Temporal Cavity Soliton Interaction in Passively Mode-Locked Semiconductor Lasers
Round 1
Reviewer 1 Report
In this paper, the authors use an asymptotic approach numerically and analytically investigate the weak interaction of temporal cavity solitons due to gain saturation and recovery in a delay differential model of a long cavity semiconductor laser. Here are some issues for authors:
(1) Line 42: Is ‘ether’ a misspelling? Should it be written as either.
(2) Line 46-48: The author say “ulike the present work, in both those papers the Kerr nonlinearity played a decisive role in the process of the pulse formation”. What is the difference between the mechanism that plays a decisive role in the process of pulse information in this article and the previous article? And the ‘ulike’ is spelling mistake?
(3) What is the application of this research, I think should be added.
(4) All image horizontal and vertical coordinates have no dimension units.
(5) Why the values corresponding to absolute values in Figures 1 (b) and 2 (b) are negative?
(6) How do Figure 3 (c) and (d) tell how many pulses are in the figure? The curves in the upper part of the image are almost parallel, how to judge the repulsion between the pulses?
Good.
Author Response
I thank the Reviewer for his/her careful reading of the manuscript and useful comments. The manuscript was revised according to his/her recommendations and the detailed responses to the comments are given below.
(1) Line 42: Is ‘ether’ a misspelling? Should it be written as either.
REPLY: The misprint was corrected in the revised manuscript.
(2) Line 46-48: The author say “ulike the present work, in both those papers the Kerr nonlinearity played a decisive role in the process of the pulse formation”. What is the difference between the mechanism that plays a decisive role in the process of pulse information in this article and the previous article? And the ‘ulike’ is spelling mistake?
REPLY: To address this comment I have modified the sentence cited by the Reviewer in the following way:
"Note, however, that unlike the present work, where the mode-locking mechanism is due to the interplay of the gain and absorption saturation and recovery [16], in both those papers the Kerr nonlinearity played a decisive role in the process of the mode-locked pulse formation."
The misprint ‘ulike’ has been corrected.
(3) What is the application of this research, I think should be added.
REPLY: To address this comment I have added the sentence: "The results of this work might be useful for pulse spacing manipulation in multipulse mode-locked lasers." at the end of the Introduction.
(4) All image horizontal and vertical coordinates have no dimension units.
REPLY: All the quantities shown in the figures are dimensionless.
(5) Why the values corresponding to absolute values in Figures 1 (b) and 2 (b) are negative?
REPLY: In fact Figures 1(b) and 2(b) show the logarithms of the absolute values, which are negative when the absolute value is small enough.
To make it clear I have corrected the vertical labels of these figures and replaced the sentences "Temporal evolution of the absolute values... in logarithmic scale." with "Temporal evolution of the logarithm of the absolute values... " in both the figure captions.
(6) How do Figure 3 (c) and (d) tell how many pulses are in the figure? The curves in the upper part of the image are almost parallel, how to judge the repulsion between the pulses?
REPLY: To answer the first question one needs to draw a horizontal line at any given round trip number (vertical position). Then one can count the number of pulses per cavity round trip on this line. To make this more clear I have added the following text to the captions of Figs. 3 and 5: "Cold cavity round trip time is $T=50$."
The repulsion is visible at the early stages of the interaction (lower part of the images). Upper part of the image corresponds to a sequence of equidistant pulses where the repulsions from two neighboring pulses compensate one another. To make this more clear I have changed the vertical scale of Figs. 3(a) and (d) in order to zoom their lower parts. Furthermore, I have added the following sentence to the description of Figs. 3(c) and 3 (d): "Here the transformation of a train of initially non-equidistant pulses into an equidistant ones clearly indicates the repulsive nature of the interaction."
Reviewer 2 Report
Journal: Optics (ISSN 2673-3269)
Manuscript ID: optics-2478932
Type: Article
Title: Temporal cavity soliton interaction in passively mode-locked semiconductor lasers.
Authors: Andrei G Vladimirov*.
a) Write the objective of the present work carefully.
b) Do you consider the topic original or relevant in the field? Does it address a specific gap in the field?
c) Please; Refer to the recent refs
DOI: https://doi.org/10.1088/1742-6596/1795/1/012042
DOI: https://doi.org/10.1088/1742-6596/1999/1/012080
Best Regards
Author Response
a) Write the objective of the present work carefully.
b) Do you consider the topic original or relevant in the field? Does it address a specific gap in the field?
REPLY: To address these two comments I have added the following text to the Introduction:
"Furthermore, among the above cited works only Refs. [13] and [15] are devoted to the pulse interaction in semiconductor lasers. However, in Ref. [13] a short cavity laser operating far away from the TCS regime was considered, while the analysis of Ref. [15] is more or less empirical. Therefore, a more rigorous analysis of the TCS interaction in semiconductor lasers taking into account such their characteristic features as linewidth enhancement factor is required. This work is aimed to fill in this gap."
c) Please; Refer to the recent refs
DOI: https://doi.org/10.1088/1742-6596/1795/1/012042
DOI: https://doi.org/10.1088/1742-6596/1999/1/012080
REPLY: Unfortunately, I have not found these references relevant to the subject of this work.
Reviewer 3 Report
This manuscript entitled “Temporal cavity soliton interaction in passively mode-locked semiconductor lasers (Manuscript ID: optics-2478932)” by A. G. Vladimirov et al., studies the weak interaction of temporal cavity solitons in a delay differential model of a long cavity semiconductor laser. After reviewing the manuscript, we have the following confusion:
1. The caption for Fig. 1: Does T0=50.138425 have practical significance? How to achieve it in the experiment?
2. What are the innovations of the model in the manuscript? Is the calculation method new?
3. What do ‘2.’ and ‘1.’ in Fig. 4(b) mean?
4. The order of the two figures in Fig. 5 needs to be reversed.
5. The caption for Fig. 1: The “Eq. (1)-(3)” is suggested to be changed as “Eqs. (1)-(3)”, and some other common problems that need to be addressed by the authors.
6. The format of the references needs to be further improved.
For example,
The ‘Nature photonics’ are suggested to be changed as ‘Nat. Photonics’,
The ‘JOSA B’ are suggested to be changed as ‘J. Opt. Soc. Am. B’,
The ‘Physical Review E’ are suggested to be changed as ‘Phys. Rev. E’,
The ‘Physical Review Letters’ are suggested to be changed as ‘Phys. Rev. Lett.’,
The ‘Optics Communications’ are suggested to be changed as ‘Opt. Commun.’.
Minor editing of English language required.
Author Response
I am thankful to the Reviewer for his/her careful reading of the manuscript and useful comments. The manuscript was revised according to his/her recommendations and the detailed responses to the comments are given below.
1. The caption for Fig. 1: Does T0=50.138425 have practical significance? How to achieve it in the experiment?
REPLY: The value T0=50.138425 shows how the solution period differs from the delay time T=50 (cold cavity round trip time). It would be hardly possible to measure it experimentally. However, it contains the information important for further analysis. Knowing this quantity is necessary to separate slow pulse interaction from the common drift of the interacting pulses. To this end the intensity time trace is split into the consecutive intervals with the duration T0 and these intervals are associated with different round trips leading to 2D interaction plots shown in Figs. 3 and 5. In order to clarify this I have added the following text at the end of the paragraph describing Fig. 3: "Note, that in order to produce Fig. 3 with minimized common TCSs drift, which is close to the single TCS drift $T_0-T$ per cavity round trip, the following procedure was used. The intensity time trace obtained by numerical solution of Eqs. (1)-(3) was split into intervals with the duration $T_0$ and consecutive intervals were associated with consecutive round trip numbers."
2. What are the innovations of the model in the manuscript? Is the calculation method new?
REPLY: The DDE mode-locked laser model was proposed earlier by me and D.Turaev in Ref. [19]. Since this model is free from the mean field aproximation and does not assume any limitations on the gain and absorber relaxation rates, it suits better to describe mode-locking in semiconductor lasers than the Haus master equation. Application of the DDE model to study asymptotically the pulse interaction in the TCS regime can be considered as innovative together with the asymptotic method to calculate the interaction coefficients K_g amd K_q using the DDE model.To stress this point I have have modified the following sentence in the Introduction as: "I show that the TCS interaction scenarios depend on the ``interaction coefficients'' introduced below and can be more rich than those described in [11,13,15]."
3. What do ‘2.’ and ‘1.’ in Fig. 4(b) mean?
In order to address this comment I have added the following sentence to the caption of Fig. 4(b): "Different curves in panel (b) correspond to different linewidth enhancement factor values, αg=0.5,1.0,1.5.2.0, indicated in the panel."
4. The order of the two figures in Fig. 5 needs to be reversed.
REPLY: The order of the figures has been reversed.
5. The caption for Fig. 1: The “Eq. (1)-(3)” is suggested to be changed as “Eqs. (1)-(3)”, and some other common problems that need to be addressed by the authors.
REPLY: The correction suggested by the Reviewer has been made in the manuscript.
6. The format of the references needs to be further improved.
For example,
The ‘Nature photonics’ are suggested to be changed as ‘Nat. Photonics’,
The ‘JOSA B’ are suggested to be changed as ‘J. Opt. Soc. Am. B’,
The ‘Physical Review E’ are suggested to be changed as ‘Phys. Rev. E’,
The ‘Physical Review Letters’ are suggested to be changed as ‘Phys. Rev. Lett.’,
The ‘Optics Communications’ are suggested to be changed as ‘Opt. Commun.’.
REPLY: The format of the references was improved following the comment of the Reviewer.
Reviewer 4 Report
The author conducted a numerical and analytical study on the interaction between two temporal cavity solitons in a delay differential model of a long cavity semiconductor laser. The study involved deriving and analyzing interaction equations that govern the slow evolution of the time separation and phase difference of the TCSs. The manuscript is well-written, demonstrating a good structure and proper assumptions during the analysis procedure. The data and results are comprehensively analyzed. I believe that the research topic of temporal cavity soliton interaction would be of interest to the audience of Optics. Furthermore, the author made certain assumptions during the derivation process, so it is recommended to provide some clarification on these assumptions and premises when drawing conclusions
Minor editing of language required
Author Response
The author conducted a numerical and analytical study on the interaction between two temporal cavity solitons in a delay differential model of a long cavity semiconductor laser. The study involved deriving and analyzing interaction equations that govern the slow evolution of the time separation and phase difference of the TCSs. The manuscript is well-written, demonstrating a good structure and proper assumptions during the analysis procedure. The data and results are comprehensively analyzed. I believe that the research topic of temporal cavity soliton interaction would be of interest to the audience of Optics. Furthermore, the author made certain assumptions during the derivation process, so it is recommended to provide some clarification on these assumptions and premises when drawing conclusions
REPLY: I thank the Reviewer for the overall positive evaluation of the manuscript. In order to provide some clarification on the assumptions made, I have added the following text to the second sentence of the Conclusion "... in the parameter range typical of semiconductor lasers, where the interaction via the gain saturation and recovery dominates over the interaction via absorber and field components."
Round 2
Reviewer 3 Report
Agree
