Supercontinuum Generation from Airy-Gaussian Pulses in Photonic Crystal Fiber with Three Zero-Dispersion Points

Round 1

Reviewer 1 Report

This paper deals with the problem of supercontinuum generation and manipulation of Airy-Gaussian pulses in photonic crystal fibers with three zero-dispersion points. By means of numerical calculation, the authors give many meaningful analytical results. The effects of four characteristic parameters (truncation factor a, distribution factor χ0, initial chirp C and central wavelength λ) on the formation of supercontinuum spectrum of Airy-Gaussian pulses are analyzed comprehensively. The content of the paper is substantial. Therefore, I can recommend for publishing this manuscript. However, there are still some issues to be addressed before publishing.

1.The abstract should not have any acronyms. The acronyms start in the introduction section.

2.In the introduce part, the authors need to discuss the differences between this manuscript with the previous published papers.

3.The literature review presented here is highly insufficient and generalized. Especially, many literatures on Airy pulse transmission are not summarized. Some typical papers as follow Phys. Rev. Lett. 107, 243901（2011），Opt. Express 19, 17298-17307 (2011)， Opt. Express 23, 2566-2576 (2015)，Opt. Express 22, 17107-17115 (2014)，J. Opt. Soc. Am. B 31(4) 889-897 (2014)，Opt. Express 22(19) 22598-22607 (2014)，Opt. Express 29, 12723-12735 (2021)，Opt. Express 31(6) 9961-9972 (2023)，Opt. Express 31(4) 6296-6303 (2023)

4.The conclusion part doesn’t illustrate the important innovations and results, so it needs to be revised carefully.

5.The grammar of the whole manuscript needs to be revised carefully.

6 The title of ref 6 is missing.

The grammar of the whole manuscript needs to be revised carefully.

Author Response

Dear Editors/Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Supercontinuum Generation from Airy-Gaussian Pulses in Photonic Fibers Crystals with Three Zero-Dispersion Point”. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:

Reviewer #1: 

This paper deals with the problem of supercontinuum generation and manipulation of Airy-Gaussian pulses in photonic crystal fibers with three zero-dispersion points. By means of numerical calculation, the authors give many meaningful analytical results. The effects of four characteristic parameters (truncation factor a, distribution factor χ0, initial chirp C and central wavelength λ) on the formation of supercontinuum spectrum of Airy-Gaussian pulses are analyzed comprehensively. The content of the paper is substantial. Therefore, I can recommend for publishing this manuscript. However, there are still some issues to be addressed before publishing.

1. The abstract should not have any acronyms. The acronyms start in the introduction section.

Response: This is my own negligence. All acronyms in the abstract are corrected to the full name.

 

2.In the introduce part, the authors need to discuss the differences between this manuscript with the previous published papers.

Response: I have explained the difference between this article and the previous research in the introduction. The corresponding modifications are as follows: Researchers have studied the generation and manipulation of supercontinuum in photonic crystal fiber with single and double zero-dispersion points and also studied the supercontinuum of conventional Gaussian pulses in photonic crystal fibers with three zero-dispersion points. Due to the quantum tunneling effect of three zero-dispersion points photonic crystal fibers, the generated supercontinuum width is larger. In addition, compared with the traditional Gaussian pulse, the Airy-Gaussian pulse with multi-peak structure can also generate a wider supercontinuum spectrum. However, at present, the research on the evolution characteristics of Airy-Gaussian pulse in photonic crystal fiber with three zero dispersion points is very limited. At the same time, how to select the appropriate barrier width of three zero-dispersion points photonic crystal fiber and pulse parameters to obtain a wider and flatter supercontinuum spectrum is also an urgent problem to be solved. Therefore, it is essential to explore further the evolution characteristics of Airy-Gaussian pulses in three-zero-dispersion photonic crystals.

 

3.The literature review presented here is highly insufficient and generalized. Especially, many literatures on Airy pulse transmission are not summarized. Some typical papers as follow Phys. Rev. Lett. 107, 243901（2011），Opt. Express 19, 17298-17307 (2011)， Opt. Express 23, 2566-2576 (2015)，Opt. Express 22, 17107-17115 (2014)，J. Opt. Soc. Am. B 31(4) 889-897 (2014)，Opt. Express 22(19) 22598-22607 (2014)，Opt. Express 29, 12723-12735 (2021)，Opt. Express 31(6) 9961-9972 (2023)，Opt. Express 31(4) 6296-6303 (2023)

Response: References have been added as follows:

15. Zhang L F, Liu K, Zhong H Z, Zhang J G, Li Y and Fan D Y. Effect of initial frequency chirp on Airy pulse propagation in an optical fiber[J]. Express 2015 23(3), 2566-2576.
16. Zhang L F and Zhong H Z. Modulation instability of finite energy Airy pulse in optical fiber[J]. Express 2014 22(14):17107-17115.
17. Zhang L F, Zhong H Z, Li Y and Fan D Y. Manipulation of Raman-induced frequency shift by use of asymmetric self-accelerating Airy pulse[J]. Express 2014 22(19):17107-17115.
18. Li H Z, Cai W Y, Zhang J, Gao Y X, Zhang L F and Fan D Y. Manipulation of dispersive waves emission via quadratic spectral phase[J]. Express 2021 29(8):12723-12735.
19. Peng W L, Zhang X, Jing L Q, Gao Y X, Deng Z X, Zhang L F and Fan D Y. Soliton-sinc optical pulse propagation in the presence of high-order effects[J]. Express 2023 31(6):9961-9972
20. Li H Z, Wang Z T, Xie Z X, Fan D Y and Zhang L F. Manipulating dispersive wave emission via temporal sinusoidal phase modulation[J]. Express 2023 31(4):6296-6303.

 

4 The conclusion part doesn’t illustrate the important innovations and results, so it needs to be revised carefully.

Response: I have made changes to the conclusion. When the pulse propagates in the PCF with three zero-dispersion points, the spectral width becomes longer due to the redshift dispersion, and the tunneling soliton effect occurs further, resulting in the broader supercontinuum spectrum than that of PCF with a one and two zero dispersion points. In addition, compared with the traditional Gaussian pulse, the Airy-Gaussian pulse with two parameters (the truncation coefficient and the distribution factor) can control the width and spectral range of the supercontinuum spectrum more flexibly. Therefore, further research was conducted on the formation mechanism of supercontinuum spectra of Airy-Gaussian pulses in PCF with Three Zero-Dispersion Points. It is found that when the width of the barrier is less than the threshold, the red-shifted dispersion wave and tunneling soliton will be formed in R3. When the barrier width continues to widen and exceeds the threshold, soliton-like pulses may appear in R4, which is leaky dispersion waves or tunneling solitons. When the barrier width is too wide, the energy of the initial soliton is almost unable to pass through the barrier region, and most of the energy exists in the form of redshift dispersion waves in R3. Therefore, reasonable adjustment of the barrier can better control the soliton tunneling and the width and flatness of the supercontinuum spectrum generated by the soliton. In addition, the smaller the truncation coefficient and distribution factor of the Airy-Gaussian pulse in the PCF with three zero-dispersion points, the larger the initial chirp and the central wavelength, and the broader the supercontinuum spectrum can be obtained. Tunneling solitons formed by Airy-Gaussian pulses in PCF with three zero-dispersion wavelengths can maintain a stable shape.

 

5. The grammar of the whole manuscript needs to be revised carefully.

Response: This is my own negligence. We have carefully checked all the contents and made corresponding modifications.

 

6. The title of ref 6 is missing.

Response: This is my own negligence. I 've added the title of ref 6.

 

We tried our best to improve the manuscript and made some changes in the manuscript.  These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

We appreciate for Editors/Reviewers warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Reviewer 2 Report

This manuscript studied the supercontinuum generation from Airy-Gaussian pulses in photonic crystal fibers with zero-dispersion point(s) in numerical simulation. The author investigated the influences of barrier width, number of zero-dispersion points, transmission distance, as well as the parameters of the Airy-Gaussian pulse including the truncation coefficient, the distribution factor, the initial chirp, and wavelength. This manuscript includes detailed results and analyses, but the following issues should be addressed before this work can be considered for publication:

 

(1) There are inappropriate expressions in the title and main text, for example, ‘photonic fibers crystals’, and ‘two/three photonic crystal fibers with zero dispersion point’. The authors should carefully check the manuscript and fix them.

 

(2) The authors should also carefully check the figures to ensure that they are appropriately presented. For example:

• There is no (a) but only (b) labeled in Figure 1;
• The y-axis names in the two plots of Figure 1 should be switched;
• The x-axis tick labels in the first plot are ‘…, 1000, 1200, 140?’
• I wonder why the plots in the manuscript have multiple different wavelength ranges?
• Please show color bars for the 2D intensity plots.
• Barrier widths should be labeled in figures or captions in Figure 2.

 

(3) The current Section 2 ‘Analysis of numerical results’ includes a lot of information but without a clear structure, so it is a bit hard for readers to read. I recommend the authors further divide this section into several subsections and arrange them in a more logical flow.

 

(4) The author mentioned that ‘After research, we found that PCF2 is the best three-zero dispersion point PCFs, and PCF2 will be used in the subsequent numerical simulation’ (page 6). However, it is not clear why PCF2 is the best. Please further explain it.

 

(5) How are the parameter’s values chosen? For example, P0 = 5kW, media length = 0.4 m, τ1=12.2fs and τ2=32fs. Please provide references if necessary.

 

(6) The authors mentioned that ‘as the transmission distance increases, of spectral broadening decreases significantly [Figure 8. (f2)]’ (line 281 on page 10). Can you explain how Figure 8. (f2) supports this claim?

 

(7) Please give the definition of ‘F(x, y)’ in Equation (4). What is ‘ST effect’ on Page 6?

 

(8) In Conclusion section, the authors said that ‘The leakage dispersive wave will dissipate soon after transmission, so it can provide a safe mode of ' burning after reading ', significantly improving communication security. In addition, tunneling solitons can maintain a stable shape and carry a lot of energy and information. Therefore, …’

I wonder how to obtain such conclusions about the dissipation property of the leakage dispersive wave and the stability of tunneling solitons’ shape from this manuscript?

If it is concluded from other works, please clarify it and provide references.

Please see the first comment above.

Author Response

Dear Editors/Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Supercontinuum Generation from Airy-Gaussian Pulses in Photonic Crystals Fibers with Three Zero-Dispersion Point”. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:

 

Reviewer #2: 

    This manuscript studied the supercontinuum generation from Airy-Gaussian pulses in photonic crystal fibers with zero-dispersion point(s) in numerical simulation. The author investigated the influences of barrier width, number of zero-dispersion points, transmission distance, as well as the parameters of the Airy-Gaussian pulse including the truncation coefficient, the distribution factor, the initial chirp, and wavelength. This manuscript includes detailed results and analyses, but the following issues should be addressed before this work can be considered for publication:

 

1. There are inappropriate expressions in the title and main text, for example, ‘photonic fibers crystals’, and ‘two/three photonic crystal fibers with zero dispersion point’. The authors should carefully check the manuscript and fix them.

Response: This is my own negligence. We have carefully checked all the contents and made corresponding modifications.

 

2. The authors should also carefully check the figures to ensure that they are appropriately presented. For example:

• There is no (a) but only (b) labeled in Figure 1;
• The y-axis names in the two plots of Figure 1 should be switched;
• The x-axis tick labels in the first plot are ‘…, 1000, 1200, 140?’
• I wonder why the plots in the manuscript have multiple different wavelength ranges?
• Please show color bars for the 2D intensity plots.
• Barrier widths should be labeled in figures or captions in Figure 2.

Response:  This is my own negligence. We have carefully checked all the contents and made corresponding modifications.

2.1 I have been labeled (a) in Figure 1.

2.2 The y-axis names of the two parts of Figure 1 have been switched.

2.3 Changes have been made to the x-axis scale labels in Figure 1.

2.4 The wavelength range of the x-axis wavelength range in Fig.1 has been modified.

2.5 The color bar of Figure 2 - Figure 7 of the two-dimensional intensity diagram has been added.

2.6 The size of the barrier width has been shown in the caption below the picture. The barrier widths of PCF1-PCF2 are 50 nm, 90 nm, 140 nm and 185 nm, respectively.

 

3. The current Section 2 ‘Analysis of numerical results’ includes a lot of information but without a clear structure, so it is a bit hard for readers to read. I recommend the authors further divide this section into several subsections and arrange them in a more logical flow.

Response: The numerical simulation results have been divided into several sections. The corresponding modifications are as follows:

2.1 Effect of barrier width of three zero-dispersion points photonic crystal fiber

2.2 Effect of the number of zero-dispersion points in photonic crystal fiber

2.3 Influence of the initial parameters of the Airy-Gaussian pulse

2.4 The detailed process of supercontinuum spectrum formation in PCF2 by Airy-Gaussian pulse

 

4. The author mentioned that ‘After research, we found that PCF2 is the best three-zero dispersion point PCFs, and PCF2 will be used in the subsequent numerical simulation’ (page 6). However, it is not clear why PCF2 is the best. Please further explain it.

Response: We have made corresponding modifications. The spectral width and flatness of the supercontinuum are the two most important parameters that need to be considered simultaneously. The quantum tunneling effect can also produce high-power spectral separation, but it may lead to the collapse of the supercontinuum structure, which seriously affects its flatness. In order to optimize the quantum tunneling effect, the barrier width needs to be adjusted to ensure that the power is supplemented in a specific spectral band. While generating longer wavelength spectrum components, it is necessary to reduce the damage of the soliton tunneling effect on the flatness of the supercontinuum spectrum. After research, we find that PCF2 is the best three-zero dispersion points PCF, and PCF2 will be used in the subsequent numerical simulation.

 

5. How are the parameter’s values chosen? For example, P0 = 5kW, media length = 0.4 m, τ1=12.2fs and τ2=32fs. Please provide references if necessary.

Response: The reference is [34]. This reference has been added to the article.

 

6. The authors mentioned that ‘as the transmission distance increases, of spectral broadening decreases significantly [Figure 8. (f2)]’ (line 281 on page 10). Can you explain how Figure 8. (f2) supports this claim?

Response: When the propagation distance of the pulse in the photonic crystal fiber reaches a certain value, the width of the supercontinuum spectrum gradually decreases. This shows that as the fiber length increases, the spectral width also increases. However, when the fiber length continues to increase, the spectral width decreases and the flatness of the spectrum becomes worse. This is because when the pulse is transmitted in the optical fiber, the pulse width will be broadened and the peak power will be reduced accordingly, thus weakening the self-phase modulation effect of spectral broadening. Therefore, under the given input pulse condition, there is a limit value of the effective broadening length.

 

7. Please give the definition of ‘F(x, y)’ in Equation (4). What is ‘ST effect’ on Page 6?

Response: This is my own negligence.

F(x, y) is the field distribution function of the fundamental mode of photonic crystal fiber.

ST is an abbreviation of soliton tunneling. The text has been modified to the full name.

 

9. In Conclusion section, the authors said that ‘The leakage dispersive wave will dissipate soon after transmission, so it can provide a safe mode of ' burning after reading ', significantly improving communication security. In addition, tunneling solitons can maintain a stable shape and carry a lot of energy and information. Therefore, …’

I wonder how to obtain such conclusions about the dissipation property of the leakage dispersive wave and the stability of tunneling solitons’ shape from this manuscript?

If it is concluded from other works, please clarify it and provide references.

Response: The conclusion section describes the results of the numerical simulation experiments. Changes have been made in the conclusions section of the article.

When the pulse propagates in the PCF with three zero-dispersion points, the spectral width becomes longer due to the redshift dispersion, and the tunneling soliton effect occurs further, resulting in the broader supercontinuum spectrum than that of PCF with a one and two zero dispersion points. In addition, compared with the traditional Gaussian pulse, the Airy-Gaussian pulse with two parameters (the truncation coefficient and the distribution factor) can control the width and spectral range of the supercontinuum spectrum more flexibly. Therefore, further research was conducted on the formation mechanism of supercontinuum spectra of Airy-Gaussian pulses in PCF with Three Zero-Dispersion Points. It is found that when the width of the barrier is less than the threshold, the red-shifted dispersion wave and tunneling soliton will be formed in R3. When the barrier width continues to widen and exceeds the threshold, soliton-like pulses may appear in R4, which is leaky dispersion waves or tunneling solitons. When the barrier width is too wide, the energy of the initial soliton is almost unable to pass through the barrier region, and most of the energy exists in the form of redshift dispersion waves in R3. Therefore, reasonable adjustment of the barrier can better control the soliton tunneling and the width and flatness of the supercontinuum spectrum generated by the soliton. In addition, the smaller the truncation coefficient and distribution factor of the Airy-Gaussian pulse in the PCF with three zero-dispersion points, the larger the initial chirp and the central wavelength, and the broader the supercontinuum spectrum can be obtained. Tunneling solitons formed by Airy-Gaussian pulses in PCF with three zero-dispersion wavelengths can maintain a stable shape.

 

We tried our best to improve the manuscript and made some changes in the manuscript.  These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

We appreciate for Editors/Reviewers warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Reviewer 3 Report

In this paper, Supercontinuum Generation using photonic crystal fibers with three zero-dispersion points are investigated.

I think some useful information is provided in this paper. Therefore, this paper is ready to be published, but

Title should be "...Photonic Crystal Fibers...", not "...Photonic Fibers Crystals..."

Author Response

List of Responses

Dear Editors/Reviewers:

Thank you for your letter and for the reviewers’ comments concerning our manuscript entitled “Supercontinuum Generation from Airy-Gaussian Pulses in Photonic Crystals Fibers with Three Zero-Dispersion Point”. Those comments are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have studied comments carefully and have made correction which we hope meet with approval. Revised portion are marked in red in the paper. The main corrections in the paper and the responds to the reviewer’s comments are as flowing:

 

Reviewer #3: 

 

In this paper, Supercontinuum Generation using photonic crystal fibers with three zero-dispersion points are investigated.

I think some useful information is provided in this paper. Therefore, this paper is ready to be published, but Title should be "...Photonic Crystal Fibers...", not "...Photonic Fibers Crystals..."

Response: Thanks for the reminder. The title of the article has been corrected.

 

We tried our best to improve the manuscript and made some changes in the manuscript.  These changes will not influence the content and framework of the paper. And here we did not list the changes but marked in red in revised paper.

We appreciate for Editors/Reviewers warm work earnestly, and hope that the correction will meet with approval.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

All my comments have been appropriately addressed, and the author has made the necessary modifications. I recommend that this paper be accepted for publication.