Spectral Broadening of Chirped Laser Pulse Caused by Four-Wave Mixing in BaWO4 Crystals
Round 1
Reviewer 1 Report (Previous Reviewer 5)
The authors replied satisfactory to most of the comments and questions and the manuscript can now be published after minor corrections, please see below the particular comments.
1. Page 2 lines 63-67: "The laser pulse was directed through a lens with the focal length of 1 m into a BWO crystal of 10 mm length. The BWO crystal was located in front of the focus of the laser beam at a distance slightly shifted from a position, where crystal optical damage appeared (the distance of 85 cm from the focusing lens). To enhance the spectral broadening, the second BWO crystal sample of 15 mm length was installed before the first BWO sample at the distance of 70 cm from the focusing lens."
Thus, according to this setup description, the _first_ crystal is operating at higher intensity. However, page 3 lines 105-106 state that
"the radiation intensity at the entrance of the first and second crystals was 0.7 GW/cm2 and 2.1 GW/cm2, respectively"
Please make the definition of the first and the second crystals consistent and use it through the entire text.
2. Page 5 line 162: "200 ps is significantly longer than the optical cycle (~10 fs)". The optical cycle is ~2.5 fs in this case.
3. Page 2, lines 55-57: "Since the seed and laser pulses were spatially and temporally coupled, the relation between their energy was not affected by an attenuator." I suggest to re-word slightly to "Since the seed and laser pulses were spatially and temporally coupled, their energy ratio was not affected by the attenuator."
4. Reply R11: "We agree that this statement has to be checked out. Therefore, it is removed from the paper." :) Removing possible hints of other physical effects under similar conditions was not my intended purpose. I suggest to return the original sentence, at least, so that potential readers can understand that other effects may take place in similar parameter ranges.
Author Response
The authors replied satisfactory to most of the comments and questions and the manuscript can now be published after minor corrections, please see below the particular comments.
C1. Page 2 lines 63-67: "The laser pulse was directed through a lens with the focal length of 1 m into a BWO crystal of 10 mm length. The BWO crystal was located in front of the focus of the laser beam at a distance slightly shifted from a position, where crystal optical damage appeared (the distance of 85 cm from the focusing lens). To enhance the spectral broadening, the second BWO crystal sample of 15 mm length was installed before the first BWO sample at the distance of 70 cm from the focusing lens."
Thus, according to this setup description, the _first_ crystal is operating at higher intensity. However, page 3 lines 105-106 state that "the radiation intensity at the entrance of the first and second crystals was 0.7 GW/cm2 and 2.1 GW/cm2, respectively"
Please make the definition of the first and the second crystals consistent and use it through the entire text.
R1. The definition of BWO crystal samples (BWO_1 and BWO_2) is introduced into the text as well as in the Fig. 1. The mismatch between sentences indicated by the Reviewer is corrected.
C2. Page 5 line 162: "200 ps is significantly longer than the optical cycle (~10 fs)". The optical cycle is ~2.5 fs in this case.
R2. The mistake is corrected.
C3. Page 2, lines 55-57: "Since the seed and laser pulses were spatially and temporally coupled, the relation between their energy was not affected by an attenuator." I suggest to re-word slightly to "Since the seed and laser pulses were spatially and temporally coupled, their energy ratio was not affected by the attenuator.".
R3. The sentence is re-worded to the form suggested by the Reviewer.
C4. Reply R11: "We agree that this statement has to be checked out. Therefore, it is removed from the paper." :) Removing possible hints of other physical effects under similar conditions was not my intended purpose. I suggest to return the original sentence, at least, so that potential readers can understand that other effects may take place in similar parameter ranges.
R4. The sentence is added as the last sentence of the Conclusions: “Also we would note that similar spectral broadening of chirped laser pulse in BaWO4 crystal can appear without external broadband seed [6]. In this case a seed could be spectral components of the main laser pulse scattered from optical elements or had other nature, which will be studied in our continue work.”
Reviewer 2 Report (Previous Reviewer 4)
I am glad that the authors have seriously considered all the suggestions made in the first review. Their revised manuscript is now well suited for publication.
Author Response
We are glad that the Reviewer is satisfied by the improved manuscript and appreciate him for the positive decision.
Reviewer 3 Report (Previous Reviewer 3)
The goal of the paper is to demonstrate the spectral broadening in crystals based on the four wave mixing process. In my first review I mentioned three points that should be clarified in order to prove this statement.
In the response to point 1, the authors added two measurement points in Fig. 2b. These demonstrate the saturation of the spectral broadening at a similar value as calculated for the phase-matching condition in the four wave mixing process. The points 2 and 3 are not really clarified. However, in my opinion, the answer to point 1 may be considered as a strong argument for their statement, even if it is not adequately sustained by additional points.
Author Response
We are glad that the Reviewer is satisfied by the improved manuscript and appreciate him for the positive decision.
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
Dear Authors, Dear Editor,
The manuscript presents some research related to spectral broadening due to four wave mixing process.
Unfortunately, the scientific discuss is not convinced. FWM mixing should surely arise for such long pulse (according to a phase matching) but the simple demonstration is not detailed. Indeed, the numerical analysis are done with strong assumptions (that are not stated) in the two cases related to SPM and FWM. Therefore, the comparison with this simulation is not sufficient to make a clear conclusion. For example, the propagation effect, pump depletion, other nonlinear effects are not included.
Other points are raised below
-I did not find where IL is defined (although we can guess the meaning).
-The comparison of the two spectra (in Fig2) is difficult. One spectrum is not normalized.
-It is not explain why the long seed comes directly from the laser.
-I found unfortunate that the quality of all the figures are not good.
-As a minor comments, there is few typos in the text.
In conclusion, the work could be interesting but I did not find the comments/results convincing to reach the conclusion. More details can provide some arguments
Best regards
Reviewer 2 Report
The authors present an experimental study of the spectral broadening of a chirped lase pulse in BaWO4 crystal. While the explanation of the exclusion of the SPM is sound, I found the argument of the FWM not complete. The manuscript reports that the phase matching condition support 25nm of bandwidth as it was observed experimentally. However, on fig. 2b the bandwidth increases almost linearly with the pump energy, so the agreement it is only on an arbitrary point. To prove that the broadening is due by FWM a better model should be presented, able to explain the behaviour of the bandwidth with the pump energy as in fig. 2a. I also found the explanation of the influence of the seed pulse in the process not clearly explained.
Reviewer 3 Report
The comments are enclosed in the uploaded file.
Comments for author File: 
Comments.pdf
Reviewer 4 Report
Dear Editor,
The manuscript entitled “Spectral broadening of chirped laser pulse by four-wave amplification in BaWO4 crystal” is a study on the effect of spectral broadening when using intense chirped laser pulses on non-linear crystals. The authors claim that among the various non-linear effects that could justify their measured broadening four wave mixing (FWM) is the best candidate. Their justification seems convincing and thus their work deserves publication in some form, but certain amendments should first be answered and included in the revised manuscript.
1. First of all the English are quite poor in certain places and need to be improved. Perhaps the authors should seek help from fluent English-speaking person. This would improve the image of the paper significantly.
2. Figures are at very low resolution, almost unreadable. They should be replaced by ones with much higher resolution.
3. Why the authors had to use two BaWO4 crystals and not one. Did they try to see the outcome from each crystal? And if yes how this affected their study in general? This should be commented in the revised manuscript.
4. How the initial 90 fs pulse was stretched to 200 ps and how were the pulses duration measured in both cases? Same for seed pulse.
5. The calculation of PM is not clear. It seems to be a variable of DE but in the figure it is given as a function of lambda. How does the variable DE is treated in the PM calculation? For example, obviously a choice of a broad enough DE would have covered all the bandwidth of the laser.
6. The model they apply to estimate the FWM gain has many assumptions. However, the result is very close to the measurement. Should this be alarming? Is it a coincidence? I mean that the authors should somehow estimate the effect and validity of their assumptions for this system to justify their result.
Reviewer 5 Report
The authors present results of an experiment where a stretched (200 ps) Ti:S laser beam was spectrally broadened when passing through two BaWO4 crystals in the presence of a low-power, 10-ns-long, broadband seed pulse. The authors analyzed SPM (Self Phase Modulation), which is a typical cause of broadening, and concluded that under their conditions this was not the main broadening reason. They also analyzed FWM (Four Wave Mixing) and it appeared that the phase matching bandwidth, 25 nm, was consisted with the broadened spectrum width at the maximum pumping conditions (6 mJ). Also, the calculated gain of the FWM process approximately corresponded to the observed gain in the experiment.
Indeed, the authors interpretation is quite plausible. However, the present version lacks experimental details and direct comparisons, when the theory prediction and experimental data are shown on the same figure. Further, the authors write that "Also we would note that similar spectral broadening of chirped laser pulse in BaWO4 crystal broadening can appear without external broadband seed." Thus, at present, I cannot exclude other possibilities, such as higher-than-expected intensity (there are many possible reasons for it, for example, smaller-than-expected beam spot, or hot spots in the near field profile, or spikes in the temporal shape), or nonlinear effects in unexpected places – such as in the air close to the focus, or in ND filters, or in the spectrometer... Such possibilities can be ruled out by a more careful description of the setup, such as specifying the focus position, beam attenuation after the interaction region, etc. Also, the FWM phase matching bandwidth is ~ 25 nm; thus, I would expect some broadening saturation when the pump energy is high, and yet I cannot see any saturation in the experimental data (Fig. 2b).
1. Setup: please provide the pump and seed beam diameters before the f = 1 m lens and their near-field mode shapes (Gaussian, flat-top, or something else). Did the near field profiles contain hot spots? Were the beams collimated? If not, provide their divergences.
2. Setup: "The BWO crystals were located before the focus of the laser beam". Please provide exact locations of the crystals.
3. Setup and Fig. 1: please describe position of the focus and show it on Fig. 1. In particular, please describe if the focus was located before or inside the spectrometer. Please provide intensity in the focus and describe if nonlinear effects could happen in the air or in the spectrometer components such as collection lens, ND filters, etc.
4. Fig. 2a: the curve 1 should also be normalized so that its peak corresponds to P = 1 arb. units.
5. Fig. 2b caption: please provide seed pulse energy as well: was it constant? Or proportional to the pump pulse energy?
6. Fig. 2b: please add theoretical curves of the pulse bandwidths due to the SPM and FWM processes. Simplified estimates will be Ok for that.
7. Results: Please provide the spectrum at the exit of crystal #1. Does it support the conclusions?
8. Results: Please provide the spectrum after both crystals in the absence of the seed pulse. If the laser is unable to generate the pump without the seed, there is a possible solution which is a band-pass filter transmitting the pump pulse only, or an IR-pass filter with the cut-off wavelength of ~740 nm.
9. Eq (1): please comment on the pump pulse intensity at the exits of the crystals #1 and #2: was it sufficiently constant during propagation in each crystal so that a product I(input)*L is adequate? Is it not necessary to integrate I(L)*dL instead?
10. Please provide data for broadening at higher IL, to see if the bandwidth saturates, or at least, starts to increase slower, when the FWM phase matching bandwidth, 25 nm, is exceeded. If the laser cannot provide > 6 mJ, there is a simple solution of shifting the crystals closer to the focus, and taking data at different pump energies – that would give a second experimental figure similar to Fig. 2b.
11. The authors write at the bottom of page 4 that "Also we would note that similar spectral broadening of chirped laser pulse in BaWO4 crystal broadening can appear without external broadband seed [6]." Please provide more details about this, such as why the authors think that the case under consideration here is the amplification of the seed while in another case [6] it is not. Without such discussion, the main conclusion cannot be justified.
