, e.g. bandwidth, spectral stability, spectral intensity correlation. We anticipate the OTS-based spectral measurement technique could provide further new insights for understanding more other complex mechanisms of seeded-SC generation.
This work was partially supported by grant from the Research Grants Council of the Hong Kong SAR, China (Project No. HKU 7172/12E, 717510E, 717911E, 720112E) and University Development Fund of HKU.
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