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Abstract
We investigated multiple spectral peak generation during a coherent supercontinuum generation process with normal-dispersion highly nonlinear fibers both numerically and experimentally. Wideband multiple spectral peak generation was achieved in the 1.6–1.7 μm range using an ultrashort-pulse fiber laser, a CH4 gas cell, and highly nonlinear fiber. The maximum signal-to-background ratio was ∼8.4. Thanks to the normal-dispersion fibers, the induced phase shifts in the absorption spectra were clearly observed on the spectra during the spectral peak generation. The intensity and phase noise properties of the generated spectral peaks were examined, and low noise properties were confirmed. The spectral peaking phenomenon was investigated experimentally in a fiber amplifier. Periodical spectral peaking was successfully observed for a soliton pulse with Kelly sidebands, and the optical pulse experienced absorption in HCN gas. It is expected that spectral peaking occurs for pulses that experience absorption in many different kinds of gas species or those with spectral peaks. This light source and phenomenon will be useful for developing novel optical frequency comb techniques and optical wavelength standards.
© 2021 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
An optical fiber is one of the most effective nonlinear optical devices [1]. In particular, significant nonlinear effects can be induced using ultrashort pulses in an optical fiber. So far, many such effects have been discovered by using a combination of optical fibers and ultrashort pulses, for example, the soliton effect, soliton self-frequency shift, supercontinuum generation, temporal and spectral compression, and pulse trapping [2–8]. They have been used for light source technology, all-optical signal processing, and wavelength conversion and have been applied to biomedical imaging, optical frequency combs, and next-generation optical communication [9–11].
Recently, we discovered the novel phenomenon of periodical spectral peaking in optical fibers [12]. In this phenomenon, when an ultrashort pulse that has experienced the sharp absorption spectrum of a molecular gas propagates along the optical fiber, the absorption spectrum exhibits peaks periodically as a function of the coupling power or fiber length. Almost-equal frequency spanning sharp spectral peaks with a linewidth on the order of a few picometers and sub-THz frequency separation can be generated. This phenomenon is useful for the generation of sub-THz frequency combs and ultrahigh-repetition-rate pulse trains. In 2004–2006, there were some reports of spectral enhancement using fiber gratings and spectral shapers [13–16]. However, wideband, very narrow, multiple, and periodical spectral peak generation has not been demonstrated yet.
In this work, we report the investigation of the characteristics of spectral peaking in optical fibers. First, spectral peaking in supercontinuum generation was investigated both numerically and experimentally. Then, the periodical spectral peaking phenomenon was investigated experimentally using an Er-doped fiber amplifier. A soliton pulse with Kelly sidebands [17] and an optical pulse that experienced absorption in HCN were used as the input pulses, and the resulting phenomena were observed and analyzed.
2. Spectral peaking in coherent supercontinuum generation
First, we examined spectral peaking in coherent supercontinuum generation. Figure 1 shows the experimental setup. A polarization-maintaining (PM) ultrashort-pulse Er-doped fiber laser using single-wall carbon nanotubes (SWNT) was used as the pulse source [18]. The repetition frequency was 28 MHz, and the center wavelength of the output pulses was 1556 nm. The net cavity dispersion was anomalous, and sech2-shaped soliton pulses with small Kelly sidebands were generated stably. The temporal width of the output pulses was 300 fs full width at half maximum (FWHM).
Fig. 1. Experimental setup for spectral peaking in optical fiber. EDF: Er-doped fiber, LPF: low-pass filter, ND-HNLF; normal- dispersion highly nonlinear fiber, BPF: band-pass filter, PD: photo-diode.
The output pulse from the fiber laser was amplified with an PM-Er-doped fiber amplifier (EDFA) with positive dispersion properties and was then introduced into polarization maintaining fiber (PMF) to generate a Raman-shifted ultrashort soliton pulse. When the length of the PMF was 100 m, a 200 fs sech2-shaped pulse was obtained at λ = 1650 nm [19]. Then, only the soliton pulse was passed through a long-pass filter and was introduced into a CH4 gas cell (Thorlabs CQ09075-CH4) having a length of 75 mm and a gas pressure of 200 Torr. When the soliton pulse passed through the CH4 gas cell, it experienced the sharp multiple-absorption spectrum of the gas. Then, the pulse was coupled into an optical fiber, and spectral peaking was induced.
We investigated the spectral peaking in supercontinuum generation both numerically and experimentally. In our previous work, for numerical analysis we considered only the absorption of the CH4 gas, ignoring the phase shift [12]. In this work, we considered not only the absorption but also the phase shift of the absorption spectrum.
Figure 2(a) shows the numerical results of optical spectrum and phase of the optical pulse after passing through the CH4 gas cell. The absorption of the CH4 gas was calculated using the HITRAN database [20]. The spectral width was ∼20 pm for a CH4 gas cell with 200 Torr gas pressure. The phase profile was calculated using the Kramers-Kronig relation [21].
Fig. 2. Numerical results of (a) pulse spectrum after experiencing absorption and phase shift in CH4 gas cell, (b) magnified view of absorption spectrum and induced phase shift around the center wavelength, and (c) corresponding temporal waveform.
Figure 2(b) shows a magnified view of the absorption spectrum and phase profile around 1650 nm. A Lorentzian-shaped spectrum was assumed for the absorption. The phase profile shows a derivative-like profile from the Kramers-Kronig relation [21,22].
Figure 2(c) shows the temporal waveform of the input pulse. We can see that an ultrahigh-repetition-rate pulse train with a temporal separation of 3 ps was formed after the main pulse. The corresponding repetition frequency was 300 GHz, which corresponds to the magnitude of the frequency separation in the absorption spectral chain of CH4 gas.
We analyzed the spectral peaking in supercontinuum generation numerically. The extended nonlinear Schr $ ö $ dinger equation was used for calculating the pulse propagation in the optical fiber [1]. As the nonlinear fiber, the normal-dispersion highly nonlinear fiber (ND-HNLF) used in the experiment was assumed. As the fiber parameters, we used β2 = 6.4 ps2/km and β3 = 0.0057 ps3/km, and the nonlinear coefficient was 23 W-1km-1 at 1.56 μm. During the propagation along the fiber, the optical spectrum was broadened through self-phase modulation, and a coherent supercontinuum was generated [23].
Figure 3(a) shows the variation of the optical spectrum as a function of the length of the ND-HNLF. The physical mechanism of periodical spectral peaking was explained in ref. 12. In the temporal domain, the sharp spectral peak corresponds to a broad and weak pulse, and the pulse spectral envelope corresponds to an ultrashort pulse with high peak power. During the propagation along the fiber, the ultrashort pulse experiences a nonlinear phase shift mainly induced by self-phase modulation (SPM). On the other hand, the nonlinear phase shift experienced by the weak broad pulse is negligible. As a result, the phase difference between the spectral pulse envelope and spectral dips changes continuously along the fiber, and spectral peaks are periodically generated. In Fig. 3(a), as the fiber length was increased, the sharp spectral dips turned into peaks, and then went back to dips, and then peaks again. Many peaks were generated simultaneously in a wide range at the same phase. When an anomalous-dispersion fiber was used, as reported in ref. 12, a phase slip was observed among the generated spectral peaks. It is considered that this phase slip was mainly induced by Raman shifting, anomalous dispersion, and the soliton effect.
Fig. 3. Numerical results of variation of (a) optical spectra and (b) spectral peak intensity in ND-HNLF as a function of fiber length. The input pulse was a 200 fs sech2-pulse with a peak power of 500 W. The green band in (a) shows the corresponding absorption spectra in (b).
Figure 3(b) shows the variation of the spectral peak as a function of propagation length. Since the temporal width of the propagating pulse became wider, the period of spectral peaking became longer, and the top of the second peak was flattened. In this area, the spectral peaks were insensitive to the fiber length and optical power, and it was expected that highly stable spectral peak generation could be obtained.
Figures 4 shows the numerical and experimental results of the variation of the optical spectrum at the output of 5 m of ND-HNLF as a function of the fiber input power. Similar to the propagation length dependence, the spectral peaks were generated periodically in a wide range. The spectral peak generation was observed 3 times when the coupling power was increased up to a maximum output power of 5 mW. When the optical power was 0.6, 2.47, and 4.94 mW, multiple spectral peaks with high signal-to-background ratios (SBRs) of 4.2, 8.4, and 8.2 were generated. The numerical results showed similar behavior to the experimental results.
Fig. 4. (a)#Numerical and (b) experimental results of variation of optical spectrum at the output of 5 m of ND-HNLF as a function of fiber input power.
Figure 5 shows the whole spectra at the fiber output for the maximum power condition. The spectra were widely broadened by 300 nm for the experiment and by 250 nm for the numerical analysis at -10 dB level. The smooth supercontinua with spectral peaks were generated stably.
When the output power was 0.19 mW, which is the middle point between the dip and peak, the average phase difference between spectral intensity dips and the pulse envelope was almost zero, and the phase profile appeared on the spectral shape.
Figure 6 shows a magnified view of the spectra when the average phase difference between the spectral intensity dip and pulse envelope was zero. In this case, we can confirm that the phase profiles are shown clearly on the pulse spectrum. The experimental results showed similar behavior to the numerical results.
Fig. 6. Magnified optical spectra when the output power was 0.19 mW and the average phase difference between the spectral dip and pulse envelope was zero: (a) numerical results and (b) experimental results. The blue line in (a) is the initial phase at the fiber input.
The blue line shows the initial phase profile of the input pulse. It was almost in agreement with the observed phase profile. It was expected that the phase profile can be obtained from the optical spectrum of the spectral peaking phenomenon.
When the conventional anomalous-dispersion fiber was used, similar to the case of ND-HNLF, the effect of induced phase shift appeared on the spectral shape. However, since the spectral shape was not flat and smooth, it was difficult to obtain the induced spectral phase directly from the spectral shape.
Next, we demonstrated RF beat measurement of the generated spectral peak with a cw-laser diode (LD).
The left figure shows the spectral peak extracted using a narrow bandpass filter. The bandwidth of the bandpass filter was 1.0 nm. As shown in Fig. 7(a), a sharp spectral peak with low background was obtained stably. The ratio of the peak to the pedestal was ∼28. The total optical power was 50 μW, and the ratio of the spectral peak part was 53%. This spectrum was overlapped with that of the stable wavelength-tunable LD, and RF beat signals were observed with a fast photodiode and an RF spectrum analyzer. As the cw-LD, we used an external-cavity-type, stable, wavelength-tunable LD (Santec TSL-510, special order). This laser was much stabler than conventional ones, but it was not stabilized by any feedback control.
Fig. 7. (a) Observed spectral peak after bandpass filter, and (b) RF beat frequency between spectral peaks and cw-LD.
Figure 7(b) shows the observed RF beats. The resolution bandwidth (RBW) of the RF spectrum analyzer was 30 kHz. The RF beats were observed with a high SNR of ∼50 dB, and a comb structure with a high SNR was confirmed.
We also examined the RF spectra and phase noise of the spectral peak. Here only the single extracted peak shown in Fig. 7(a) was radiated on a fast pin photo-diode, and RF signals were observed. A very clean RF spectrum was observed, and the SNR was up to 75 dB. Figure 8(b) shows the phase noise observed using an RF spectrum analyzer (Anritsu MS2830A). We used the optional function for phase noise measurement in the RF spectrum analyzer. From Fig. 8, we confirmed that both the noise level and phase noise were low, and they were not increased for the spectral peak component. From these experiments, and considering the physical mechanism, we consider that the spectral peak component retains the coherence properties of the passively mode-locked fs ultrashort pump pulses.
Figure 9 shows the optical spectrum of spectral peaking when a 75 fs ultrashort pulse was used as the input. Here, 5 m of PMF was used for the Raman-shifted soliton pulse generation in Fig. 1. The output power was 14.5 mW. The spectral peaks corresponding to the whole absorption spectra of the CH4 gas from 1630 to 1700 nm were obtained simultaneously, and spectral peaking was observed for a wide wavelength range. The inset shows the whole spectra of the output pulse. The generated supercontinuum was broadened from 1.35 to 1.95 μm with high flatness.
Fig. 9. Experimental results of optical spectrum at the output of 5 m of ND-HNLF when 75 fs sech2-pulse was used as the input pulse and the output power was 14.5 mW. The inset shows the whole spectra of output pulse.
3. Spectral peaking in fiber amplifier
3.1 Kelly sideband variation
So far, we have investigated the spectral peaking phenomenon when the input pulse experiences sharp absorption in the gas cell. In principle, spectral peaking should occur when it starts from a pulse spectrum with a sharp spectral peak.
We investigated the spectral peaking phenomenon when an ultrashort pulse with some spectral peaks was amplified in the EDFA. The output pulse from the EDFA in Fig. 1 was observed. Since the propagating pulse was amplified and the nonlinear effect was induced effectively in the fiber amplifier, the spectral peaking was easily observed. As the input pulse, we used the output pulse from the soliton-mode-locked fiber laser in Fig. 1. In this case, the output pulse from the fiber laser had Kelly sidebands [17], and they served as the initial peak of the optical pulse spectrum for the spectral peaking.
Figure 10 shows the variation of the optical spectrum when the pump power of the EDF was increased. As the pump power was increased, the pulse envelope was gradually broadened through SPM. On the other hand, the Kelly sideband components showed the behavior of spectral peaking, and they turned into dips, and then became peaks again. This is the numerically predicted behavior of spectral peaking starting from a sharp spectral peak. We confirmed that the spectral peaking occurred when it started from a sharp spectral peak in place of the dip.
Fig. 10. Variation of optical spectrum at the output of EDFA when sech2 pulse with Kelly sidebands was used.
3.2 HCN gas cell
So far, the periodical spectral peaking phenomenon in a gas cell has been investigated using only the CH4 gas cell. Next, we examined spectral peaking in the case of an HCN gas cell, which has sharp fingerprint absorptions around the 1555 nm region.
Figure 11 shows the experimental setup. The output of an Er-doped SWNT fiber laser was amplified in PM-EDF, and the optical spectrum was broadened by SPM. Then the output pulse was passed through a band-pass filter (BPF) with 10 nm bandwidth at the center wavelength of 1555 nm, and a part of the optical pulse spectrum was picked off and used as the pulse source. Then the extracted optical pulse was introduced into the HCN gas cell with fiber pigtails (Wavelength Reference, HCN-13-H(16.5)-100-FCAPC), and it experienced the fingerprint, sharp multiple absorptions of the HCN. Then the extracted output pulse was introduced into a commercially available EDFA (Pritel FA-30), and the optical pulse was amplified in the EDFA. The output pulses were observed with an optical spectrum analyzer (Anritsu MS7412).
Figure 12 shows the variation of the optical pulse spectrum at the output of the EDFA. When the current of the pump LD was ∼zero, sharp multiple absorptions with a spectral separation of ∼100 GHz were observed on the pulse spectral envelope. As the optical pulse was amplified in the EDFA, the optical spectrum was broadened by SPM. The spectral dips turned into peaks, and then went back to dips, and turned into peaks again as the pump LD power was increased. Although the pulse envelope varied through the nonlinear effects, the periodical spectral peaking was clearly observed for the HCN gas cell for the first time. In principle, the spectral peaking occurs for any gas molecular absorption, and it is expected that the spectral peaking will be observed in a wide wavelength range using different gas molecules.
Fig. 12. Variation of optical spectrum at the output of the EDFA when an optical pulse that experienced absorption in HCN was used as the input.
4. Conclusions
In conclusion, we investigated the characteristics of spectral peaking in optical fibers. First, we investigated the spectral peaking phenomenon during the supercontinuum generation process in a normal-dispersion highly nonlinear fiber (ND-HNLF) both numerically and experimentally. In the numerical analysis, we considered not only the sharp absorptions but also the accompanying phase shift. Sharp multiple spectral peaks were generated simultaneously using a 200 fs soliton pulse, a CH4 gas cell, and an ND-HNLF. Stable spectral peak generation with a high signal-to-background ratio (SBR) of ∼8.4 was achieved during coherent supercontinuum generation. The induced phase shifts in the absorption spectra were observed clearly on the spectra during the spectral peak generation. The intensity and phase noise of the generated spectral peaks were examined, and low noise properties were confirmed. The numerical results were almost in agreement with the experimental ones. Simultaneous spectral peak generation from the whole absorption spectra of CH4 around the 1.6–1.7 μm range was achieved using a 75 fs ultrashort soliton pulse. When the conventional anomalous-dispersion fiber was used, since the spectral shape was not flat and smooth, it was difficult to obtain the induced phase shifts directly from the spectral shape.
Next, we investigated the spectral peaking phenomenon in a fiber amplifier. Since a nonlinear phase shift is induced by an amplified pulse, it is easy to observe the spectral peaking using a fiber amplifier. First, we used the output pulse from a soliton-mode-locked fiber laser, which is a sech2-shaped pulse with Kelly sidebands. At the output of the fiber amplifier, we observed that the Kelly sidebands were transformed into sharp dips, which then turned back to the peaks again at the same wavelengths. We confirmed that the periodical spectral peaking occurred when the initial input pulse was a pulse with spectral peaks in place of dips. Finally, multiple, periodical spectral peak generation was observed using an HCN gas cell. This is the first report of spectral peaking using a gas cell other than CH4. It is expected that the spectral peak generation will be observed in a wide wavelength range using absorption in various gases. This phenomenon will be useful for novel optical frequency comb techniques and wavelength standards.
Acknowledgement
The authors thank Y. Sakakibara, E. Omoda, and H. Kataura in AIST for providing the SWNT films.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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