Mid-Infrared Ultraflat Broadband Supercontinuum Generation with 10 dB Bandwidth of 2340 nm in a Tapered Fluorotellurite Fiber

Comments 1: The Introduction describes many works on the generation of a supercontinuum in the middle IR in fluorotellurite fibers but it is not said whether Raman solitons were used in this process. If this is the case, is the novelty of the work under consideration precisely the use of Raman solitons to generate a supercontinuum? What is the main novelty of the proposed work compared to previous ones?

Response 1: Thank you for pointing this out. We agree with this comment. The pump light sources used in many of the works described in the introduction are 2 μm light sources and broad-spectrum light sources. Therefore, we have added relevant descriptions in the revised manuscript. Page 2, lines 59-62. “As the 2 μm light source or broad-spectrum light source used by the above researchers to pump the fluorotellurite fiber, the energy of the pump pulse is mainly concentrated at ~2 μm, resulting in low energy proportion at the long wavelength of the SC spectrum.” The pump source used in the last work described in the introduction is the Raman soliton source, which can significantly broaden the spectrum. The relevant description is on page 2, lines 63-65. “The broadband and flat SC are caused by the excitation of 2180 nm as well as 2350 nm dual Raman soliton lasers.” We also used a Raman soliton light source in the experiment.

However, due to the limitation of long-wavelength absorption loss of fluorotellurite fiber, the existing work can not achieve further spectral broadening. We have added relevant descriptions in the revised manuscript. Page 2, lines 65-67. “Although the SC spectrum has been effectively extended by improving the light source, due to the long-wavelength absorption loss of the fluorotellurite fiber, the spectrum is limited to within ~4 μm.” Our main novelty of the proposed work compared to previous ones is to use large core diameter fluorotellurite fiber with a tapered end to enhance the nonlinear effect and further broaden the spectrum. The relevant description is on page 2, lines 69-73. “In this paper, we experimentally demonstrate a MIR ultraflat broadband SC with a long-wavelength edge beyond 4700 nm, the 10 dB bandwidth is about 2340 nm, generated in tapered fluorotellurite fibers pumped by a Raman soliton source. By introducing a tapered fiber part at the end of the LMA fluorotellurite fiber, the dispersion is regulated and the nonlinear effect is enhanced.”

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Comments 2: What does the symbol (15 dB/div) mean in the axis caption in Fig. 4a? What is a div?

Response 2: Thank you for your valuable comment. The symbol (15dB/div) means to 15dB difference between each grid of every spectrum intensity in Fig. 4(a). We have added markers of 10dB difference in Fig.4(a).

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Comments 3: What is the reason for the downward deflection in values of power percentage in Fig. 4c at pumping capacities > 12 W?

Response 3: Thank you for your valuable comment. When testing the spectrum, the rotation angle of the filter will cause a certain error. We retested the spectrum after tapered fluorotellurite (TBY) fiber, and the results are shown in Fig. 4 in the revised manuscript. The propagation loss spectrum of the TBY glass fiber is shown in Res.Fig.1 below. When the wavelength exceeds 4 μm, the loss of the TBY fiber increases exponentially with the wavelength. In the case of pumping capacities > 12 W, with the increase of pump power, the loss at the long-wavelength edge of the spectrum begins to increase sharply. This caused the downward deflection in values of power percentage in Fig. 4c at pumping capacities > 12 W. We have added relevant descriptions in the revised manuscript. Page 5, lines 173-176. “When the pump power exceeds 12 W, the decrease of the >3 μm power percentage in the SC spectrum is due to the increased fiber loss as the spectrum extends towards longer wavelengths, resulting in energy loss in the long wavelength portion. Corresponding to this process is a slower increase for >3 μm power of SC spectrum.”

Res. Fig. 1 Loss spectrum of the TeO₂-BaF₂-Y₂O₃ (TBY) glass.

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Comments 1: The flatness of the generated supercontinuum should be quantified. The coherence performance should also be evaluated, either in experiments or in simulations.

Response 1: Thank you for pointing this out. As you mentioned, the flatness of the generated supercontinuum is very important. In this paper, we evaluate the spectral range using a 10dB bandwidth, used to represent the flatness of the spectrum. The 10 dB bandwidth of the generated SC light was about 2340 nm in the experiment, excluding the pump light, and the corresponding spectral range was from 1880 to 4220 nm. The described spectral range is all within the 10dB bandwidth.

Due to the lack of corresponding evaluation instruments, coherence performance cannot be assessed in experiments. We have added the simulation of the temporal evolution of SC generation in LMA silica fiber and tapered TBY fiber at a 20 W pump power, as shown in Fig.8 in the revised manuscript. In addition, we have added relevant descriptions in the revised manuscript on page 8, lines 248-251. “The simulated spectral and temporal evolution process of the pulse in the LMA silica fiber as well as in the LMA TBY fiber are shown in Fig.7 and Fig.8, respectively. For the pump pulse propagation inside the silica fiber segment from 0 to 0.05 m, the spectral broadening was caused by self-phase modulation (SPM).” Due to various nonlinear effects, laser pulses undergo high-order soliton splitting and other processes during propagation in TBY fibers, resulting in poor temporal coherence performance.

Fig.8. Simulated temporal evolution of SC generation in LMA silica fiber and tapered TBY fiber at a 20 W pump power.

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Comments 2: The conversion efficiency of 75% is impressive. The methodology for calculating efficiency should be clarified. It is also recommended to include a table comparing supercontinuum performance, including output power, flatness, conversion efficiency, etc.

Response 2: Thank you for your valuable comment. We agree with your suggestion and have added the table.1 comparing supercontinuum performance in the revised manuscript on page 7. For the conversion efficiency of 75%, we add a supplement “(1.38W to 1.04W)” after “75%”. The calculation method for conversion efficiency is the ratio of the tapered TBY fiber output power in Fig.4(b) to the LMA silica fiber output power in Fig.3(b).

Table 1. Parameters of TBY fiber-based SC laser sources.

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Comments 3: The comparison in Fig.5 is not convincing. The bandwidth is slightly wider, but the output power is quite weak.

Response 3: Thank you for your valuable comment. As you mentioned, the bandwidth is slightly wider, but the output power is quite weak in our results. This is due to the low repetition rate (980 kHz) of the Raman soliton light source we are using. The light source used in reference [25] has a high repetition rate (16.64 MHz). At this stage, we only verified the feasibility of broadening and flattening the spectrum by tapering the LMA TBY fiber. And this paper proves that the method is effective. In the future, we will optimize the pump light source and increase the repetition frequency of the pump source to further increase the power of the SC spectrum.

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Comments 1: Lines 41-42: The manuscript states that fluoride fibers have low nonlinearity. Whether the nonlinearity of a material is low or high depends on the reference material it is compared to. I suggest removing this sentence unless fluoride glasses are explicitly compared to other glasses in terms of their nonlinearity.

Response 1: Thank you very much for your valuable suggestions! We agree with this comment and remove this sentence from lines 41-43. “Additionally, fluoride fiber materials have low nonlinearity, necessitating a smaller core size and longer length fiber only to broaden the spectrum effectively.”

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Comments 2: Line 98: The phrase "Fig. 2 shows an experimental setup..." should be revised by replacing "an" with "the".

Response 2: Thank you for your valuable comment. We agree with your suggestion and revised the error by replacing "an" with "the" in the revised manuscript. Line 104.

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Comments 3: Line 104: The acronym CFBG should be defined upon first use.

Response 3: Thank you for your valuable comment. We agree with your suggestion. We have defined “chirped fiber Bragg grating (CFBG)” in the revised manuscript. Line 110.

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Comments 4: Line 154: "mw" should be corrected to "mW".

Response 4: Thank you for your valuable comment. We agree with your suggestion and revised the error by replacing "mw" with "mW" in the revised manuscript. Line 148.

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Comments 5: Section 3: I personally find the expression "theoretical simulation" or "theoretically simulated" somewhat misleading, as theory and simulations are distinct concepts. I suggest removing the words "theoretical" and "theoretically" throughout this section.

Response 5: Thank you for your valuable comment. We agree with your suggestion and removed the words "theoretical" and "theoretically" throughout this section in the revised manuscript.

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Comments 6: Simulation details: The simulations are performed by solving the GNLSE. This should be described in more detail—what terms are included in the GNLSE? Additionally, I believe it would be useful to cite relevant papers on the use of GNLSE for simulating soliton propagation in LMA fibers. The Authors may consider referencing the works of Wabnitz’s and Wise’s groups.

Response 6: Thank you for your valuable comment. We agree with your suggestion. We have referred to the works of Wabnitz’s and Wise’s groups and provided a more detailed description of the simulations by solving the GNLSE in the revised manuscript. Page 7, lines 217-235. As follows：

              (1)

where A(z,t) is the complex temporal profile, α is the fiber loss, β_n is the dispersion coefficient associated with the Taylor expansion of the propagation constant at the reference frequency, γ is the nonlinear coefficient, and τ_shock is the additional shock time. R(t) is the Raman response function that includes both instantaneous electronic and delayed Raman contributions.

The initial pump pulses possessed a hyperbolic secant field profile:

                                                               (2)

where P₀ and T₀ are the peak power and input pulse width, respectively. The Raman soliton order of the pump pulse was calculated as:

                                                               (3)

The split-step Fourier method was used to solve the GNLSE, and 2¹⁷ time and frequency discretization points and a longitudinal step size <5 µm were used to ensure the accuracy of the numerical simulations.

In our numerical simulation, the pulse propagation is divided into four stages: a 23-cm-long LMA silica fiber, a 0.34-m-long LMA TBY fiber, a 2-cm-long taper region of TBY fiber, and a 4-cm-long small core diameter TBY fiber, which corresponds to the fibers used in the experiment.

We have added relevant descriptions in the revised manuscript. Lines 238-241. “The Raman response function of the silica fiber is described in the paper [32] and the Ra-man response function of the TBY fiber is derived from the Raman gain spectrum of fluorotellurite glass [23].” We have added Fig.8 and the descriptions of the simulation about the temporal evolution process of the pulse in the revised manuscript. Lines 249-252. “The simulated spectral and temporal evolution process of the pulse in the LMA silica fiber as well as in the LMA TBY fiber are shown in Fig.7 and Fig.8, respectively. For the pump pulse propagation inside the silica fiber segment from 0 to 0.05 m, the spectral broadening was caused by self-phase modulation (SPM).” Lines 259-263. “According to Fig.1(c), as the fiber core diameter decreases to 14 μm, above 4.5 μm wave-length is located in the anomalous dispersion region of the fiber. However, in the simulations and experiments, we did not observe the formation of dispersion waves at about 5 μm. This can be explained by the higher transmission loss of TBY fiber at longer wavelengths.” Lines 265-267. “The engineering of the nonlinearity and dispersion of a nonlinear fiber could be a more promising way to further improve the performance of the SC spectrum.”

The references to works of Wabnitz’s and Wise’s groups in the revised manuscript. Reference [30], [31].

“[30]. Eftekhar, M. A.; Lopez-Aviles H.; Wise F. W.; Amezcua-Correa R.; Christodoulides. D. N. General theory and observation of Cherenkov radiation induced by multimode solitons. Communications Physics 2021, 4, 1-7.

[31]. Wright, L. G.; Wabnitz S.; Christodoulides D. N.; Wise F. W. Ultrabroadband dispersive radiation by spatiotemporal oscillation of multimode waves. Physical Review Letters 2015, 115, 223902.”

Fig.8. Simulated temporal evolution of SC generation in LMA silica fiber and tapered TBY fiber at a 20 W pump power.

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Comments 7: Line 180: "KHz" should be corrected to "kHz".

Response 7: Thank you for your valuable comment. We agree with your suggestion and revised the error by replacing "KHz" with "kHz" in the revised manuscript. Line 236.

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