Ultrashort pulses and optical fibers can be used to induce significant nonlinear effects that can be exploited in a wide variety of optical control techniques [1]. So far, many effects have been discovered, for example, the soliton effect, soliton self-frequency shifting (SSFS), and supercontinuum generation [1–3]. 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, spectroscopy, and optical communication [4].

Optical frequency combs work as highly accurate optical frequency rulers and have been widely used for high-speed or highly accurate spectroscopy and metrology. However, since the number of comb modes is huge, it is difficult to handle them, and the optical energy per mode is too small for some applications. Thus, it is important to realize a technique for selecting and enhancing specific comb modes for highly sensitive spectroscopic applications [5].

In 2020, Nishizawa and Yamanaka discovered the novel phenomenon of periodical spectral peaking in optical fibers [6,7]. When an ultrashort pulse that suffers sharp molecular gas absorption propagates along a fiber, the ultrashort pulse experiences nonlinear phase shift but the spectral dips do not. Then, the sharp absorption dips turn into spectral peaks periodically as the result of interference. If we use a molecular gas cell inside a passively mode-locked ultrashort pulse fiber laser oscillator, intense spectral peaks are generated through multiple roundtrips of the mode-locked pulse [8]. The generated spectral peaks, however, are limited by the properties of the molecular gases used.

From 2004 to 2006, there were some reports of spectral enhancement using fiber gratings and spectral shapers [9–11]. However, the generation of wideband, very narrow, multiple, and periodical spectral peaks has not been demonstrated yet.

Here we report, for the first time, the demonstration of controllable, intense spectral peaking using a high-resolution spectral filter with a liquid-crystal-on-silicon spatial light modulator (LCOS-SLM). The characteristics of spectral peaking in normal- and anomalous-dispersion nonlinear fibers were investigated both experimentally and numerically. Intense, sharp, single and multiple spectral peaks were generated at arbitrary wavelengths in a wide wavelength range. An extremely high signal-to-background ratio (SBR) of up to 30 dB and a large enhancement factor of more than 10 were observed for spectral peaking. This technique is very useful for highly sensitive spectroscopy, mode selection of optical frequency combs, and ultrahigh-repetition-rate pulse train generation.

Figure 1 shows the experimental setup for spectral peaking using an LCOS spectral filter. A passively mode-locked Er-doped ultrashort pulse fiber laser was used as the seed pulse source. A polyimide film in which single wall carbon nanotubes (SWNTs) were dispersed was used as the mode-locker. The net cavity dispersion was anomalous, and stable soliton mode-locking was achieved. The repetition frequency was 28 MHz. The output pulse was amplified in an Er-doped fiber amplifier and was then introduced into an anomalous-dispersion polarization-maintaining fiber. At the fiber output, an ultrashort pulse was generated at a center wavelength of 1.65 μm by SSFS [6,7].

 

Fig. 1. Experimental setup of controllable spectral peak generation using arbitrarily controllable spectral filter with LCOS-SLM.

Download Full Size | PDF

The generated soliton pulse was introduced into a beam expander to enlarge the beam diameter, and then the optical beam was introduced into a diffraction grating, where the optical spectrum was spatially dispersed. Next the diffracted beam was collimated with a concave mirror, and the resulting beam was radiated onto the LCOS-SLM device. The LCOS-SLM device (Hamamatsu Photonics, X15213) had 1280 × 1024 pixels and dimensions 15.9 mm × 12.8 mm. A periodical pattern, which worked as the diffraction grating, was displayed on the LCOS-SLM. Intensity modulation could be applied by changing the contrast of the displayed diffraction grating, and phase modulation could be applied by shifting the grating pattern in the vertical direction.

The beam diffracted at the LCOS-SLM traveled back along the same optical path and was coupled into the optical fibers, and spectral peaking was induced. The output beam was observed with an optical spectrum analyzer and a power meter.

First, we investigated the spectral peaking in a normal-dispersion highly nonlinear fiber (ND-HNLF). The magnitude of the nonlinear coefficient γ was 23, the mode-field diameter (MFD) was 3.0 μm, the second-order dispersion β₂ was +6 ps²/km, and the third-order dispersion β₃ was 0.0057 ps³/km.

Figure 2(a) shows experimental results for the variation of the output spectrum from 5 m of ND-HNLF as a function of the fiber input power. A π phase shift was applied at the center part of the spectrum. Five pixels at a wavelength of 1.65 μm were used for the phase filter. As the fiber input power was increased, the pulse spectral envelope was broadened through self-phase modulation, and spectral peaks were generated periodically by the interference between the spectral peak and spectral envelope [6]. For the 2nd peak in Fig. 2(a), a high SBR of up to 42 was observed. The width of the spectral peak was 0.23 nm full width at half maximum (FWHM).

 

Fig. 2. Variation of optical spectra at the output of 5 m of ND-HNLF as a function of fiber input power when phase modulation was applied at the center wavelength: (a) experimental, and (b) numerical results. N represents the soliton order at input. Resolution bandwidth (RBW) was 30 pm in (a).

Download Full Size | PDF

Figure 2(b) shows the corresponding numerical results for the variation of the optical spectrum. The extended nonlinear Schrödinger equation was used for the analysis [7]. The numerical results were almost in agreement with the experimental ones. The spectral width was 0.25 nm FWHM. The observed SBR was ∼43. When a CH₄ gas cell was used, the maximum SBR was 8.4 [6,7].

Figure 3 shows the numerical results for the variation of the optical spectrum during fiber propagation. The input pulse conditions were the same as those of the 2nd peak in Fig. 2(b). Spectral peaks were generated periodically along the fiber. The highest peak was generated at a propagation distance of 0.6 m. Compared with the input spectrum, the magnitude of the central spectrum was enhanced by a factor of 5. When the spectral intensity filter was applied, the enhancement factor was 1.1, which was much smaller than that of the phase filtering (see Fig. S1 in Supplement 1).

 

Fig. 3. (a) Numerically obtained evolution of optical spectra in ND-HNLF with spectral phase modulation at the center wavelength. (b) Variation of generated spectral peak intensity along the fiber.

Download Full Size | PDF

Figure 3(b) shows the variation of the spectral peak intensity as a function of the propagation length. Since the pulse width was broadened and the peak power was decreased along the fiber propagation owing to the normal-dispersion properties, the period of spectral peaking became longer along with fiber propagation.

Next, in order to discuss the physical mechanism involved, we investigated the characteristics of spectral peak generation. Figure 4(a) shows a comparison of optical spectra for the 1st peak condition in Fig. 3. We can see that when the spectral filter was applied, the intensity of the spectral envelope was slightly decreased over the whole spectrum and an intense spectral peak was constructed. From this figure, we can see that part of the optical energy from the whole pulse spectrum was concentrated in the spectral peak, and an intense spectral peak was generated.

 

Fig. 4. Enlarged spectra when (a) 1st, and (b) 2nd peaks were generated in Fig. 3(a). Blue lines are spectra without (w/o) phase filter and red ones are those with (w/) phase filter.

Download Full Size | PDF

Figure 4(b) shows the optical spectra when the 2nd peak was generated. It is interesting to note that there were no dips around the center part when the spectral filter was not applied; in contrast, when the spectral phase filter was applied, an intense spectral peak was generated, and spectral dips and small bumps appeared around the peak. In terms of the temporal profile, it was considered that these spectral variations were caused by cross-phase modulation (XPM) between the spectral peaks and the pulse envelope (see Fig. S2 in Supplement 1). These spectral dips contributed to the enhancement of the SBR for these spectra.

Figure 5 shows the wavelength tunable operation of the spectral peaking. Using the LCOS-SLM, we can generate spectral peaks at arbitrary wavelengths within the pump pulse spectrum. From Fig. 5, we confirmed controllable spectral peaking over a wide range.

 

Fig. 5. Wavelength tunable spectral peak generation with LCOS-SLM.

Download Full Size | PDF

Next, we examined multiple spectral peak generation.

Figure 6 shows the experimental results of multiple spectral peak generation. Here spectral phase filtering with a π phase shift was applied to 10 spectral components with 5-nm and 1.5-nm separations. The pulse width was 83 fs. As shown in Fig. 6, 10 intense, sharp spectral peaks were generated simultaneously over a wide range. The higher peaks were generated around the center wavelength of the pulse in Fig. 6(a). From a comparison with the input pulse, a maximum gain of about 5 was observed at the center wavelength of 1.65 μm. It is worth noting that an ultrahigh-repetition-rate pulse train with 1.9-ps constant interval was clearly generated in the temporal domain (see Fig. S3 in Supplement 1).

 

Fig. 6. Multiple spectral peak generation at intervals of: (a) 5.0 nm, and (b) 1.5 nm. RBW was 30 pm.

Download Full Size | PDF

When the spectral peak interval was 1.5 nm, four-wave mixing (FWM) components were generated clearly at both the longer and shorter wavelength sides in Fig. 6(b). Here the fiber input power was 3.9 mW, and the 2nd peaks with extremely high SBRs of up to 143 (21.6 dB) were observed.

Figure 7 shows the enlarged 10 spectral peaks with 1.5-nm separation when the fiber input power was 1.3 mW and the 1st peaks were generated. It is surprising that the non-filtering parts almost disappeared, and extremely high SBRs of up to 30 dB were observed. These extremely high values were obtained as a result of interference, as well as the additional assistance of XPM. Since the targeted molecules can be excited effectively, it is expected that such spectral peaks will be extremely useful for spectroscopic applications.

 

Fig. 7. Enlarged optical spectra when 10 peaks with 1.5-nm intervals were generated: (a) linear, and (b) log scale. The fiber input power was 1.3 mW.

Download Full Size | PDF

Next, we investigated the spectral peaking in anomalous-dispersion fiber. As the sample fiber, we used 5 m of small-core polarization-maintaining fiber (SC-PMF) to enhance the nonlinear effects. The MFD was 5 μm and β₂ was –15 ps²/km.

Figure 8 shows the variation of the optical spectrum at the output of the SC-PMF. The input pulse width was 200 fs. The same spectral phase filter used in Figs. 2 and 3 was applied. As the fiber input power was increased, spectral peaks and dips appeared periodically. Compared to the results in the case of the ND-HNLF, a much more intense spectral peak was generated. As the fiber input power was increased, the spectral envelope was varied due to the nonlinear effects, and the center wavelength was gradually shifted toward the longer wavelength side. The numerical results showed similar behavior to the experimental ones.

 

Fig. 8. Variation of optical spectra at the output of 5 m of SC-PMF as a function of fiber input power when phase modulation was applied at the center wavelength: (a) experimental, and (b) numerical results. N represents the soliton order at fiber input. RBW was 30 pm in (a).

Download Full Size | PDF

Figure 9 shows the numerical results for the variation of the optical spectrum along the fiber when a single spectral phase filter was applied at the center wavelength. As the propagation distance along the fiber increased, intense, sharp spectral peaks were generated periodically. When the first peak was generated at a propagation distance of 1.7 m, the magnitude of the spectral peak was about 10 times as large as the initial spectral intensity at the center part. This shows that a large enhancement factor of ∼10 could be achieved for the spectral peaking effect. Then the ultrashort pulse suffered SSFS, and the center wavelength was gradually shifted toward the longer wavelength side. As a result, the intensity of the spectral peaks decreased during the propagation along the fiber.

 

Fig. 9. (a) Numerically obtained evolution of optical spectra in SC-PMF with spectral phase modulation at the center wavelength. (b) Variation of generated spectral peak intensity along the fiber. The input pulse conditions are the same as those in Fig. 8(b), 2nd peak condition (top).

Download Full Size | PDF

Figure 10 shows the variation of the enhancement factor and power of spectral peaks and soliton order N where the 1st peak was generated. The pulse width was 200 fs and the SC-PMF was assumed as the sample fiber. Thanks to the soliton spectral compression, the highest peak gain of 14.5 was achieved when the pulse peak power was 180 W. The corresponding soliton order N was 0.6. The spectral peak power was increased as the input power was increased.

 

Fig. 10. Characteristics of spectral peaking for anomalous-dispersion SC-PMF.

Download Full Size | PDF

Figure 11 shows the generation of 10 multiple spectral peaks in the SC-PMF. The intense spectral peaks were generated stably and simultaneously over a wide range. Like the single peak generation case, the peak intensities were higher than those in the ND-HNLF.

 

Fig. 11. Multiple spectral peak generation at intervals of (a) 2.5 nm, and (b) 1.5 nm. RBW was 30 pm.

Download Full Size | PDF

We also examined the RF spectra and phase noise of the spectral peak component, and low-noise properties and long-term stability were confirmed (see Fig. S4 in Supplement 1). This means that the comb structure and coherent properties were preserved inside the spectral peaks [7]. It is considered that spectral peaking is useful for the mode selection of optical frequency combs.

In conclusion, we investigated controllable spectral peak generation using a high-resolution spectral filter with an LCOS-SLM. Intense and sharp, single and multiple spectral peaks were generated periodically by spectral phase filtering. In ND-HNLF, an extremely high SBR of up to 30 dB was observed successfully. When an anomalous-dispersion fiber was used, an intense spectral peak was generated, and a large enhancement factor of more than 10 was observed. Low-noise, stable properties were confirmed. This light source technology is very useful for arbitrary optical frequency comb mode selection and enhancement. In principle, this phenomenon occurs in any wavelength range, and the generated spectra will be useful for highly sensitive spectroscopy, control of optical frequency combs, and ultrahigh-repetition-rate pulse train generation. This technique opens up new aspects and applications of ultrafast nonlinear fiber optics.