We experimentally demonstrate the 2-8 μm high-power supercontinuum generation and theoretically propose a statistical method for precise estimation of the multi-pulse spectral evolution in the ZBLAN and As2S3 fiber cascaded all-fiber structured nonlinear system. In the experiment, with the aid of the ultra-low loss fusion splice technology, high-efficiency fiber butt-coupling technology and precise thermal management technology, we obtained a record-breaking supercontinuum source with a spectrum spanning from 2 μm to 8 μm at a power of 730 mW. Considering the strong pulse splitting and soliton fission effects in fibers, to precisely estimate the multi-pulse spectral evolution in this system, we, for the first time, built a multi-pulse pump model with the Pearson product-moment correlation coefficient method based multi-pulse selection mechanism. In combination with the existing approaches and some new programmatic work, finally, we verified that the simulation results are in good agreement with the experimental one.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
The all-fiber structured mid-infrared supercontinuum (MIR-SC) source possesses merits of high compactness, high power stability and excellent beam quality, which has been widely used in infrared remote sensing [1,2], medical biological imaging , molecular fingerprinting [4,5] and so on. However, since hindered by the high absorption loss of silica fiber in the MIR region, the SC spectral extension is cut off at 2.7 μm. To further extend the SC spectrum towards a longer MIR region, many works that have ever been reported were mainly focused on the adoption of fibers made from various materials, including fluoride and CCl4 . However, limited by the strong material multi-phonon absorption edge and the transmission bandwidth, the generated MIR-SC spectral long-wavelength edges are mostly limited to near 5 µm; moreover, although some advanced technologies such as OPCPA [7 8] and intra-pulse difference frequency generation  had also been tried, they seem more useful in high-energy short-pulse laser generation, the laser spectral coverage is limited. The SC wavelength beyond 5 μm covers many important molecular fingerprint spectra, such as CO, NO, and so on, which is of great importance in environmental gas monitoring and sensing. This means the urgency and significance of developing long-wave infrared SC sources. The commercialized chalcogenide glass (ChG) fibers, such as As2S3  and As2Se3 fibers with wider infrared transmission bandwidth and higher nonlinearity are very powerful candidates for extending the SC long-wavelength edge beyond 5 μm. Therefore, in recent years, the MIR-SC generation in ChG fibers has been extensively explored , such as using the OPA femtosecond lasers to pump high-nonlinear ChG fibers with varies of structures and material compositions, the generated MIR-SC spectral long-wavelength edge can be extended to far beyond 10 μm [7,12]. However, there are many deficiencies in these works including the experimental installations are costly, bulky, and not easy to maintain. Besides, the compactness and robustness of system are poor, and the output power is limited to several milli-watts, making it difficult to satisfy the requirements in high-power applications, such as hyper-spectral imaging and remote sensing. In the past decade, for the developing a small size, low cost and high-compact SC source with high intensity and broadband mid-infrared spectral bandwidth, researchers had devoted themselves to using high-power fiber lasers instead of the cumbersome solid-state lasers as the source to pump the fluoride and ChG fibers represented soft-glass fibers. In 2016, Petersen et al. demonstrated a MIR SC source with spectral long-wavelength edge extension to above 7 μm in the high-nonlinear suspended-core ChG fibers . In 2017, Yin et al. built an all-fiber structured silica, ZBLAN and step-index As2S3 fiber integrated MIR-SC generation system, and obtained the MIR-SC source with a spectral coverage of 2-5 μm and a maximum output power of 97.1 mW . In 2018, Francis et al. reported a 200-mW high-flatness 1.9-6.4 µm MIR-SC generation in the step-index InF3 and As2Se3 concatenated fibers . In the same year, Ramon et al. achieved a MIR-SC source with the spectrum spanning in As2S3 fiber from 2 µm to 6.5 µm and output power as high as 1.39 W. By splicing a section of As2Se3 fiber, they continued to broaden the spectrum to 11 µm, the corresponding power is up to 417 mW . In 2020, Robichaud et al. used an Er3+-doped ZBLAN fiber amplifier to pump a several tens of centimeters long As2Se3 fiber, with the aid of their advanced anti-reflection film coating technology, they achieved the SC power as high as 825 mW and spectrum covering 2-5 μm . In 2021, Woyessa et al. built an ultra-compact MIR-SC laser source with a spectral coverage of 1.5-10.5 µm and an output power of 86.6 mW by using advanced ChG fiber anti-reflection film coating technology . Very recently, our work systematically explored the butt-coupling technology between ZBLAN and step-index As2S3 fibers in high-power pumping conditions, concluded the relationship between coupling efficiency, As2S3 fiber damage threshold and coupling distance experimentally and theoretically, and gained the optimum coupling distance between ZBLAN and As2S3 fibers in butt-coupling process. Eventually, we obtained a MIR-SC source with a spectrum covering 2-6.5 μm and the corresponding power of as high as 1.13 W . Besides, we also proposed a multi-pulse pump model for a deep insight into the multi-pulse transmission and spectral evolution in fibers, providing a more precise way to evaluate the SC generation in that system.
To readily learn the progress in As2S3 fiber-based high-power infrared SC generation with all-fiber structured cascading pumping mechanism, we have listed the reported works in the past few years in Table 1, including the key parameters in their works. Comparatively speaking, our work has distinct advantages in SC bandwidth and power.
However, there are still two common issues in all the above-mentioned works, the first one is the SC spectral long-wavelength edge extension was limited to 6.5 μm in As2S3 fiber, even at a relatively high pump power condition, the second one is the lack of an effective way to precisely evaluate the multi-pulse transmission and spectral evolution in multiple fibers cascaded system.
To address these problems, in this work, by optimizing the front-end pump laser performances, lowering the fusion splicing loss between silica and ZBLAN fibers, and improving the butt-coupling efficiency between ZBLAN and As2S3 fibers, for the first time, we achieved an SC with spectrum covering 2-8 μm and output power as high as 730 mW in a ZBLAN and As2S3 fibers cascaded all-fiber structured nonlinear system. Furthermore, to estimate the SC spectral evolution more precisely in these fibers, we introduced a statistical algorithm to intelligently select the representative pulses as the pump of the following As2S3 fiber, and then, built a multi-pulse pump model. With this approach, we obtained the simulated SC spectrum in good consistency with the experimental one.
2. Experimental setup
The schematic of the all-fiber structured 2-8 μm MIR-SC source is shown in Fig. 1. The seed laser is a 1.55 μm distributed feedback pulsed laser (DFBL, VENUS-M, Connet Inc.) with 1 ns the pulse duration and 600 kHz the repetition rate, which is followed by a piece of single-mode fiber (SMF-28) (Nufern Inc.) to transfer the pulse energy from 1.55 μm to around 2 μm. Due to the presence of 1.55 μm residual pump light, a single-mode thulium-doped fiber (SM-TDF) (Nufern Inc.) with core/cladding diameter of 9/125 μm and a core absorption coefficient of 9 dB/m at 1.55 μm is used for spectral shaping, thereby the signal at 2 μm is enhanced and the 1.55 μm residual pump is well absorbed. To match the mode field between the 9/125 μm SM-TDF and the 25/400 μm large-mode-area thulium-doped fiber (LMA-TDF) (Nufern Inc.), a customized small-to-large mode field adapter (MFA) is adopted. The shaped 2 μm signal is then delivered into the 25/400 μm fiber-based LMA-TDFA system to promote the 2 μm signal power to a several-tens-watt level. For easily fusion splice with the followed ZBLAN fiber, a large-to-small MFA is spliced in-between the LMA fiber and SM1950 fiber (Nufern Inc.). The SM1950 fiber with a core/cladding diameter of 7/125 μm and a numerical aperture (NA) of 0.15, which can well match with the ZBLAN fiber. A 7 m-long ZBLAN fiber with core/cladding diameter of 7.5/148 μm, a NA of 0.2 and a zero-dispersion wavelength (ZDW) of 1.62μm (France, Le Verre Floure Inc.) is fusion spliced to a 50 cm-long the SM1950 fiber which is the pigtail of the MFA, by using the special fiber fusion splicer (Vytran GPX3800, Thorlabs Inc.). For a high coupling efficiency between ZBLAN and As2S3 fibers, and to avoid the fiber end-facet damage in high-power pumping conditions, we eventually adopted the butt-coupling scheme, with a coupling distance of 40 μm . A 4 m-long As2S3 fiber (core/cladding diameter of 9/170 µm, NA of 0.3, ZDW of 6.8 μm) is adopted in our work for long-wave SC broadening, and the fiber was supplied by IR-flex company. In butt-coupling, the distances between the two soft-glass fibers were carefully optimized, to prevent end-facet damage in high-power pumping conditions. Meanwhile, the end-facet of the ZBLAN fiber was angle cleaved at 8 degrees to reduce the Fresnel back reflection. To prevent ZBLAN fiber from deliquesce and to speed up the heat dissipation of fiber in high-power and long-term usage, we performed a nitrogen purge sweeping at the fiber butt-coupling position.
To precisely manage the heat of amplifiers and splicing point between SM1950 and ZBLAN fibers, the specially designed and customized aluminum water-cooling plates and package units (the water cooler temperature is set to 15°C) are adopted. In addition, to check the MIR-SC beam profile, a MIR laser beam profiler (SP90405, Ophir-Spiricon Inc.) is used. The end-facet of the soft-glass fibers was processed using a special fiber cleaver (Vytran LDC401A, Thorlab Inc.). A set of MIR spectrometer assembled with a liquid-nitrogen-cooled HgCdTe detector (Zolix Inc.), a grating-based monochromator (Omni-λ300i, Zolix Inc.), a lock-in amplifier (Stanford Inc.) and a chopper (Zolix Inc.) was employed to record the output SC spectrum. The spectral resolution of this optical spectrum analyzer is 0.4 nm in 0.8-5 µm, 0.8 nm in 5-10 µm and 1.6 nm in 10-22 µm, which means its available spectral range covers 0.8-22 µm. To avoid any overlap of the short-wavelength diffraction light overlap with long-wavelength components, in this spectrometer, a set of built-in long-pass filters were properly installed. The output power was measured with a Thorlabs PM200 power meter.
3. Results and discussion
To achieve a 2 µm seed laser, the wavelength conversion from 1.5 µm to 2 µm in silica fiber by nonlinear effect is conducted. As can be seen from Fig. 2(a), the loss in SMF-28 increases exponentially with the wavelength when the spectral long-wavelength edge extends to above 2.4 µm. To give a more distinguished display of spectral long-wavelength-edge extension in this figure, the spectral intensity was firstly taken logarithm and was then normalized. With the increase of SMF-28 length, the spectrum is well broadened while the output power decreases rapidly, therefore, it is a tradeoff between spectral width and output power. However, it is beneficial for subsequent pulse amplification when concentrating energy in the bands centered by 2 μm.
Therefore, we explored the SC spectral broadening and output power variation in SMF-28 with different lengths (2 m, 5 m, 10 m, 15 m, and 20 m) by using a commercial pulsed laser with a repetition rate of 600 kHz, power of 6.2 W, and a pulse width of 1 ns as the pump source, the results are shown in Fig. 2(a). Considering the output spectrum and power, the most appropriate SMF-28 length is finally 5 m. However, to further eliminate the residual pump light at 1.55 μm, we used a piece of 9/125 μm SM-TDF to absorb the energy at 1.55 μm and then transfer it to the 2 μm band, as shown in Fig. 2(b). As we estimated, the longer the SM-TDF length, the weaker the pump residual. When the SM-TDF length is 2 m, there is a small residual signal presence at 1.55 μm, the residual peak nearly disappeared by increasing the fiber length to 3 m, and when the fiber length was increased to 4 m, the residual peak is completely disappeared. Considering the output power, we eventually used a 3 m-long SM-TDF in our work and the signal light with a spectral coverage of 1.8-2.4 μm and an average output power of 3.3 W was realized. It is worth noting that for showing the variation tendency of the residual pump explicitly at 1550 nm, in Fig. 2(b), the spectral intensity is shown in linear scale and was normalized. To further scale the 2 μm signal to several-tens-watt level, we delivered the broad-band supercontinuum into a 25/400-LMA fiber amplifier with three 50 W, 793 nm, central wavelength locked LDs as the pump. The pump LDs are combined by a high-power pump combiner as the pump, the combined total output power is up to 120 W. The power and spectra output from the amplifier are as shown in Fig. 3(a).
As can be seen from Fig. 3(a), the overall trend is that with the enhancement of the pump power, the SC spectrum is broadened in the LMA-TDFA system accordingly. When the pump power increases from 20 W to 100 W, the output signal power rises almost linearly from 2.43 W to 19.42 W and the spectral coverage is 1.95-2.66 μm. It is worth noting that when the pump power is increased from 40 W to 60 W, the SC spectral long-wavelength edge is broadened by 0.1 μm, and the corresponding output power is also increased by 5.66 W. The slope efficiency slightly reduced by increasing the pump power, which means that the long-wavelength edge is broadened to the high attenuation region of the silica fiber.
Followed by the main power amplifier, a large-to-small MFA is used for light mode transition from LMA fiber to SM1950 fiber. Figure 3(b) gives the output power and spectral evolution in SM1950 fiber with different pump powers in LMA-TDFA. When the pump power is adjusted to 100 W, the maximum power output from SM1950 fiber is 8.17 W and the long-wavelength edge of the SC spectrum is extended to 2.85 μm, comparing with the output spectrum output from the LMA-TDFA system (as shown in Fig. 3(a)), the spectral flatness has been greatly improved and the long-wavelength edge of the SC spectrum is continually broadened by 0.21 μm. The high attenuation from LMA fiber to SM1950 fiber is attributed to two main factors: one is the high insertion loss of MFA due to the large mode area difference between 7/125 μm the SM1950 fiber and 25/400 μm the LMA fiber, the other is the SC spectrum is intensively broadened in so small core the SM1950 fiber, which resulted in the high transmission loss .
To further broaden the SC spectrum, the pulse output from SM1950 fiber was then coupled into the ZBLAN fiber. Figure 4(a) shows the output spectra from ZBLAN fiber under different pump powers while SM1950 was well spliced with a 7 m-long ZBLAN fiber. When the pump power is increased to 80 W, the maximum output power from ZBLAN fiber is up to 4.13 W, the corresponding SC spectrum covering 2-4.25 μm with high flatness. Figure 4(b) gives the corresponding output spectra from ZBLAN fiber using the butt-coupling technology between SM1950 and ZBLAN fibers. As can be seen that under the same pump power condition, compared with the use of splicing scheme, the output spectral coverage range is narrower, power is lower and there are more fluctuations on the spectrum due to the strong Fresnel reflection and thermal instability in butt-coupling in high-power pumping conditions. Figure 4(c) shows the output efficiency in the two different coupling mechanisms. It is worth noting that their coupling efficiencies also have a relatively larger difference in high-power pumping conditions than that in low power conditions.
The spectral evolution in a 4 m-long As2S3 fiber with different output power is depicted in Fig. 5(a). With the increase of the pump power from 20 W to 60 W, the output SC power rises accordingly, at the same time, the intensity of long-wavelength components is also improved gradually. Nonetheless, it is long-wavelength edges are limited to 8 μm due to the exponential increment of the As2S3 fiber loss. When the output power is at 350 mW, in the low-pump power conditions, there is a large dip appeared in the SC spectrum at 4 μm due to the absorption of S-H bonds. With the increase of pump power, the small dip in spectrum at 4 μm band disappears gradually due to the strong nonlinearity of As2S3 fiber Fig. 5(b) shows the output power variation with the pump powers in ZBLAN and As2S3 fibers. We can see that the linearity of the power output from ZBLAN fiber is not so good and there is an inflection point in the curve at pump power around 40 W, due to the intense spectrum spanning, the long-wavelength edge of spectrum entered the high attenuation area, power scaling and spectrum extension lead to the overall efficiency suffers from a decay. It can also be seen from the inset of Fig. 5(b), the power stability of the output power from As2S3 fiber is not as good as expected, the measured power root-mean-square (RMS) value in two hours is 0.56%. By analyzing this power stability curve, it can be found that in the first two hours, the power is stable, but tends to increase later. We believe that this is mainly resulted from the heat accumulation in the package parts in the long-term running condition, which in turn affects the system stability. We also measured the far-field beam profile and quality of SC output from As2S3 fiber, as shown in Fig. 5(c), the beam with Mx2 of 1.435 and My2 of 1.449 was achieved, this means a very good beam intensity distribution in spatial.
4. Theoretical analysis on SC generation
For a detailed analysis of the input pulse evolution temporally and spectrally, it was given by a time-domain generalized nonlinear Schrödinger equation (GNLSE) :
where A is the slowly varying amplitude of the pulse envelope, α is the fiber loss, w0 is the central frequency of the input pulse, α1=dα/dw, βn represents the nth order dispersion, γ is the nonlinear coefficient, γ1=dγ/dw, R(t’) is the Raman response function. The split-step Fourier method (SSFM) was used to solve the pulse-propagation problem in fibers.
In the simulation, the number of grid points was set as 218 and the time window width was set as 240 ps for enabling a more precise operation. In addition, the Gaussian white noise disturbance was also considered to make the simulation results more convincing and more consistent with the experimental one.
4.1 Spectral evolution in ZBLAN fiber with different lengths
For a further analysis of the pulse evolution in ZBLAN fiber, according to the detailed parameters of the front-end amplifier, the output pulses have a spectral distribution ranging mainly from 2 μm to 2.4 μm, we set the input pulse at 2 µm in the simulation. As for the pulse duration setting, to simplify the calculation, a representative sample pulse was selected. For a more precise estimation, we considered the influence of the initial pulse splitting in TDFA, statistically analyzed the output pulse from SM1950 fiber, and combined the multiple comparisons of the simulation results with the experimental one, eventually, defined the pulse duration as 0.12 ps. The simulated and the measured SC spectra in 7-m ZBLAN fiber are shown in Fig. 6(a). Other parameters including the pulse peak power, the pulse signal to noise ratio were set as 5.4 kW and 38 dB, respectively. To more precise insight into the pulse evolution process, we optimized the dispersion coefficient βn of this ZBLAN fiber to 10th order in calculation. The ZBLAN fiber loss variation with wavelength was also considered, and the original data related to this fiber was provided by the fiber supplier (France, Le Verre Floure Inc.). The nonlinear coefficient γ of 0.25396 W-1·m-1 was calculated by the Mode Solution Software, and the Raman related parameters used were referenced from the published papers [23,24].
As shown in Fig. 6(b) and (c), the pulse temporal and the spectral evolution in ZBLAN fibers are presented, we can see that the pulse experienced a process of initially stretching, then splitting and eventually generation of multi-pulse in the time domain. In frequency, the pulse bandwidth continuously broadened in the 7 m-long ZBLAN fiber. This is in theory well in accordance with our expectations, since the pump wavelength locates at the anomalous dispersion region of this fiber, and the pulse was initially stretched temporally and has a balance with nonlinear chirp induced by the SPM effect, which is known as soliton formation. The formed high-order solitons then continue to split due to the interaction of pulses with noise, high-order dispersion, and high-order nonlinear effects in fiber, which is known as the soliton fission effect, this result is also supported by many recently reported works [25–28]. In this process, the combined complex nonlinear effects interplay with dispersion, which results in the nonstop spectral broadening.
Therefore, a new problem arises, that is, how to precisely simulate the SC spectral evolution in the next stage ChG fiber. The initial input pulse setting is traditionally assumed single, however the solitons in ZBLAN fiber break up into thousands of small pulses, the system is cascaded, it’s difficult to process so many input pulses simultaneously in program.
4.2 Spectral evolution in As2S3 fiber
To solve the above-mentioned problem, we try to establish a multi-pulse pump model by using the statistical way to analyze the pulse duration distribution firstly, and then we will use a Pearson product-moment correlation coefficient method (PMCCM) to pick the representative pulses in each pulse duration and intensity range out. The selected pulses will be set as the new input of the ChG fiber.
The pulse duration distribution was counted as shown in Fig. 7, most of the pulse durations distribute in-between 0 and 300 fs, a very small portion above 300 fs. Based on these data, we can then divide the pulses into four groups by duration, which are 0 to 50 fs, 50 to 150 fs, 150 to 275 fs and 275 to 400 fs, respectively.
In the pulse picking process, we mainly consider the characteristic parameters of pulse duration and intensity, since these quantities affect the pulse spectral evolution the most. Considering the precision and complexity of the numerical calculation, the PMCCM was adopted to select the four representative output pulses with different pulse duration and pulse intensity mathematically. The PMCCM is defined as
where ρxy is the correlation coefficient, when 0.95<|ρxy|<1, it means that the selected samples (pulse duration and pulse intensity) are highly correlated. X and Y are the pulse duration and pulse peak power of the sample, respectively. Xi represents the ith pulse duration, and Yj represents the corresponding jth pulse intensity. Based on the previous statistic results, four appropriate sets of samples with durations of 10 fs, 120 fs, 274 fs and 383 fs, and corresponding peak powers of 2.1 kW, 0.56 kW, 0.78 kW and 1.2 kW were selected, the detailed parameters are shown in Table 2.
In combination with the selected pulses and multi-pulse pump model that we have established. A simple flowchart for showing the overview of the simulation of SC generation in the cascade and the multi-pulse pumping system is given in Fig. 8.
As for some other key parameters of pulses and fibers setting in the calculation, the As2S3 fiber dispersion was optimized to the 10th order, and the calculated nonlinear coefficient γ is set as 0.44741 W-1·m-1, respectively. The original data of As2S3 fiber loss was provided by the supplier (America, IR-flex Inc.). The Raman response function is given by
In both simulation and experiment, the spectral long-wavelength edges are all extended to 8 µm. However, there are many dips in the measured spectrum, the dips are presented in the spectrum at 5.1 µm and 7.5, which are rightly the high attenuation bands of As2S3 fiber.
For a deep insight into the impact of the initial pulse parameters on the output spectrum, we explored the output SC under different pump mechanisms, including the single pulse, random multi-pulse and selected multi-pulse pump conditions.
In performing this simulation, to control the variables, their central wavelengths were set at 3.2 μm and the fiber length was set as 4 m, other detailed parameters on pulses are listed in Table 3. Figure 10(a) shows the output spectrum in the single-pulse pump condition with a peak power of 5 kW and a pulse duration of 300 fs. Since the pump pulse central wavelength was set at 3.2 μm (this is the central wavelength of spectrum from ZBLAN fiber), which is in the positive dispersion region of the As2S3 fiber. Femtosecond unchirped pulse transmission in this dispersion mechanism, the dominated nonlinear effect for spectrum broadening is SPM, which results in the spectrum was broadened symmetrically with a longer wavelength edge of 3.95 μm. Figure 10(b) shows the output SC spectrum in multi-pulse pumping conditions. The four randomly selected pulse durations are 50 fs, 120 fs, 200 fs and 320 fs, with corresponding peak powers of 1.2 kW, 0.56 kW, 2.4 kW and 0.7 kW, respectively. In this figure, it can be found that the SC spectrum has experienced a rapid broadening process because of the combined multiple complex nonlinear effects, including the SPM effect, the stimulated Raman scattering effect, the wave-mixing effects and so on. Additionally, more soliton pulses are perturbed by higher order dispersion resulted in the soliton fission effect and more complex interplay in pulses happened when the wavelength extended beyond 6 μm, this dominates the spectral long-wavelength edge broadening process.
Figure 10(c) shows the output spectra from the As2S3 fiber by adopting the PMCCM in representative pulses selection. The four selected pulse durations were 10 fs, 120 fs, 274 fs and 383 fs, with corresponding peak powers of 2.1 kW, 0.56 kW, 0.78 kW and 1.2 kW, respectively. It is worth mentioning that in the determine of pulse duration and energy, the statistical results on the distribution of these parameters were fully considered. We can see that with the increase of the As2S3 fiber length, more and more soliton energy transfer towards the negative dispersion region (6-8 μm) of the As2S3 fiber. Eventually, the SC spectrum is broadened to 8 μm in the 4 m-long As2S3 fiber, and the spectrum covering all the 2-8 μm in mid-infrared region.
The above comparison results show that with the changes of the pump pulse modality, the output spectrum and spectral evolution maps are of great difference with each other. The key factor that gives rise to the differences between single-pulse pumped and multi-pulse pumped SC generation is the interactions among pulses in multi-pulse transmission condition. This makes the nonlinear process very different from each other.
In summary, we have demonstrated the feasibility in the realization of the high-power (730 mW) SC generation with spectrum covering 2-8 μm in an As2S3 fiber-based all-fiber structured nonlinear system experimentally and theoretically. In this process, we found that the quality of seed laser, the way of coupling, the precision of heat management, and the skills in coupling point encapsulation have a noticeable impact on the SC spectral long-wavelength extension and energy distribution of different spectral components. In addition, in multi-pulse pump conditions, the pulse spectral evolution in fibers is always challenging in simulation, especially in a cascading nonlinear system. To solve this problem, firstly, we analyzed the pulse duration distribution in a statistical way, and then used the PMCCM to pick four representative pulses out. In combination with the building of a multi-pulse pump model and some programmatic work, we have successfully achieved the simulated SC spectrum in multi-pulse pump conditions, which is in good agreement with the experimental one, even in some details. To verify the necessity and importance of this work, we also did some supplementary work, including the simulation of the evolution and output of the SC using single and multiple pulses as pump lasers, respectively. The large differences among these results further verified the availability of the PMCCM adopted in this work. The above-mentioned works are all reported for the first time, to the best of our knowledge. Hopefully, it can be helpful to researchers working in this field.
National Natural Science Foundation of China(NSFC) (61627815, 61905126, 62090064, 61935006); Natural Science Foundation of Zhejiang Province of China (LQ21F050005), K. C. Wong Magna Fund in Ningbo University.
The authors declare no conflicts of interest.
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.
1. M. F. S. Ferreira, E. Castro-Camus, D. J. Ottaway, J. M. Lopez-Higuera, X. Feng, W. Jin, Y. Jeong, N. Picque, L. Tong, B. M. Reinhard, P. M. Pellegrino, A. Mendez, M. Diem, F. Vollmer, and Q. Quan, “Roadmap on optical sensors,” J. Opt. 19(8), 083001 (2017). [CrossRef]
2. K. Eslami Jahromi, Q. Pan, A. Khodabakhsh, C. Sikkens, P. Assman, S. M. Cristescu, P. M. Moselund, M. Janssens, B. E. Verlinden, and F. J. M. Harren, “A Broadband Mid-Infrared Trace Gas Sensor Using Supercontinuum Light Source: Applications for Real-Time Quality Control for Fruit Storage,” Sensors 19(10), 2334 (2019). [CrossRef]
3. S. Dupont, C. Petersen, J. Thogersen, C. Agger, O. Bang, and S. R. Keiding, “IR microscopy utilizing intense supercontinuum light source,” Opt. Express 20(5), 4887–4892 (2012). [CrossRef]
4. H. Yang, X. Bu, Y. Cao, and Y. Song, “A methane telemetry sensor based on near-infrared laser absorption spectroscopy,” Infrared Physics & Technology 114, 103670 (2021). [CrossRef]
5. K. Eslami Jahromi, M. Nematollahi, Q. Pan, M. A. Abbas, S. M. Cristescu, F. J. M. Harren, and A. Khodabakhsh, “Sensitive multi-species trace gas sensor based on a high repetition rate mid-infrared supercontinuum source,” Opt. Express 28(18), 26091–26101 (2020). [CrossRef]
6. V. T. Hoang, R. Kasztelanic, A. Filipkowski, M. Klimczak, D. Pysz, G. Stepniewski, K. D. Xuan, and R. Buczynski, “Photonic Crystal Fiber Infiltrated with Carbon Tetrachloride for Supercontinuum Generation,” Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO Europe and EQEC), (2019).
7. K Jiao, J. Yao, X. Wang, X Wang, Z Zhao, B Zhang, N Si, J Liu, X Shen, P Zhang, S Dai, Q Nie, and R Wang, “1.2–15.2 μm supercontinuum generation in a low-loss chalcohalide fiber pumped at a deep anomalous-dispersion region,” Opt. Lett. 44(22), 5545–5548 (2019). [CrossRef]
8. O. Novak, P. R. Krogen, T. Kroh, T. Mocek, F. X. Kartner, and K. H. Hong, “Femtosecond 8.5 μm source based on intrapulse difference-frequency generation of 2.1 μm pulses,” Opt. Lett. 43(6), 1335–1338 (2018). [CrossRef]
9. Q. Wang, J. Zhang, A. Kessel, N. Nagl, V. Pervak, O. Pronin, and K. F. Mak, “Broadband mid-infrared coverage (2-17 μm) with few-cycle pulses via cascaded parametric processes,” Opt. Lett. 44(10), 2566–2569 (2019). [CrossRef]
10. R. R. Gattass, L. Brandon Shaw, V. Q. Nguyen, P. C. Pureza, I. D. Aggarwal, and J. S. Sanghera, “All-fiber chalcogenide-based mid-infrared supercontinuum source,” Opt. Fiber Technol. 18(5), 345–348 (2012). [CrossRef]
11. M. Zhang, L. Li, T. Li, F. Wang, K. Tian, H. Tao, X. Feng, A. Yang, and Z. Yang, “Mid-infrared supercontinuum generation in chalcogenide fibers with high laser damage threshold,” Opt. Express 27(20), 29287–29296 (2019). [CrossRef]
12. T. Cheng, K. Nagasaka, T. H. Tuan, X. Xue, M. Matsumoto, H. Tezuka, T. Suzuki, and Y. Ohishi, “Mid-infrared supercontinuum generation spanning 2.0 to 15.1 μm in a chalcogenide step-index fiber,” Opt. Lett. 41(9), 2117–2120 (2016). [CrossRef]
13. C. R. Petersen, P. M. Moselund, C. Petersen, U. Moller, and O. Bang, “Spectral-temporal composition matters when cascading supercontinua into the mid-infrared,” Opt. Express 24(2), 749–758 (2016). [CrossRef]
14. K. Yin, B. Zhang, J. Yao, Z. Cai, G. Liu, and J. Hou, “Toward High-Power All-Fiber C2–C2 μm Supercontinuum Generation in Chalcogenide Step-Index Fiber,” J. Lightwave Technol. 35(20), 4535–4539 (2017). [CrossRef]
15. F. Theberge, N. Berube, S. Poulain, S. Cozic, S. Chatigny, L. R. Robichaud, L. P. Pleau, M. Bernier, and R. Vallee, “Infrared supercontinuum generated in concatenated InF3 and As2Se3 fibers,” Opt. Express 26(11), 13952–13960 (2018). [CrossRef]
16. R. A. Martinez, G. Plant, K. Guo, B. Janiszewski, M. J. Freeman, R. L. Maynard, M. N. Islam, F. L. Terry, O. Alvarez, F. Chenard, R. Bedford, R. Gibson, and A. I. Ifarraguerri, “Mid-infrared supercontinuum generation from 1.6 to >11 µm using concatenated step-index fluoride and chalcogenide fibers,” Opt. Lett. 43(2), 296–299 (2018). [CrossRef]
17. L. R. Robichaud, S. Duval, L. P. Pleau, V. Fortin, S. T. Bah, S. Chatigny, R. Vallee, and M. Bernier, “High-power supercontinuum generation in the mid-infrared pumped by a soliton self-frequency shifted source,” Opt. Express 28(1), 107–115 (2020). [CrossRef]
18. G. Woyessa, K. Kwarkye, M. K. Dasa, C. R. Petersen, R. Sidharthan, S. Chen, S. Yoo, and O. Bang, “Power stable 1.5-10.5 µm cascaded mid-infrared supercontinuum laser without thulium amplifier,” Opt. Lett. 46(5), 1129–1132 (2021). [CrossRef]
19. B. Yan, T. Huang, W. Zhang, J. Wang, L. Yang, P. Yang, K. Xia, S. Bai, R. Zhao, D. Wu, Y. Liu, X. Li, S. Dai, and Q. Nie, “Generation of watt-level supercontinuum covering 2-6.5 µm in an all-fiber structured infrared nonlinear transmission system,” Opt. Express 29(3), 4048–4057 (2021). [CrossRef]
20. J. Swiderski and P. Grzes, “High-power mid-IR supercontinuum generation in fluoroindate and arsenic sulfide fibers pumped by a broadband 1.9–2.7 μm all-fiber laser source,” Opt. Laser Technol. 141, 107178 (2021). [CrossRef]
21. K. Xia, L. Yang, B. Yan, J. Liu, X. Li, R. Zhao, P. Yang, S. Dai, and Q. Nie, “Watt-level ultra-flattened mid-infrared supercontinuum with high power stability generation in an all-fiber structured Tm-doped fiber amplifier pumped ZBLAN single-mode fiber,” Opt. Laser Technol. 127, 106204 (2020). [CrossRef]
22. K. T. Mori and H., “Flatly broadened supercontinuum spectrum generated in a dispersion decreasing fibre with convex dispersion profile,” Electron. Lett. 33(21), 1806–1808 (1997). [CrossRef]
23. C. P. Christian Agger, Sune Dupont, Henrik Steffensen, Jens Kristian Lyngsø, Carsten L. Thomsen, Jan Thøgersen, Søren R. Keiding, and Ole Bang, “Supercontinuum generation in ZBLAN fibers—detailed comparison between measurement and simulation,” J. Opt. Soc. Am. B 29(4), 635–645 (2012). [CrossRef]
24. G. P. Agrawal, “Nonlinear fiber optics: its history and recent progress [Invited],” J. Opt. Soc. Am. B 28(12), A1–A10 (2011). [CrossRef]
25. Z. Li, Z. Jia, C. Yao, Z. Zhao, N. Li, M. Hu, Y. Ohishi, W. Qin, and G. Qin, “22.7 W mid-infrared supercontinuum generation in fluorotellurite fibers,” Opt. Lett. 45(7), 1882–1885 (2020). [CrossRef]
26. J. Lai, J. Yuan, Y. Cheng, C. Mei, X. Zhou, Q. Wu, B. Yan, K. Wang, K. Long, C. Yu, and X. Sang, “Dispersion-engineered T-type germanium waveguide for mid-infrared supercontinuum and frequency comb generations in all-normal dispersion region,” OSA Continuum 3(9), 2320–2331 (2020). [CrossRef]
27. K. Yin, R. Zhu, B. Zhang, T. Jiang, S. Chen, and J. Hou, “Ultrahigh-brightness, spectrally-flat, short-wave infrared supercontinuum source for long-range atmospheric applications,” Opt. Express 24(18), 20010–20020 (2016). [CrossRef]
28. C. Yao, Z. Jia, Z. Li, S. Jia, Z. Zhao, L. Zhang, Y. Feng, G. Qin, Y. Ohishi, and W. Qin, “High-power mid-infrared supercontinuum laser source using fluorotellurite fiber,” Optica 5(10), 1264–1270 (2018). [CrossRef]
29. A. Jin, . Wang, B. Hou, Z. Zhang, and Jiang, “Mid-infrared supercontinuum generation in arsenic trisulfide microstructured optical fibers,” Proc.SPIE 8307, 83070 (2011). [CrossRef]