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Abstract
Spectral peak generation is a recently reported phenomenon that narrow spectral dips of the optical spectrum turn into sharp peaks as they propagate through nonlinear optical fibers. We demonstrated the nonlinear polarization rotation-based spectral peak mode filtering to increase the signal-to-background ratio (SBR). The spectral peaks with almost constant frequency separation were generated from the femtosecond pulses absorbed by the CH4 gas through the highly nonlinear fiber. The generated spectral peaks were filtered through the polarizing beam splitter by the nonlinear polarization rotation, and the SBR was improved from 9 dB to ∼20 dB. The spectral peak generation phenomenon and the mode filtering were numerically confirmed by solving the coupled nonlinear Schrödinger equations. The demonstrated method can generate strong comb modes with wide frequency spacing which are useful for highly sensitive environmental gas sensing spectroscopy. The wavelengths of the spectral peaks are fixed by the absorption spectra of the used gas cells. Therefore, this method can generate high quality spectral peaks of any wavelengths with wide spectral ranges through proper combinations of gas cells.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical frequency combs are very useful sources for high resolution molecular spectroscopy, as they have broadband optical spectra and stably fixed coherent comb lines [1]. For highly sensitive spectroscopy, it can be desirable to use frequency combs which have high power per each comb mode to measure the meaningful signals with a high signal-to-noise ratio [2] without saturation of the photodiodes. In the comb spectroscopy, unnecessary comb modes result in saturation of photodiodes which generate nonlinearity. The nonlinearity of the photodiodes can make huge 24% error in gas concentration [3]. Even it shifts the absorption wavelength and distorts the absorption spectral intensity and phase [4,5].
Recently reported spectral peaking phenomenon [6–12] which can obtain peak mode intervals with nm levels (∼100 GHz) can be attractive to make freely controllable high power comb modes. The spectral peaking is a recently reported phenomenon that narrow dips of the optical spectrum turn into sharp spectral peaks as they propagate through nonlinear optical fibers. Therefore, a few comb modes at the spectral dip locations can be selectively amplified. The signal-to-background ratio (SBR) of the spectral peak modes with ∼3 nm nearly periodical spacing was reported as 9.2 dB which were generated from CH4 gas-absorbed nearly periodical spectral dips at 1650 nm center wavelength [7]. However, a large amount of energy is concentrated on the background components which result in the photodiode nonlinearity in the comb spectroscopy. Therefore, it is worthwhile to improve the SBR for highly sensitive spectroscopic applications. Note that we defined the SBR as maximum power ratio of local maximum single peak to adjacent minimum pedestal component.
In this paper, we investigated nonlinear polarization rotation (NPR)-based spectral peak mode filtering from CH4-absorbed spectrum of a mode-locked Er-fiber femtosecond laser. NPR has been used for passive mode-locking in fiber lasers [13], pulse shaping [14–16], and all-optical switching [17]. We newly introduced an NPR-based filtering system to suppress broadband background pedestal in a previous spectral peaking experimental setup [7]. The SBR of the spectral peak signals was improved to ∼20 dB at 1650 nm center wavelength with ∼3 nm spacing. We investigated spectral peak generation and mode filtering quality at different fiber lengths and dispersion regions. We also conducted numerical simulations of the nonlinear polarization rotations in various optical fibers to support our experimental results. By improving the spectral peak signal qualities, we give a way for practical usage of the spectral peaking phenomenon for highly sensitive spectroscopic applications such as trace gas detections.
2. Operating mechanism and numerical analysis for spectral peak generation and mode filtering
Figure 1 shows the principle of mode filtering of spectral peaks using NPR. When ultrashort pulses pass through the molecular gas cell, they experience sharp multiple absorptions. Then the ultrashort pulses are coupled into an optical fiber. Two different phenomena occur in the nonlinear fiber, one is spectral peak generation, and the other is nonlinear polarization rotation. As the first step, as the optical power of the sharp spectral dips are very weak, they are hardly affected by nonlinear effects inside the fiber. On the other hand, the remaining broadband spectra which take charge of most of the power, experience strong nonlinear phase shift. When the nonlinear phase differences between them get π with the same polarization, constructive interferences occur, and the spectral dips turn into the spectral peaks. As the second step, the spectral peak signals are separated from the remaining broadband pedestals by the NPR. As the spectral peak signals and the broadband pedestals experience different nonlinear phase shift and polarization rotations, the two components can be separated through a polarizing beam splitter (PBS) and waveplates. To satisfy these two different steps at the same time, we inserted waveplates set at input and output of the nonlinear fiber respectively.
Fig. 1. Operating mechanism of the spectral peak generation and mode filtering. PBS, polarizing beam splitter.
In order to analyze the spectral peaks generation and mode filtering by the NPR, we conducted the numerical analysis. Here we used the coupled nonlinear Schrödinger equations [18,19] given by the following (Eq. (1) and Eq. (2)).
First, we discuss the nonlinear properties when we used a normal dispersion highly nonlinear fiber (ND-HNLF). As the parameters of the fiber, β2 = 6 ps2/km, β3 = 0.01 ps3/km, and the nonlinear coefficient γ was 21.3 W−1km−1 at 1650 nm. The pulse peak power was 2.4 kW (12 mW average power). Figure 2(a) shows the variation of the two output powers of the PBS depending on the fiber propagation length. Here the angles of the half-wave plates at the fiber input and output were set to 15 and 27.5 degrees to the principal axis of the fiber respectively, which were one of the high signal to background ratio points. The corresponding input power ratio between the principal axes was 63:37 at the 15 degree. To find this condition, we investigated all the combinations of the angles systematically. As the propagation along the fiber, NPR occurred and the powers from the two PBS output ports varied continuously. The output power of the port 1 decreased, but the port 2 increased. Figure 2(b) shows the variation of spectral peak intensity and signal to background ratio. During the fiber propagation, the spectral peak intensity changes periodically. It means that the spectral peak signals and dips are generated alternately. It is because of nonlinear phase difference change in the fiber propagation. The spectral peaks and the remaining broadband pedestals experience different nonlinear phase shift. When they satisfy constructive interference conditions, the spectral peaks are generated, but the spectral dips are obtained at destructive interference conditions. This phenomenon can be confirmed in the experimental results which will be explained in the later section. The magnitudes of the local maximum spectral peaks were gradually decreased along the fiber. It is because the spectral shape is broadened through self-phase modulation (SPM). When the polarizations of the background pedestals were matched to the PBS by the NPR through the fiber propagation, the spectral peaks and broadband pedestals can be separated, and high SBR is obtained. Note that the spectral peak intensity and the SBR inserted in the graphs are only for one best peak. The multiple spectral peaks have different peak intensities and SBRs along the wavelengths. They get higher when their initial absorption dips are stronger. However, the moving trends are the same along the wavelengths. If one peak gets higher, the others also get higher. Therefore, one peak can represent the performance.
Fig. 2. Nonlinear phenomenon according to the propagation length of the ND-HNLF. (a) The output powers after the PBS. (b) Spectral peak intensity and signal-to-background ratio at the one output port of the PBS.
Figure 3 shows the variations of the two output powers after the PBS, spectral peak intensity, and SBR at the one output port of the PBS as a function of fiber input power. Here the length of the ND-HNLF was fixed at 5 m, which was used in the experiment. As the fiber input power increased, the output powers after the PBS changed nonlinearly by NPR phenomenon. The magnitudes of spectral peaks changed almost periodically for the fiber input power because of the interference condition variation. When the input average power was 11-17 mW, the third- and fourth-peaks were generated, and the highest SBR was obtained at the one output port of the PBS. The maximum SBR was up to 560 (27 dB).
Fig. 3. Variations of (a) the output powers after the PBS and (b) spectral peak intensity and SBR at the one output port of the PBS as a function of the input power with 5 m ND-HNLF.
Figure 4 shows the optical spectra when the intense spectral peaks with high SBR are obtained in Fig. 2 and 3. The corresponding ND-HNLF length was 5 m, and the fiber input power was 11 mW. Figure 4(a) shows the optical spectra of the propagating pulses along the two birefringent axes. The spectral shapes were smoothly broadened by SPM and normal dispersion for each axis. On the pulse spectra, the spectral peaks with dips were generated through the spectral peaking phenomenon. Figure 4(b) shows the optical spectra at the two output ports of the PBS. The main background pedestal components came out from the port 2, and the high spectral peaks with high SBR were obtained from the port 1. Figure 4(c) shows the enlarged optical spectra around the center wavelength. We could observe the dispersive waveform at the port 2. This pattern occurs at the transient region between spectral dips and peaks by the gradual phase difference inversion. We could confirm that the narrow spectral peaks with high contrast were obtained from the port 1. The estimated SBR was 25 dB. These characteristics are almost in agreement with the experimental ones, which will be explained in later sections.
Fig. 4. Optical spectra at the 5 m ND-HNLF and 11 mW fiber input power conditions. (a) The fiber outputs of the two orthogonal polarization axes. (b) The PBS outputs. (c) Enlarged spectra at the PBS outputs.
Next, we examined the spectral peaks filtering at small core anomalous dispersion fiber. As the parameters of the fiber, β2 = -25 ps2/km, β3 = 0.177 ps3/km, and the nonlinear coefficient γ was 4.8 W−1km−1 at 1650 nm. Figure 5(a) shows the variations of the spectral peak and SBR at the PBS output port 1. Here the average power of 10 mW was assumed. The angles of half-waveplates at the input and output of the fiber were 8 and 15 degrees, respectively. During the propagation along the fiber, the spectral peaks and dips were generated alternately with almost constant period, and the high SBR was obtained at some fiber lengths. Figure 5(b) shows the optical spectra of the propagating pulses along two orthogonal fiber axes. In contrast to the previous ND-HNLF results, the ultrashort main pulses were shifted to the longer wavelength side through Raman soliton self-frequency shift at the anomalous dispersion regime [20]. However, the generated spectral peaks remained at the initial wavelengths. It’s interesting to note that the small spectral component along the orthogonal axis was trapped by the intense soliton pulse and co-propagated along the fiber. Thanks to this pulse trapping effect [18], the remaining background pedestal components at the initial wavelength were suppressed well. Figure 5(c),(d) shows the optical spectra at the two PBS output ports. We could see that almost all of the spectral peaks went out from the one port, and background pedestals went out from the other port. The estimated SBR at the one port was up to 43 dB.
Fig. 5. Simulation results at the anomalous dispersion fiber. (a) Variations of the spectral peak intensity and the SBR according to the fiber propagation length. (b)-(d) Optical spectra at (b) the 5 m fiber outputs and (c),(d) the PBS outputs.
3. Experimental results
3.1 Spectral peak generation and NPR-based mode filtering using a normal dispersion highly nonlinear fiber (ND-HNLF)
Figure 6 shows the schematic of the spectral peak generation and the NPR-based mode filtering method. A carbon nanotube saturable absorber-based mode-locked Er-fiber laser with 50 MHz repetition rate was used. To access to CH4 absorption spectrum, the 1556 nm center wavelength was shifted to 1650 nm through a 100 m polarization-maintaining single-mode fiber with 44 mW input power. Pulse duration was preserved to 191 fs, thanks to Raman-shifted soliton pulse generation through the fiber [20]. The soliton pulses were passed through a 75 mm CH4 gas cell with 200 Torr, and spectral dips with almost constant frequency separation were generated (Fig. 7(a)). After blocking the 1556 nm residual components using a long-pass filter, the soliton pulses experienced the spectral peaking phenomenon through a 5 m normal dispersion highly nonlinear fiber (ND-HNLF). The spectral peak signals with ∼3 nm spacing were generated with broadband background pedestal (Fig. 7(b)-(d)). The spectral peak signals and dips were generated alternately by the fiber input power, because of the constructive/destructive interference conditions depending on the nonlinear phase shift changes. When the input power was 7 mW for the 5 m ND-HNLF, the maximum spectral peak intensity was achieved.
Fig. 6. Schematic of the spectral peak generation and the NPR-based mode filtering. PM-SMF, polarization-maintaining single-mode fiber; EDFA, Er-doped fiber amplifier; LPF, long-pass filter; ND-HNLF, normal dispersion highly nonlinear fiber.
Fig. 7. Alternate generations of the spectral peaks and dips depending on the fiber input power. (a) Just after the CH4 gas cell. (b)-(d) After the ND-HNLF at the different fiber input power conditions.
To separate the signals from the broadband pedestal, the NPR was used. We just rotated the four waveplates randomly and found the optimized result through an optical spectrum analyzer. This process is exactly same with finding mode-locking of NPR-based lasers. As the spectral peak signals and the broadband pedestal experience different nonlinear phase shifts and the polarization rotations, the two components can be separated through the PBS and the waveplates. At the optimized waveplates conditions, the SBR of the spectral peak signals was maintained stably in the experimental room unless the placement of the ND-HNLF changed. Figure 8 shows the spectral peak mode filtering results through the PBS, when the average input power is 7 mW into the 5 m ND-HNLF (Fig. 7(d)). The SBR of the spectral peak signals before the filtering was 9 dB. After filtering them through the PBS, ∼20 dB SBR was obtained at the one port with 309 µW average power. Most of the optical power was concentrated at the broadband background pedestal, so the pedestals which intensively experienced the nonlinear polarization rotation mainly moved to the other port, and the maximum SBR was improved from 9 dB to ∼20 dB. The multiple spectral peaks have different SBRs. It is because that the NPR effect is different along the wavelength. We rotated the waveplates to minimize the background pedestal near the center of the spectral peaks. In addition, the spectral peaks powers are also different along the wavelength. They get higher when their initial absorption dips are stronger. The wavelength spacing of the spectral peaks was ∼3 nm. In Fig. 8(c), the background pedestal which contained comb modes was close to the spectrum analyzer measurement limit (−63 dBm), but it was not limited by this level yet.
Fig. 8. Separation of the spectral peak signals from the broadband pedestals with 7 mW input to the 5 m ND-HNLF. (a) The pedestal port of the PBS output. (b) The spectral peaking port of the PBS. (c) The spectral peaking port of the PBS in log scale.
Figure 9 shows the comparison of the spectral peaks (data from the Fig. 8(b)) to the HITRAN data [21] in linear scale. As the calibration error of the old optical spectrum analyzer, there are ∼600 pm wavelength shifts from the HITRAN data. The spectral peaks get weak at the side wavelength because the original spectral dips are weak at the side. See the Fig. 7(a).
Figure 10 shows the nonlinear properties of the two PBS output powers. When the incident average power was small, the split ratio of the PBS was similar. As the input power increased, the pedestal components which were mixed at the spectral peaking port started to move to the pedestal port. Therefore, the average power at the spectral peaking port decreased. This phenomenon is consistent with the simulation result (Fig. 3(a)).
3.2 Quality enhancement of the spectral peak signals
To improve the SBR and to generate more spectral peak signals, it is necessary to increase the nonlinearity. We decreased the length of 100 m Raman shifting fiber (PM-SMF in Fig. 6) before the CH4 gas cell to increase the average power and to broaden the optical spectrum. As Raman shifting effect is weaker at a shorter fiber, higher power is necessary to shift the 1556 nm center wavelength from the laser to 1650 nm of CH4 absorption wavelength. We increased the EDFA pumping power to increase the laser power. Figure 11 shows the optical spectrum at the different fiber lengths. At threshold power inside the fiber, the soliton pulse split. As the optical power increased, the residual component shape changed, but the center wavelength remained at the 1556 nm. On the other hand, the split soliton maintained the waveform, and the wavelength was shifted. The average power increased to 99 mW from 49 mW at the 1650 nm center wavelength by shortening the fiber length from 100 m to 5 m, and the pulse width became 95 fs from 191 fs. Therefore, the spectrum was broadened, and stronger absorption spectra occurred.
Fig. 11. Increasing the average input power to the CH4 gas cell and broadening the spectrum by reducing the fiber length. (a) After 5 m PM-SMF in the full spectral range. (b) After 5 m / 10 m / 100 m PM-SMF near the 1650 nm. (c) After the CH4 gas cell at the each fiber length.
Figure 12 shows the comparison of the 5 m and 100 m fiber length results. They were measured at the spectral peaking port of the PBS output (Fig. 6). At the 5 m PM-SMF result, the maximum spectral peak intensity occurred at 14 mW input average power into the 5 m ND-HNLF which corresponded to 5th local maximum point. The average output power at the spectral peaking port of the PBS was 1 mW, and the power efficiencies through the PBS filtering in terms of only spectral peaks components were 40%. The broadband pedestals were suppressed in ∼3 dB at the 14 mW result (red box in Fig. 12), and new peak signals were generated near 1680 nm (blue box in Fig. 12). It is because that the NPR effect is stronger at the higher power, and the spectral peaks powers get higher when their initial absorption dips are stronger. Compare the absorption spectrum near 1660 nm in Fig. 11(c).
Fig. 12. Comparison of the spectral peak signals quality of 100 m and 5 m Raman shifting fiber (PM-SMF). (a) Spectral peaking port with average 7 mW ND-HNLF input power and (b) with 14 mW input. Note that we changed the length of the PM-SMF for broadening the spectrum and increasing peak power in Raman shifting process. Spectral peak generation and NPR occur at the ND-HNLF of the same length. The broadband pedestals (the red box) were suppressed more, and more peak signals (the blue box) were generated at the (b) 14 mW input compared to the (a) 7 mW input.
Figure 13 shows the detailed shapes of the spectral peaks which were measured by the high-resolution optical spectrum analyzer with 5 pm resolution bandwidth. The linewidth was 20 pm which was nearly consistent with the HITRAN’s absorption linewidth of the CH4 gas at 200 Torr [21]. This result shows that the absorption linewidths are preserved in the spectral peak generation process. As the calibration error of the optical spectrum analyzer, there are ∼15 pm wavelength shifts from the HITRAN data.
The average power at the spectral peaking port of the PBS was 1 mW. It can be not enough for some sensitive spectroscopic applications. For the practical usage of the spectral peaks, we inserted a fiber-coupled semiconductor optical amplifier (SOA, Thorlabs, BOA1084P) at the spectral peaking port of the PBS output (Fig. 6). Figure 14 shows the amplification results. The peak signals were evenly amplified by ∼10 dB, but the broadband pedestals which took most of the power with short pulsewidth were saturated, so the amplification factor was below 10 dB at the side wavelengths of the main peaks. Even it was suppressed below 1575 nm, thanks to the limited gain-bandwidth of the SOA. As a result, the SBR was improved through the broad spectral range. The average power was 1 mW which was the same with that before amplification. It’s because the amplified peaks and the suppressed pedestals were balanced. We also checked whether we could amplify arbitrary peak modes using optical bandpass filters. Figure 14(b),(c) show the amplification results after a bandpass filter with center wavelength of 1650 nm and FWHM bandwidth of 12 nm. The average power of 0.6 mW was obtained. The peak intensities increased, but the pedestals decreased compared to the without bandpass filter result. This implies that the peak power can increase more using a narrower bandpass filter.
Fig. 14. Spectral peak signal amplification by the SOA. (a) Comparison of output spectra before and after amplification without the bandpass filter. (b) Amplification results with/without bandpass filter. (c) Amplification result with the bandpass filter in linear scale.
3.3 Spectral peak generation and mode filtering using an anomalous dispersion fiber
In the previous sections (3.1 and 3.2), we dealt with the spectral peak generation and mode filtering at the normal dispersion fiber. In this section, we investigate what happens in the anomalous dispersion fiber. The 5 m PM-SMF was used as a Raman shifting fiber, but the 5 m ND-HNLF was replaced by 3 m / 5 m / 30 m anomalous dispersion fibers. Figure 15 shows the optical spectra at the spectral peaking port of the PBS output. The average input powers into the anomalous dispersion fibers were 10 mW, 13 mW, and 8.5 mW at the 3 m, 5 m, and 30 m fibers, respectively. As the simulation results (Fig. 5), Raman soliton shift occurred in the anomalous dispersion fibers. The soliton pulses maintained their shapes and were shifted to longer wavelength continuously as increasing the fiber input power. On the other hand, the spectral peaks remained in the initial wavelength. At the longer fiber, Raman shifting effect is stronger, so the main soliton pulse and the spectral peaks could split completely at the 30 m fiber result. Note that the main soliton pulse moved to longer wavelength than 1700 nm which is the measurement limit of our optical spectrum analyzer.
Fig. 15. Spectral peak signals at the one port of the PBS outputs, when the 5 m ND-HNLF was replaced by the anomalous dispersion fibers of (a) 3 m, (b) 5 m, and (c) 30 m.
Figure 16 shows the spectral peak mode filtering effect using the 30 m anomalous dispersion fiber. In contrast to the normal dispersion fiber results, the background pedestal suppression was not high (just ∼5 dB), but in terms of the spectral peak signals, large amounts of peaks moved to the spectral peaking port. So, the spectral peak signals were suppressed as ∼7 dB at the pedestal port, and the power efficiencies through the PBS filtering in terms of only spectral peaks components were 80% at the spectral peaking port. As a result, the spectral peaks with ∼15 dB SBR were obtained at the spectral peaking port. When we compare this result to the numerical result in Fig. 5, the SBR is not high as 43 dB of the numerical result. In the numerical calculation, almost perfect soliton was shifted to long wavelength, and the remaining components near 1650 nm were very little. However, in the experiment, imperfect residual soliton remained near 1650 nm, therefore the SBR was lower than the normal dispersion result.
Fig. 16. Optical spectra at (a) the 30 m anomalous fiber output and (b),(c) the two PBS output ports.
4. Conclusion
We proposed and demonstrated the nonlinear polarization rotation (NPR)-based spectral peak mode filtering method to increase the signal-to-background ratio (SBR) of the spectral peak signals. The spectral peaks with almost constant frequency separation were generated from the CH4-absorbed Er-fiber femtosecond laser through the highly nonlinear fiber. The generated spectral peaks were filtered through the PBS by the NPR principle, and the SBR was improved from 9 dB to ∼20 dB. The wavelength spacing of the spectral peaks was ∼3 nm at 1650 nm center wavelength, and the linewidth was 20 pm which was consistent with theoretical CH4 absorption linewidth. The spectral peak generation phenomenon and the mode filtering were numerically confirmed by solving the coupled nonlinear Schrödinger equations. We also investigated how to improve the SBR and signal peak power by the different fiber length and dispersion regimes, incident power on the fibers, and the amplification by the semiconductor optical amplifier. In terms of HNLF dispersion, the anomalous dispersion fiber resulted in Raman soliton shift, and this phenomenon made higher SBR in the simulation. However, in the experiment, imperfect soliton components remained in the original positions without wavelength shift which hindered the separation of the spectral peak signals from the background pedestal (remaining soliton). In contrast, the normal dispersion fiber worked well, and we think that more input power can improve the SBR further.
The wavelengths of the spectral peaks are fixed by the absorption spectra of the used gas cells. Therefore, this method works for any wavelengths with wide spectral range through proper combinations of the gas cells. We showed the way to practical usage of the spectral peaking phenomenon for highly sensitive spectroscopic applications such as trace gas detections. We can compare the demonstrated method to our previous method for the comb mode filtering [8]. Using a spatial light modulator and a highly nonlinear fiber, we generated spectral peaks with 30 dB SBR and +7 dB spectral peak gain [8]. In contrast, the demonstrated method in this paper has ∼20 dB SBR with −7 ∼ −10 dB spectral peak gains. This loss can be improved if the molecular absorption depths get dipper by a longer gas cell. The active modulation method with spectral peaking generation can filter arbitrary comb modes with higher SBR and stronger peak intensities, however the linewidth of the spectral peaks is limited to 200 pm by the resolution of the spatial light modulator, and complex alignments are required. The spatial light modulator can be also used to filter already-generated spectral peaks by some methods. However, such a sharp filtering is difficult by the rack of spectral sharpness of the active filters. Depending on applications, we can select the preferable methods.
Funding
Japan Science and Technology Agency Core Research for Evolutional Science and Technology (CREST) (JPMJCR2104).
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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