Ultrashort-pulse fiber lasers are stable and practical ultrashort-pulse light sources, and they are widely used for ultrashort-pulse applications, such as biomedical imaging, ultrashort-pulse processing, and optical frequency combs. By using a combination of ultrashort-pulse fiber lasers and optical fibers, nonlinear optical effects are induced effectively, such as soliton self-frequency shifting, supercontinuum generation, temporal and spectral broadening and compression, and pulse trapping [1–7]. These effects are useful for highly functional and wideband light sources and optical signal processing, and have been applied to biomedical imaging and optical communications [8–10].

In 2020, Nishizawa and Yamanaka [11,12] discovered the novel phenomenon of periodical spectral peaking in optical fibers. When an ultrashort pulse with sharp spectral dips is coupled into an optical fiber, the spectral dips are transferred into spectral peaks periodically along the optical fiber. If a molecular gas cell is used for the absorption source, sharp spectral peaks with ∼20 pm spectral width and sub-THz spectral interval are generated simultaneously and stably. It is expected that these spectral peaks will be useful for optical wavelength standards and mode selection in optical frequency combs.

In 2010, Kalashnikov and Sorokin [13] and Kalashnikov et al. [14] reported their investigation of a passively mode-locked ultrashort-pulse solid state laser with molecular gas inside the laser cavity, in terms of its application to spectroscopy. It was shown that the absorption spectra of molecular gases were overlapped with the optical spectra of output pulses from the laser as peaks. The output pulse spectra look very similar to those of periodical spectral peaking in optical fibers. It is expected that this phenomenon will be useful for the amplification of spectral peaks, which is important for highly sensitive spectroscopic applications. However, the physical mechanism is not yet clear enough, and there have been only a few reports about this phenomenon so far [13,14].

In this work, we report the investigation of a spectral peaking phenomenon in a passively mode-locked ultrashort-pulse fiber laser for the first time. An Er-doped ultrashort-pulse fiber laser with single-wall carbon nanotubes (SWNTs) was used as the laser source, and an HCN gas cell was inserted into this fiber laser cavity to induce spectral peaking. Ultrashort pulses with intense spectral peaks were generated stably at the fiber laser output. The characteristics of the output pulses were analyzed both experimentally and numerically. The physical mechanisms involved were discussed through numerical simulations.

Figure 1 shows the experimental setup for spectral peaking in a fiber laser. An Er-doped ultrashort-pulse fiber laser using SWNTs was used as the fiber laser [15]. A 50 cm length of highly Er-doped fiber with positive dispersion properties (LIEKKI Er110-4/125) was used as the gain fiber, and it was pumped with a 976 nm high-power laser diode (LD). A hybrid-type wavelength division multiplexed (WDM) coupler with an isolator and a hybrid-type output coupler with an 80% output ratio and an isolator were used to construct the fiber laser cavity. As the mode-locker, we used a polyimide film device containing dispersed SWNTs. SWNTs synthesized with a high-pressure CO method were used [15]. The net cavity dispersion was –0.05 ps², and self-starting passive mode-locking was obtained just by increasing the pump power. A polarization controller was used to optimize the mode-locking condition. A stable, clean sech²-shaped soliton pulse was obtained at the fiber laser output, as shown in Fig. 2(b). The spectral width was 7.8 nm and the output power was 15.6 mW.

 

Fig. 1. Setup for spectral peaking in the fiber laser with a molecular gas cell.

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Fig. 2. Optical spectra of the output pulse (a) below and (b) above the mode-locking pumping threshold. The dashed line shows the spectrum without (w/o) the HCN gas cell.

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Then, the HCN gas cell (wavelength references HCN-13-H(16.5)-25-FCAPC) was inserted inside the fiber laser cavity, as shown in Fig. 1. It had fiber pigtails and was easily inserted into the fiber laser cavity. Figure 2 shows the optical spectra of the output pulse. When the pump power was below the threshold of passive mode-locking, a spectrum of amplified spontaneous emission (ASE) with the deep absorption spectra of HCN was observed. When the pump power was increased above the threshold of mode-locking, a stable sech²-shaped pulse with multiple intense spectral peaks was obtained, as shown in Fig. 2(b). The output power was 21 mW. The optical spectra were stable for a few hours.

Figure 3 shows the characteristics of the output pulse with spectral peaks. In the autocorrelation trace in Fig. 3(a), a clean trace without a pedestal component was observed. The temporal width was 367 fs, and the corresponding pulse width was 238 fs under the assumption of a sech²-shaped pulse. In the enlarged autocorrelation trace with a wide temporal range shown in Fig. 3(b), small peaks with almost equal intervals of 9.5 ps were observed around the main peak. It was considered that these small peaks were accumulated free induction decay (FID) pulses generated in the HCN gas cell [16]. For the RF spectra shown in Fig. 3(c), clean RF spectra with constant intensity and high SNR were clearly observed. For the enlarged fundamental RF spectrum shown in Fig. 3(d), the SNR was 70 dB, and thus low noise properties were confirmed.

 

Fig. 3. Characteristics of the output pulse from the fiber laser with HCN: (a) autocorrelation trace; (b) enlarged autocorrelation trace for a wide range; (c), (d) RF spectra.

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Then, the output pulse from the fiber laser was coupled into 5 m of normally dispersive highly nonlinear fiber (ND-HNLF), and spectral peaking was induced. In the ND-HNLF, the core diameter was 3.6 µm, and the second-order dispersion was +8 ps²/km [12]. Figure 4 shows the observed spectra when the spectral peaking was induced. The output power was 3.7 mW. Multiple peaks with a high signal-to-background ratio (SBR) of ∼7.5 were generated stably.

 

Fig. 4. Observed spectra at the output of highly nonlinear fiber pumped with the output of the spectral peaking fiber laser.

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For comparison, we generated a clean sech²-shaped soliton pulse from the same fiber laser cavity without the HCN gas cell, and then the output pulse was passed through the HCN gas cell to be subjected to the molecular absorption. Here, a SMF with almost the same length as that of the HCN gas cell module was inserted inside the fiber laser cavity to maintain the cavity length. Figure 5(a) shows the optical spectra of the output pulses. An optical pulse spectrum with HCN gas absorption was observed. The maximum magnitude of absorption was ∼30%. The temporal width was 233 fs, and the optical power was 17 mW.

 

Fig. 5. Optical spectra of output pulse (a) after the HCN gas cell and (b) the ND-HNLF.

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Figure 5(b) shows the optical spectra of the generated multiple spectral peaks when the soliton pulse subjected to HCN absorption was coupled into the ND-HNLF. Stable spectral peaks were observed, but since the magnitude of absorption was small, the magnitudes of the generated spectral peaks were lower than those in Fig. 4. The estimated maximum SBR was 0.8. From a comparison between Figs. 4 and 5(b), we confirmed a large enhancement of the spectral peak components in the fiber laser with the molecular gas cell.

Next, in order to discuss the physical mechanism involved, we performed numerical simulation of spectral peaking in a fiber laser. The Ginzburg–Landau equation with a spectral filter formed of a gas cell was used for the numerical analysis. [8,17] The same fiber laser configuration used in the experiment was assumed in the numerical model. The experimentally observed saturable absorption properties were used as the properties of the SWNTs [15,17]. As the input pulse, both ASE random noise and an ultrashort pulse with stable conditions were examined. The absorption spectra of the HCN gas were calculated using the datasheet of the HCN gas module, and the accompanying phases were calculated using the Kramers–Kronig relation [12].

Figure 6 shows the characteristics of output pulses when the maximum absorption of the HCN was 0, 30, and 90%. When the absorption was 0%, a clean sech²-shaped pulse was obtained. When the absorption of HCN gas was assumed, sharp multiple peaks were generated on the pulse spectra. The optical spectrum for 30% absorption, which corresponds to the gas cell used in the experiment, was almost in agreement with the experimentally observed one in Fig. 2(b). When the maximum absorption was 90%, very intense peaks whose magnitude was five times larger than that of the original pulse spectral intensity were successfully generated.

 

Fig. 6. Numerical results of the characteristics of the output pulse: (a) optical spectra; (b) temporal profiles when the maximum absorption was 90%.

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In the temporal domain, as shown in Fig. 6(b), FID pulses with equal temporal separation were observed after the main ultrashort pulse, and their magnitudes increased as the magnitude of the absorption was increased.

Figure 7 shows the variation of the spectral peak intensity as a function of the maximum absorption of the HCN gas. The intensity of the spectral peaks increased exponentially as a function of the maximum absorption. When the maximum absorption was 99%, the pulses were divided into many pulses, and stable single-pulse mode-locking was not obtained.

 

Fig. 7. Numerical results of the variation of normalized spectral peaks as a function of the maximum absorption of HCN gas absorption.

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Next, in order to discuss the physical mechanism involved, we examined some artificial filters for spectral peaking. Figure 8(a) shows the output pulse spectrum when only the absorption of the HCN was considered and the effect of phase shifting was ignored. In this case, the sharp and weak absorption dips were formed on the output pulse spectrum. Figure 8(b) shows the output pulse spectrum when only the phase of the HCN gas was considered and the absorption was ignored. Here, intense spectral peaks and dips corresponding to the induced phase profiles were generated on the pulse spectrum. From Fig. 8, we confirm that the effect of phase is much larger than that of absorption for the spectral peaks in a soliton mode-locked fiber laser. The spectrum in Fig. 6(a) corresponds to the summation of Figs. 8(a) and 8(b).

 

Fig. 8. Optical spectra of output pulses when only (a) absorption and (b) phase were considered. The optical spectrum without (w/o) the gas cell is shown with a dashed line for comparison. The maximum absorption was 50%.

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Next, we performed an analysis where the HCN gas cell was inserted into the fiber laser cavity in the stable condition. Figure 9 shows the variation of the spectral and temporal shapes of the output pulses before and after the HCN gas cell was inserted into the fiber laser cavity. For the stable condition, a clean sech²-shaped pulse with almost no sidebands and pedestals was generated. When the HCN gas cell was inserted into the fiber laser cavity, spectral dips with almost equal frequency intervals were formed at the beginning. In the temporal domain, FID pulses with equal temporal separation of 9.5 ps were generated. For every round trip, these components generated by the HCN gas were overlapped and accumulated. The absorption dips were degraded through the self-phase modulation (SPM), and the effect of phase components gradually became dominant. Finally, intense spectral peaks were formed by the accumulation of the generated components from the HCN gas and the balance between the induced effects. The spectral shape was almost constant in the fiber laser oscillator.

 

Fig. 9. Variation of optical spectra and temporal waveforms for (a), (d) the stable condition without (w/o) HCN, (b), (e) after two round trips, and (c), (f) 40 round trips from insertion of the HCN gas cell (Visualization 1). The maximum absorption was 50%.

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We also analyzed the spectral peaking in a dissipative soliton (DS) mode-locked fiber laser. The net cavity dispersion was +0.08 ps². When the HCN gas was not used, a clean pulse with sharp spectral edges was generated stably, and a clean DS pulse was generated. On the other hand, when HCN gas was inserted in the DS fiber laser in a stable condition, the spectral shapes were degraded, and a DS soliton with multiple peaks was generated. Here the magnitudes of the generated peaks were not so large, and the phase profiles appeared on the spectral shape. It is interesting to note that the enhancement of the spectral peaks was observed at the spectral edges. This behavior was in agreement with previous work on a solid state laser [14]. When the magnitude of absorption was larger than 30%, stable mode-locking was not obtained.

Figure 10(b) shows the temporal shapes of the output pulses. The temporal width was ∼10 ps, and the oscillating pulse was overlapped with the first FID pulse. As a result, the generated FID components were not distinct, and their magnitudes were weak.

 

Fig. 10. Numerical results of the output pulse for the DS mode-locked fiber laser: (a) optical spectra; (b) temporal profiles when the maximum absorption was 20%. The dashed line shows the optical spectrum without (w/o) HCN (Visualization 2).

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Finally, we assumed a spectral filter in place of the gas cell and examined the properties of spectral peaking in the fiber laser. Figure 11 shows the optical spectra when a mono-line spectral filter was used. A Lorentzian-shaped phase filter with a spectral width of 20 pm and a magnitude of π was assumed. As shown in Fig. 11, an intense, stable spectral peak was generated under stable conditions. The generated peak corresponded well to the accumulation of the phase profile of the filter. From this analysis, it is considered that the spectral peaks were generated when we used a spectral phase filter in place of a gas molecule. Generation of intense, controllable spectral peaks is expected by using a controllable spectral filter.

 

Fig. 11. (a) Spectral and (b) temporal waveforms of the output pulse from the soliton mode-locked fiber laser with (w/) and without (w/o) a mono-line spectral phase filter. The waveforms w/o the filter are shown with dashed lines.

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In conclusion, we demonstrated a spectral peaking phenomenon in a fiber laser oscillator. An HCN gas cell was inserted in an ultrashort-pulse Er-doped fiber laser with SWNTs. Sech²-shaped ultrashort pulses with intense multiple sharp spectral peaks were stably generated. When the generated pulses were coupled into highly nonlinear fiber, intense multiple spectral peaks were generated by periodical spectral peaking in the optical fibers, which were more than two times larger than those generated with an output pulse subjected to the same absorption of the HCN gas cell. The characteristics and physical mechanism of spectral peaking in a fiber laser were investigated via numerical simulations. As the maximum absorption was increased, the magnitudes of the generated spectral peaks increased almost exponentially. The spectral peaks were not as large for DS mode-locking. It was clarified that the spectral peaks were generated through the accumulation of filtering components generated in each round trip. It was shown numerically that the spectral peaks are generated by spectral filters in the place of a molecular gas cell. This light source will be useful for generating intense spectral peaks, which is important for highly sensitivity spectroscopic applications.