A Strategy for Achieving Smooth Filamentation Cutting of Transparent Materials with Ultrafast Lasers

Round 1

Reviewer 1 Report

This manuscript is an excellent work on how to cut transparent materials via filamentation. The idea is not completely new in the sense that several already published papers indicate the experimental possibility of drilling structures or refractive index changes in the interior of a transparent dielectric material. 

However my decision for accepting this manuscript is based on the fact of the novel and very detailed description of the model they propose and the idea of smooth filamentation that seem to me quite novel and of high potential interest. 

The idea of extended length focusing using the axicon can be of great applicability.

In summary, the manuscript has two fundamental strengths:

One is the idea of smooth and deep filamentation. 

Two, is the very precise and detailed description of the modeling and the realistic parameters.

Therefore the paper can be published in its present form.

 

Author Response

Reviewer 1

Open Review

(x) I would not like to sign my review report
( ) I would like to sign my review report

English language and style

( ) Extensive editing of English language and style required
( ) Moderate English changes required
(x) English language and style are fine/minor spell check required
( ) I don't feel qualified to judge about the English language and style

 

	Yes	Can be improved	Must be improved	Not applicable
Does the introduction provide sufficient background and include all relevant references?	(x)	( )	( )	( )
Is the research design appropriate?	(x)	( )	( )	( )
Are the methods adequately described?	(x)	( )	( )	( )
Are the results clearly presented?	(x)	( )	( )	( )
Are the conclusions supported by the results?	(x)	( )	( )	( )

 

Comments and Suggestions for Authors

This manuscript is an excellent work on how to cut transparent materials via filamentation. The idea is not completely new in the sense that several already published papers indicate the experimental possibility of drilling structures or refractive index changes in the interior of a transparent dielectric material. 

However my decision for accepting this manuscript is based on the fact of the novel and very detailed description of the model they propose and the idea of smooth filamentation that seem to me quite novel and of high potential interest. 

The idea of extended length focusing using the axicon can be of great applicability.

In summary, the manuscript has two fundamental strengths:

One is the idea of smooth and deep filamentation. 

Two, is the very precise and detailed description of the modeling and the realistic parameters.

Therefore the paper can be published in its present form.

 Submission Date 30 December 2020                                     Date of this review 06 Jan 2021 20:01:28

 

Response

Dear Mr/Mrs Reviewer

 

I highly appreciate your positive and kind review of the paper.

 

Please see below my comments to your review:

1.This manuscript is an excellent work on how to cut transparent materials via filamentation. The idea is not completely new in the sense that several already published papers indicate the experimental possibility of drilling structures or refractive index changes in the interior of a transparent dielectric material. 

*The laser filamentation cutting (LFC) considered in this paper is still different from the mentioned processes “of drilling structures or refractive index changes in the interior of a transparent dielectric materials”, as LFC demands an obtaining not a single filament or a drilled hole, but an array of filaments along the track of pulse-periodic laser beam moving in the material. In this case, some new parameters become important - a step of filaments following and a pulse repetition frequency, not considered before, when a single filament is created.

There exist experimental papers on LFC. But we propose a theoretical paper on this subject. The emphasis is to find the conditions for obtaining a practically interesting and useful effect of a so-called “smooth filamentation cutting” and also to find quantitatively corresponding parameters for material and irradiation. Such model for LFC is given for the first time.

2.*I am glad that you have noticed the particularity of the proposed in the paper model of the complex process of LFC: our model predicts quantitatively and adequately the main 4 irradiation parameters completely defining the LFC (energy of the pulse, its duration, step of filaments in the material and pulse repetition rate) and uses for it the realistic material parameters. We tried to construct an adequate quantitative model for LFC, and it is important for this that model relies on realistic input parameters – of material and irradiation.

 

Thank you very much for the time and forces you spent to review this long manuscript!

 

Best regards.

Sincerely.

Vladimir Tokarev

 

Reviewer 2 Report

The authors of this manuscript present an interesting and novel  analytical model of laser filamentation cutting of transparent  materials. The proposed systematic methodology is aimed to predict   the process parameters for achieving high cutting speeds which might be very importnat both from a fundamental point of viewe as well as for targeted applications.  The quality of presentation is high and both the modelling approach and methodology lie within the scope of teh special issue. Therefore, I would recommend the publication of this manuscript in this journal and the special issue. As a minor comment for revision, I suggest the authors prepare and submit a version in which the quality of the illustrations is  better

Author Response

Open Review

(x) I would not like to sign my review report
( ) I would like to sign my review report

English language and style

( ) Extensive editing of English language and style required
( ) Moderate English changes required
(x) English language and style are fine/minor spell check required
( ) I don't feel qualified to judge about the English language and style

 

	Yes	Can be improved	Must be improved	Not applicable
Does the introduction provide sufficient background and include all relevant references?	(x)	( )	( )	( )
Is the research design appropriate?	(x)	( )	( )	( )
Are the methods adequately described?	(x)	( )	( )	( )
Are the results clearly presented?	(x)	( )	( )	( )
Are the conclusions supported by the results?	(x)	( )	( )	( )

 

Comments and Suggestions for Authors

The authors of this manuscript present an interesting and novel analytical model of laser filamentation cutting of transparent  materials. The proposed systematic methodology is aimed to predict   the process parameters for achieving high cutting speeds which might be very importnat both from a fundamental point of viewe as well as for targeted applications.  The quality of presentation is high and both the modelling approach and methodology lie within the scope of teh special issue. Therefore, I would recommend the publication of this manuscript in this journal and the special issue. As a minor comment for revision, I suggest the authors prepare and submit a version in which the quality of the illustrations is better

Submission Date 30 December 2020         Date of this review 11 Jan 2021 10:50:44

 

Dear Mr/Mrs Reviewer

 

Thank you for your positive review of the paper!

 

* As for your comment on the quality of the illustrations, I could say that what you have read is only a manuscript version for review purposes. The resolution and quality of the drawings in such a manuscript may be low. However, the individual files for each Figure submitted to the editorial board are of very high quality. This ensures that the final journal version of the paper (and not this manuscript), when these high-quality drawings are embedded in the final journal version by the editorial staff using professional layout, will necessarily be presented with a much higher quality of illustrations compared to the manuscript.

Best regards.

Sincerely,

Vladimir Tokarev

Reviewer 3 Report

The paper "Strategy for obtaining smooth filamentation cutting transparent materials with ultrafast laser" is an extensive theoretical and practical work. It is well written and suggests a complex, but comprehensive approach for improving laser-based micromachining of transparent media. I recommend the paper for publication after some minor revision regarding the English language. For instance, even the title seems to be incomplete: "Strategy for obtaining smooth filamentation cutting OF transparent materials with ultrafast laser" instead of "Strategy for obtaining smooth filamentation cutting transparent materials with ultrafast laser".

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 4 Report

The manuscript by V.N. Tokarev entitled “Strategy for obtaining smooth filamentation cutting transparent materials with ultrafast laser”, presents a model on cutting of transparent material by filamentation under the action of an ultrafast laser beam. This is a very interesting field of research, and theoretical works as the one here presented are necessary. Nevertheless, the manuscript needs to be amended prior to acceptance. Here are the main aspects to be considered:

 

1. It is difficult to know the degree of novelty of the present paper, since authors seem to have another paper about a model on the same subject, but not available to the public yet: Ref [38] Tokarev VN, Melnikov IV. Elimination of thermal emission losses in laser filamentation cutting transparent materials.(To be published). This paper is cited repeatedly. It is suggested that paper [38] is published previously to acceptance of the present manuscript.
2. In the abstract it is said (line 22): “The model shows good agreement with experiments on sapphire and tempered glass”. Authors devote section 4 to compare the model with the results shown by just two papers:
   1. Reference [19] is a divulgation paper. The results shown in this paper are just to show some examples of possibilities of femtosecond laser, but not in depth information is given. Therefore, please show a more scientific demonstration that corroborates that the model reported in the manuscript is valid.
   2. Reference [5] is an industrial paper from a conference. This is perfectly valid for a conference, but please again show a scientific demonstration that your model fits the real experiments.
3. In line 1169 it is said: “An algorithm for a sequential calculation of the parameters E1, t, s1 and f in the model is shown in Fig. 7”. But Figure 7 does not show the algorithm. Figure 7 just gives the collection of Input parameters and parameters to be calculated. No indication about the algorithm is given in figure 7.
4. Please give the meaning of NA (numerical aperture) and M² (laser beam quality). In Figures 1, 2 M² should be linked to the laser beam instead of the focusing system, since M² is a parameter that depends on the laser beam.

Other comments:

5. Please rewrite the following sentence (lines 212-213) to make it clearer to the potential reader: “This is followed up by a conversion of the plasma energy into the material modification due to the energy dissipation over some cylindrical volume around the filament”.
6. In line 284 it is said: “for a submicron filament radius rf = 0.25-0.5 μm in a glass” Please specify the type/composition of the glass.
7. Please replace the letter и by & throughout the whole manuscript.

Author Response

Dear Mr/Mrs Reviewer

 

I highly appreciate your positive and kind review of the paper.

 

Please see below my comments to your review:

Open Review

(x) I would not like to sign my review report
( ) I would like to sign my review report

English language and style

( ) Extensive editing of English language and style required
(x) Moderate English changes required 

*We have performed an additional editing the text for the correction of English and some misprints (see corrected version with highlighted corrections). 

( ) English language and style are fine/minor spell check required
( ) I don't feel qualified to judge about the English language and style

 

	Yes	Can be improved	Must be improved	Not applicable
Does the introduction provide sufficient background and include all relevant references?	(x)	( )	( )	( )
Is the research design appropriate? *In the main text - additional formulas (10), (11), (14), (47) and (48) are introduced to define more precisely the conditions of modeling; - the misprint in the formula (13), p. 10, is corrected: the missed factor Ktw is introduced; - numbers in Table 1 (p.11) are changed in accordance with corrected formula (13) on p.10.	( )	( )	(x)	( )
Are the methods adequately described? * We have improved the text in the Section “Methods”. Some new references are added for more precise characterization of time scales of different processes participating in the laser filamentation cutting (LFC).	( )	( )	(x)	( )
Are the results clearly presented? -*Fig. 6b (p.28) is corrected – the curve 2 (forgotten previously) is introduced to explain clearer obtaining a smooth or not smooth separation depending on material properties; - In the section “Conclusions” some changes are also introduced for better presentation of results (see the next point below for details).	( )	(x)	( )	( )
Are the conclusions supported by the results? *The Section "Conclusions” has been rewritten to make conclusions clearer and to mention more results obtained.  1) “We have proposed an algorithm for the sequential calculation of E1, τ, s1 and f as a function of these numerous parameters. A comparison of the calculation according to this algorithm with the LFC experiments for sapphire and tempered glass shows a good agreement for the entire set of E1, τ, s1 and f, which indicates the reliability and adequacy of the constructed model. Besides, from this comparison, it is found that the experimental values of VED w both for sapphire and tempered glass satisfy the inequality w < w1. According to the condition (12) obtained, it corresponds to the practical elimination of the filament energy losses for thermal emission.” 2) “Materials with a fairly long de-excitation time, tE >> tP2 (that is, tE >> 0.4-0.8 ns according to the estimates of the pressure confinement time tP2 made in Section 3.1 for rf = 0.25-0.5 µm) may also provide the dominance of the thermal mechanism – see the inequality (48).  For such tE, a significant decrease in the amplitude of the shock wave and a corresponding decrease in the radius of modification due to the shock-wave mechanism RSW is expected, which can be preferable for obtaining a smoother separation.” (p.40).	( )	( )	(x)	( )

Comments and Suggestions for Authors

The manuscript by V.N. Tokarev entitled “Strategy for obtaining smooth filamentation cutting transparent materials with ultrafast laser”, presents a model on cutting of transparent material by filamentation under the action of an ultrafast laser beam. This is a very interesting field of research, and theoretical works as the one here presented are necessary. Nevertheless, the manuscript needs to be amended prior to acceptance. Here are the main aspects to be considered:

 It is difficult to know the degree of novelty of the present paper, since authors seem to have another paper about a model on the same subject, but not available to the public yet: Ref [38] Tokarev VN, Melnikov IV. Elimination of thermal emission losses in laser filamentation cutting transparent materials.(To be published). This paper is cited repeatedly. It is suggested that paper [38] is published previously to acceptance of the present manuscript.

       *Indeed, there is another paper, Ref. [39] in the new edited list of references (not [38],  as it was in the previous version), Tokarev V.N., Melnikov I.V. Elimination of thermal emission losses in laser filamentation cutting transparent materials. Las Phys Lett 2021 (in press).

       This another paper in accordance with its title considers quite another effect: Elimination of thermal emission losses in laser filamentation cutting transparent materials. But this paper [39] does not consider the “strategy of obtaining smooth separation…”- a subject of the given manuscript entitled “Strategy for obtaining smooth filamentation cutting transparent materials with ultrafast laser”. Therefore “the degree of novelty of the present paper” compared to the Ref. [39] is evident even from the titles of these two papers.  

       Moreover, as I see from the "Author's Guidelines” of this journal, a reference to an unpublished work with the status “in press” is allowed.

 

1. In the abstract it is said (line 22): “The model shows good agreement with experiments on sapphire and tempered glass”. Authors devote section 4 to compare the model with the results shown by just two papers:
1. Reference [19] is a divulgation paper. The results shown in this paper are just to show some examples of possibilities of femtosecond laser, but not in depth information is given. Therefore, please show a more scientific demonstration that corroborates that the model reported in the manuscript is valid.

              

1. Reference [5] is an industrial paper from a conference. This is perfectly valid for a conference, but please again show a scientific demonstration that your model fits the real experiments.

     * The papers [20] and [5,6] (Ref [19] and Ref [5] in the previous version of the manuscript) were chosen by us because they have an important advantage - they provide reliable, well-documented experimental results regarding the irradiation parameters, which, according to our model, determine the process of LFC - the step of the filaments in the material s₁, the energy of the laser pulse E₁, its duration τ, the pulse repetition frequency f, as well as the associated with these 4 parameters scanning speed u and the average laser power of the pulsed periodic beam P. Besides, the papers [5,6] represent the only published example of a really smooth separation in the literature, and also accompanied with some important for us data on the used irradiation parameters.

     These experimental data represent the undoubted scientific value of these papers, regardless of whether they use or do not use any models, or regardless of a level and a “depth” of the authors understanding of the physics of the process, or the level of presentation - in the form of a report at a conference or as a publication in a journal. And for us, these experimental data are sufficient for the comparison of the model and the experiment.

     The mentioned above parameters are exactly ones that are necessary and sufficient to verify the adequacy of the LFC model constructed by us to obtain the effect of a smoother separation. It is important to note that a close agreement between the model and the experiment is obtained not for one or two, but all of six parameters indicated, both for tempered glass and sapphire. In our opinion, this is a strong proof of the reliability of the model.

     In any case, references to such articles are not lower in status than references such as [personal communication] or [in press], although such kind of references are also allowed in this journal by the "Author's guidelines".

     “Just two papers” were chosen for comparison only out of a desire not to overload the article, which is already quite long. Detailed mathematical analysis and discussion of these references occupy a large place in the manuscript.

 

1. In line 1169 it is said: “An algorithm for a sequential calculation of the parameters E1, t, s1 and f in the model is shown in Fig. 7”. But Figure 7 does not show the algorithm. Figure 7 just gives the collection of Input parameters and parameters to be calculated. No indication about the algorithm is given in figure 7.

*Yes, you are right that Fig.7 does not show and does not explain the algorithm. It shows a “schematic of the algorithm…”. The corresponding correction is introduced into the caption of Fig. 7 on p. 32: “Figure 7. Schematic of the algorithm for calculating the main irradiation parameters…”

As for the algorithm itself, it is explained and described in details for particular materials (sapphire and tempered glass) in the Section 4 “Discussion and comparison with experiments” (see pp. 32-37).  

 

1. Please give the meaning of NA (numerical aperture) and M² (laser beam quality). In Figures 1, 2 M² should be linked to the laser beam instead of the focusing system, since M² is a parameter that depends on the laser beam.

* Yes, it is corrected. In the caption of Fig. 1 (p. 2), it is written now: “The focusing system and the laser beam are described by the standard parameters NA and M².”

In the caption of Fig. 2 (p. 4) parameters NA and M² are not mentioned.

Other comments:

1. Please rewrite the following sentence (lines 212-213) to make it clearer to the potential reader: “This is followed up by a conversion of the plasma energy into the material modification due to the energy dissipation over some cylindrical volume around the filament”.

* Yes, it is corrected. It is written now:

“This is followed by a conversion of the plasma energy into a modification of the material due to the radial transfer and dissipation of the plasma energy from the filament axis over a certain cylindrical volume around the filament. Such an impact zone is formed due to thermal conductivity and/or shock wave. The conversion coefficient of the plasma energy into the energy released is A_P-H. This indirect laser action concept is universal in the sense that it does not depend on whether the material is transparent or opaque…”. (at the bottom of p. 5)

 

 

1. In line 284 it is said: “for a submicron filament radius rf = 0.25-0.5 μm in a glass” Please specify the type/composition of the glass.

*Yes, it is written now “in fused silica glass”- see the paragraph just after the formula (4) on p. 7. The same correction is made in the line just after the formula (7) on p. 9.

 

1. Please replace the letter и by & throughout the whole manuscript.

*Yes, it is corrected.

Also the word «где» is replaced by “where” in formulae (66) and (68), pp. 24, 25.

 

Submission Date   30 December 2020                                   Date of this review 18 Jan 2021 10:41:19

 

Author Response File: Author Response.pdf

Round 2

Reviewer 4 Report

Authors partially corrected the manuscript following this reviewer suggestions. Here are the pending aspects:

 

1. Please provide internally, through the manuscript submission application, the manuscript of your in press article Ref [39] “Tokarev VN, Melnikov IV. Elimination of thermal emission losses in laser filamentation cutting transparent materials” in order to evaluate the degree of novelty of the present paper.
2. In the abstract it is said (lines 23-24): “The model shows good agreement with experiments on sapphire and tempered glass”. Authors devote section 4 to compare the model with the results shown by three papers:
   1. References [6] and [20] are divulgation papers. The results given in these two papers have not been reviewed by other researchers in the field. These papers are non-peer reviewed publications. The results shown in these papers are just to show some examples of possibilities of femtosecond laser, but not in depth information is given. Therefore, please show a more scientific demonstration that corroborates that the model reported in the manuscript is valid.
   2. Reference [5] is an industrial paper from a conference. This is perfectly valid for a conference, but please again show a scientific demonstration that your model fits the real experiments.
3. Please give the meaning of NA (numerical aperture) and M² (laser beam quality) in the caption of figures 1 and 2, since these two parameters appear in both figures.

Author Response

To Reviewer 4

The paper "Strategy for obtaining smooth filamentation cutting
transparent materials with ultrafast laser" is an extensive theoretical
and practical work. It is well written and suggests a complex, but
comprehensive approach for improving laser-based micromachining of
transparent media. I recommend the paper for publication after some
minor revision regarding the English language. For instance, even the
title seems to be incomplete: "Strategy for obtaining smooth
filamentation cutting OF transparent materials with ultrafast laser"
instead of "Strategy for obtaining smooth filamentation cutting
transparent materials with ultrafast laser".

 

*   Dear Mr/Mrs Reviewer

I highly appreciate your careful and positive review of the paper.

Thank you very much for the time and forces you spent!  

Please find below my response to your review.

 

*Indeed, there is another paper, Ref. [39]  Tokarev V.N., Melnikov I.V. Elimination of thermal emission losses in laser filamentation cutting transparent materials. Las Phys Lett 2021 (in press).

This another paper in accordance with its title considers quite another effect: Elimination of thermal emission losses in laser filamentation cutting transparent materials. But this paper [39] does not consider the “strategy of obtaining smooth separation…”- a subject of the given manuscript entitled “Strategy for obtaining smooth filamentation cutting transparent materials with ultrafast laser”. Therefore “the degree of novelty of the present paper” compared to the Ref. [39] is evident even from the titles of these two papers.  

Moreover, as I see from the "Author's Guidelines” of this journal, a reference to an unpublished work with the status “in press” or “to be published” is allowed.

  The paper you ask to present to you Tokarev V.N., Melnikov I.V. Elimination of thermal emission losses in laser filamentation cutting transparent materials. Las Phys Lett 2021 (in press) is now in processing by reviewers and therefore has no final version, similar to the paper considered here. That is why I would not like to submit you the full text before the publication. I send you only the abstract:   

Elimination of thermal emission losses in laser filamentation cutting transparent materials

Vladimir N. Tokarev1 and Igor V. Melnikov2

1 Prokhorov General Physics Institute of the Russian Academy of Sciences, 38 Vavilov st., Moscow 119991, Russian Federation

2 Moscow Institute of Physics and Technology, 4 Nauchny per., Dolgoprudny, Moscow Region 141701, Russian Federation

Abstract

The paper considers a problem of unwanted losses of filament energy via thermal emission in the known process of laser filamentation cutting (LFC) transparent materials with a moving pulse-periodic ultrafast laser beam. The proposed analytical model shows that the waste black-body emission becomes a dominant part of laser pulse energy when a filament volumetric energy density (VED) w is in the range w1 < w < w2. Otherwise, for w taken either as w ≤ w1 or w ≥ w2, these losses are insignificant, thus providing for an energy-efficient LFC. The bounds w1 and w2 are estimated to be about a few hundred kJ/cm3 and are defined by thermophysical and optical properties of the material and by a laser focusing. It is shown that, in particular, for sapphire and Corning Gorilla Glass 5, a decrease in the filament radius to about 0.25 μm or less makes the window w1 < w < w2 to shrink and even to disappear. Using the VED w with the obtained limitation, alongside with a filament length and radius, allows calculating pulse energy and duration when each filament is produced with a single laser pulse. Estimates of the duration and energy of the pulse from the burst and of the entire burst of pulses are also obtained for filament generation with a burst of few pulses. The comparison of the model with experiments on LFC of tempered and non-tempered glass, and also sapphire, both in the form of thin (up to 0.70 mm thickness) and thick plates (with a thickness 7-10 mm or more), demonstrates a good agreement and allows to find quantitatively the filament VED and temperature in the LFC. It also shows that bounds w1 and w2 can be achieved in experiments.          In the abstract it is said (lines 23-24): “The model shows good
agreement with experiments on sapphire and tempered glass”. Authors
devote section 4 to compare the model with the results shown by three
papers:
         References [6] and [20] are divulgation papers. The results
given in these two papers have not been reviewed by other researchers in
the field. These papers are non-peer reviewed publications. The results
shown in these papers are just to show some examples of possibilities of
femtosecond laser, but not in depth information is given. Therefore,
please show a more scientific demonstration that corroborates that the
model reported in the manuscript is valid.
         Reference [5] is an industrial paper from a conference. This is
perfectly valid for a conference, but please again show a scientific
demonstration that your model fits the real experiments. I repeat below my opinion concerning the cited papers [5,6,20] and have nothing more to add: 

  * The papers [20] and [5,6] were chosen by us because they have an important advantage - they provide reliable, well-documented experimental results regarding the irradiation parameters, which, according to our model, determine the process of LFC - the step of the filaments in the material s1, the energy of the laser pulse E1, its duration τ, the pulse repetition frequency f, as well as the associated with these 4 parameters the scanning speed u and the average laser power of the pulsed periodic beam P.

In my opinion, these experimental data represent the undoubted scientific value of these papers, regardless of whether they use or do not use any models, or regardless of a level and a “depth” of the authors understanding of the physics of the process, or the level of presentation - in the form of a report at a conference or as a publication in a journal. And for us, these experimental data are sufficient for the comparison of the model and the experiment.

The mentioned above parameters are exactly ones that are necessary and sufficient to verify the adequacy of the LFC model constructed by us to obtain the effect of more smooth separation walls. It is important to note that a close agreement between the model and the experiment is obtained not for one or two, but all of six parameters indicated, both for tempered glass and sapphire. In our opinion, this is a strong proof of the reliability of the model.

       In any case, references to such articles are not lower in status than references such as [personal communication] or [in press], although such kind of references is also allowed in this journal by the "Author's guidelines".

       “Just two papers” were chosen for comparison with the model only out of a desire do not overload the article, which is already too long.

       Please give the meaning of NA (numerical aperture) and M2 (laser
beam quality) in the caption of figures 1 and 2, since these two
parameters appear in both figures. I repeat what I wrote already in the previous response:

* Yes, it is corrected. In the caption of Fig. 1 (p. 2), it is written now: “The focusing system and the laser beam are described by the standard parameters NA and M2.”

In the caption of Fig. 2 (p. 4) parameters NA and M2 are not mentioned at all. 

 

Best regards.

Sincerely.

Vladimir Tokarev

 

My comments

1. *We have performed additional editing of the text for the correction of English and some misprints (see the corrected version with highlighted corrections). 

 

2. *We also have corrected the title of the paper according to your recommendation. 

       Now it is: "Strategy for obtaining smooth filamentation cutting of transparent materials with ultrafast laser".