Maximum Operational Fluence Limits for Temporally Shaped Nanosecond Long Pulses

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Review of the manuscript entitled ‘Maximum operational fluency limits for temporally shaped nanosecond long pulses’ (Manuscript ID:  applsci-2905536, Type: Article) presented by Pedro Oliveira and co-authors, to be considered for publication in Applied Sciences.

In this work, the authors explore the combined effect of peak intensity and thermal load on the maximum fluence to operate a laser for any temporal pulse shape. The presented method pushes forward the current state of the art where partial or incomplete assessments of the maximum energy are sometimes used. The work can be reconsidered in Applied Sciences for publication after the following comments are addressed.

Major comments:

 

1.        Introduction: “The maximum fluency at which a laser can operate is closely linked to the laser damage threshold, attributed to various causes [15–20], including local thermal effects and thermally induced stress [18,21,22] driving damage.” Detail more those works referenced in 15-20.

 

2.        What is the origin of Eq. (2)? Is it taken from literature?

 

3.        In Eq. 3, p(t) is normalized to 1. Is that a requirement or an irrelevant condition, provided the normalization of Eq. (4). Would make sense normalizing to unity the temporal integral of p(t)? In this case, is it relevant the amount of signal that can be cropped in the tails of the pulse?

 

4.        In the results, the authors test different pulse shapes. It is surprising that a Gaussian or a sech^2 shape is not tested, while pulse can often be modelled that way. Is there any reason for that? Otherwise, could that case be included?

 

5.        The method is irrespective of the pulse shape but needs to know the pulse shape. Therefore, the work should be completed by the way the authors obtain the pulse shape (in their case, in the ns scale; but also, other appropriate scales can be welcomed). Is just the temporal intensity needed or does the phase play any role, especially for broadband pulses where wavelength-dependent effects may arise? The need of pulse profile knowledge should be more clearly stated in the introduction and along the manuscript.

 

6.        The authors test the effect of 10% noise added to the pulse. But could they try with uncertainty in the pulse duration measurement?

 

7.        What are the limitations of the method in the time scale, for shorter / longer pulses?

 

8.        Their method is a generalization including both effects (peak intensity and thermal load). How is it verified for limit situations in which only one of these effects appear?

 

9.        The authors comment on the influence of longitudinal modes in the abstract. Did they perform any test on it? What about transverse modes? The spatial profile is very relevant in high energy infrastructures so, could the authors discuss deep on the spatiotemporal effects?

 

10.   The pulse profile is relevant, but it can considerably vary along the laser chain. How is it dealt with along their method?

 

11.   In the results, could the authors include a real case with their measured pulse being applied to the proposed method?

Minor comments:

1.        While in the literature both fluence and fluency (the one used by the authors) terms are found, I am more used to find the first one (it is used in the label of Fig. 1; in any case, unify terms).

2.        Line 70: “based on the dimensions of our system, which exceed 100 ps and are thus distant from”. Exceed/exceeds if 100 ps is referred to dimensions/system.

3.        Define what “the impulse response function of the diffusion process” is.

4.        Line 78, “are proportionate to the intensity and diffuse”, instead of proportionate, which can be interpreted as proportional, simply the dependence can be stated as given by Eq. (2).

5.        Line 109, punctuation.

6.        Caption Fig. 2-4, punctuation.

Author Response

We must thank the reviewers for their time and guidance. We have tried to answer all the comments and correct where possible. We will respond to each points one by one:

1. We have tried to detail in more detail the causes of damage on each of these references.
2. Equation 2 is taken from reference 26. Carr et al. The effect of laser pulse shape and duration on 229 the size at which damage sites initiate and the implications to subsequent repair. Opt. Express 230 2011, 19 and especially Carr, C.; Trenholme, J.; Spaeth, M. Effect of temporal pulse shape on optical damage. Applied Physics Letters 2007, 90. To give a context, Carr applied this to a Gaussian profiles and adopts an appropriate green function for these pulses. This work tries to expand it to all the other pulse shapes.
3. Thank you for your comment, and yes normalized to 1 is not important and neither would be any normalization, we have taken this out.
4. Sech^2 and Gaussian pulses are not time limited and hence are outside the scope of this article.
5. The temporal profile is measured by a photodiode (similar to a fast photodiode DET08) these are nanosecond pulses (injected by a single linewidth laser); we would not need a nonlinear process to measure the pulse profile (unlike what happened on femtosecond laser pulses). Some facilities have used streak cameras for higher temporal resolution. However, we opted for photodiodes in order to guarantee linearity. Damage on chirped pulses might not directly translate from a single linewidth laser. Not only does damage vary with wavelength but also diffraction will vary over time, this has actually been used to increase the operational energy on a compressor. https://opg.optica.org/oe/fulltext.cfm?uri=oe-31-20-33753&id=539678
6. We could but since we are operating in the nanosecond regime the pulse duration is well known.
7. This method should hold has long as damage is cumulative, hence, thermal and mechanical effects can be considered, and for shorter pulses where photoionization are guided by peak intensity hence, this would not apply.
8. This is a generalization depends on damage being accumulated in the laser.
9. We are dealing with fluence and the longitudinal mode. The transverse mode is outside the scope of the work. But please note that since this is a nanosecond laser not a femtosecond one we do not expect a significant spatial time coupling. Even so this does not mean that the transverse profile is constant but the Fluence would be the important factor here.
10. This is definitely the next iteration of this work.
11. We have disassemble part of this laser (as part of an upgrade that will take a few years) so we would not be able to do this at this moment. But please note that the shapes chosen closely resembled the ones observed experimentally.

Minor comments:

1. Thank you for your comments we have unified the terms as fluence.
2. My apologies for the imprecision. The minimum pulse duration on this system (that is driven by fast electronics) is 200 ps, there can be no features bellow 100 ps, we have corrected the text to clarify what we meant. Please remember that if we are dealing with avalanche ionization we will not be in a cumulative process but simply in a process that depends on the maximum intensity.
3. We have corrected the text and added a reference for context.
4. Thank you for the comment corrected accordingly.
5. Thank you for your comment, corrected accordingly.
6. Thank you for your comment, corrected accordingly.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript will benefit from minor edition changes that will fix a few small errors and will improve on the article readability.

First the minor errors:
A) line 2 damage.In - space needed.
B) line 12 damage,nanosecond - space needed
C) Equation 7 - please fix the expression by bringing the lim on the height of the = sign and have t->0 as subscript
D) line 108 in Fig.3 for fit function 1 and Fig.4.
I would expect that the intended text was or similar
in Fig.3 for fit function 1 and in Fig.4 for fit function 2.

I would recommend some editions to the text of the article:
A) line 68 after mentioning damage particles even though a citation is present, it would be good to add a sentence very briefly describing the used term of damaged particles.
B) line 69 We justify this assumption based on the dimensions of our system, which exceed 100 ps and are thus distant from avalanche and multi-photon ionization phenomena [23]
Could you clarify which dimension/dimensions of the system exceed 100 ps?
C) line 119
 As anticipated, this temporal profile yields the highest intensity for a given energy, and the pulse length corresponding to the smallest fluency is observed (curve e)).
It will be beneficial if this sentence is rewritten such as the first part concerning the top hat profile joins with the previous sentence and the second part concerning the curve e is its separate statement.
D) line 124
This indicates that significantly shaped pulses necessitate a higher level of precision compared to other shapes.
Please elaborate on the statement by explaining (or giving example) what is meant by higher level of precision.

Comments on the Quality of English Language

Small corrections of the English needed as stated in the Comments for Authors.

Author Response

We must thank the reviewer for his time and guidance. We have tried to answer all the comments and correct where possible. We will respond to each points one by one:

Minor errors:

1. Thank you corrected accordingly.
2. Thank you corrected accordingly.
3. Thank you corrected accordingly.
4. Thank you corrected accordingly.

Editions to the text

1. Thank you I have added another reference and a sentence clarifying it.
2. My apologies, I meant that the minimum pulse duration of our system is 200 ps and the smallest features are on the order of 100 ps, limited by fast electronics. Therefore, we are far from the femtosecond regime where multiphoton ionization prevails and is directly related to peak intensity. If that were the case, then damage would not be cumulative. I have corrected the sentence to reflect this.
3. Thank you we have corrected this.
4. We thank you for your comments. The sentence was poorly justified we replaced it with “This indicates that for most shapes (a to d) the maximum fluence we can operate is not dependent on the fit function used.” Which is supported by the calculations and a comparison between Fig. 3 and 4.

We hope we have responded to everything satisfactory.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

I would like to thank the authors for their effort to clarify their findings and to answer my concerns.