Review Reports

Round 1

Reviewer 1 Report

This paper theoretically and experimentally explores the optical bistability and thermal mode hopping in external cavity feedback semiconductor laser. Overall, this paper is well written and I recommend this paper to be published in MDPI Photonics. I suggest that the paper can be improved from the following two points. Firstly, In the introduction, the authors mention the narrow linewidth semiconductor laser. In addition to the external cavity laser, quantum dot lasers can also achieve narrow linewidths through the gain medium itself and have good temperature stability. I think the author can add some comments on quantum dot lasers based on the papers of Applied Physics Letters, 112, 121102 (2018) and Optica, 6(8), 2019. Secondly, in line 47, "a isolator" should be changed as "an isolator".

Good.

Author Response

Dear Reviewers:

We are very grateful to you for reviewing our paper.

Responds to the reviewers' comments：

1. "Firstly, In the introduction, the authors mention the narrow linewidth semiconductor laser. In addition to the external cavity laser, quantum dot lasers can also achieve narrow linewidths through the gain medium itself and have good temperature stability. I think the author can add some comments on quantum dot lasers based on the papers of Applied Physics Letters, 112, 121102 (2018) and Optica, 6(8), 2019. "

Response: We appreciate it very much for this good suggestion. According to your ideas. We have added quantum dot lasers to our introduction and inserted relevant literature references. We highlighted this modification on page 1, line 22, in the attached article.

 

2. "Secondly, in line 47, 'a isolator' should be changed as 'an isolator'."

Response:  We are very sorry for our incorrect writing and it is rectified on page 2, line 50. In the attached article, we have also highlighted this change.

Thank you again for reviewing our paper. Best wishes！

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper deals with the very interesting topic of bistability and mode hopping in an external cavity laser under thermal tuning. Due to temperature changes the effective optical distance which determines the longitudinal-mode comb increases with temperature. Within the filter profile of the FP-cavity two competitive longitudinal modes are active. It is known that in case of 2 competing next-neighbor longitudinal modes in a semiconductor laser, strong mode interaction occurs that is not time-reversal symmetric due to the linewidth enhancement (alpha) parameter (Bogatov effect). Especially in the external-cavity laser the mode spacing is very small (~3.8GHz), causes very strong asymmetric mode-suppression effects, in such a way that the red-shifted mode is significantly more stable than the blue shifted mode (see Optics Express 22, 2014, 8143-8149, DOI:10.1364/OE.22008143 and references therein). In the process of increasing-temperature tuning, the comb moves upwards in wavelength through the FP-filter profile, which is at the basis of the observed bistability and hysteresis.

The authors have built their own theory without reference to the above-mentioned Bogatov effect and without any stability analysis. The explanation in sec.3 is phenomenological and lacks proper description of the equations underlying the simulations shown in Figs. 4 d & e. Especially, it is unclear how the mode hops are incorporated in the model.

The relevance of the analysis of Fig. 3 b, c & d is not clear in view of what is stated in line 134, namely “Each data point is a steady-state result measured after thermal equilibrium”.

There is a discrepancy between figures 1 b and 4 d. In Fig. 1 b, it seems that the FP filter moves to the red with increasing temperature, while in Fig. 4 d it moves to the blue. This seems to indicate that what matters here is the comb motion relative to the FP filter towards the red.

In conclusion, the paper reports an interesting experimental result, for which a phenomenological description is given rather than an explanation. This paper can be accepted only if the authors give more details and clarification on the model underlying the simulations of Fig. 4 and especially the mode hopping mechanisms.

English language is not perfect, but the text is fully understandable.

Author Response

Dear Reviewers:

We are very grateful to you for reviewing our paper.

We have carefully considered the suggestion of you and tried our best to improve and made some changes in the manuscript.

Responds to the reviewers' comments：

1. "It is known that in case of 2 competing next-neighbor longitudinal modes in a semiconductor laser, strong mode interaction occurs that is not time-reversal symmetric due to the linewidth enhancement (alpha) parameter (Bogatov effect). Especially in the external-cavity laser the mode spacing is very small (~3.8GHz), causes very strong asymmetric mode-suppression effects, in such a way that the red-shifted mode is significantly more stable than the blue shifted mode (see Optics Express 22, 2014, 8143-8149, DOI:10.1364/OE.22008143 and references therein). In the process of increasing-temperature tuning, the comb moves upwards in wavelength through the FP-filter profile, which is at the basis of the observed bistability and hysteresis.

The authors have built their own theory without reference to the above-mentioned Bogatov effect and without any stability analysis. The explanation in sec.3 is phenomenological and lacks proper description of the equations underlying the simulations shown in Figs. 4 d & e. Especially, it is unclear how the mode hops are incorporated in the model.

...

This paper can be accepted only if the authors give more details and clarification on the model underlying the simulations of Fig. 4 and especially the mode hopping mechanisms."

Response: We appreciate it very much for this good suggestion. We spent a week introducing the Bogatov effect into our model and recalculating the results.

The relevant derivation has been added to the Configuration and Methods section. The new content is highlighted on pages 4-5 and lines 122-146 of the attached document.

In Figures 2c and d, we have added the calculation results with the addition of the Bogatov effect. It is highlighted on pages 6 of the attached document.

We also adds an explanation for the breaking of symmetry by the Bogatov effect and explains the necessity of subsequent thermal analysis. This is added on page 7, lines 202 to 218, and highlighted in the attachment.

Finally, considering the Bogatov effect, we redrawn Figure 4 based on the calculation results. And we have restated the corresponding analysis process, highlighted on pages 8-9, lines 252-301 of the attachment.

In summary, the Bogatov effect always gives long wavelength modes an advantage in mode competition. This results in an asymmetric shape in the temperature tuning curve. And the three-step process sequences, which is caused by temperature, allows the tuning direction to affect the tuning result. This causes inconsistency in the heating and cooling tuning curves of our laser.

 

2. "The relevance of the analysis of Fig. 3 b, c & d is not clear in view of what is stated in line 134, namely 'Each data point is a steady-state result measured after thermal equilibrium'."

Response:  Dear reviewer, we agree with you to some extent. This is our understanding of this issue. Figures 3b is intended to illustrate " the thermal stability time of the gain chip is in the order of 10^-3 seconds under conventional pump current injection." Figures 3c and d are both intended to illustrate "the thermal balance time of the FP is as long as 3 seconds approximately." In order to introduce the " the three-step process sequences" of the following text. It illustrates a dynamic process. “'Each data point is a steady-state result measured after thermal equilibrium” indicates that the results we measure are the results presented after the dynamic process reaches its steady state, rather than an uncertain temporary state during the process. These two points are not conflicting, nor are they completely unrelated. The purpose of the two explanations is different.

 

3. "There is a discrepancy between figures 1 b and 4 d. In Fig. 1 b, it seems that the FP filter moves to the red with increasing temperature, while in Fig. 4 d it moves to the blue. This seems to indicate that what matters here is the comb motion relative to the FP filter towards the red."

Dear reviewer, in our simulation, we moved the optical comb and FP towards each other. We agree with this point. However, this setup is not necessary. Whether the two move in opposite directions does not affect the results. If mode hopping occurs, the conditions before moving must be favorable for the original mode, while the conditions after moving must be more favorable for the new mode. However, the hysteresis of thermal conduction causes the conditions to be frozen at the original conditions during mode competition. This leads to the need to tune more temperatures in order for mode hopping to occur. This results in the mode hopping temperature being affected by the tuning direction.

Thank you again for reviewing our paper. Best wishes！

Author Response File: Author Response.pdf

Reviewer 3 Report

In this paper, the authors discuss thermal mode hopping in semiconductor laser with external cavity. Analytical discussions of the laser dynamics and bistability are given, which are in good agreement with experimental results. I recommend that this paper be published as an ``Photonics'' journal.

Author Response

Dear Reviewers:

We are very grateful to you for reviewing our paper.

Responds to the reviewers' comments：

Our article has been updated based on the feedback of various reviewers. The updated paper is attached as an attachment. Thank you for your review.

Best wishes！

Author Response File: Author Response.pdf

Reviewer 4 Report

The details of comments are attached in the file.

Comments for author File: Comments.pdf

Author Response

Dear Reviewers:

We are very grateful to you for reviewing our paper.

We have carefully considered the suggestion of you and make some changes.

Responds to the reviewers' comments：

1. "Semiconductor lasers with optical feedback from external cavity has been extensively studied in the past, and shown to exhibits a range of complex dynamics, such as stable fixed points, quasi periodic, chaos, etc. In the introduction, authors have talked only bitsability, not others. I suggest to add the details of other complex dynamics as well as the related literature."

Response: We appreciate it very much for this good suggestion. According to your ideas. We have added description of other dynamics to our introduction and inserted relevant literature references. We highlighted this modification on page 1, line 28-31, in the attached article.

2. "In Fig. 1, mention the parameters corresponding to experimental results."

Response: We are very sorry for our forgetting. The relevant measurement conditions have been annotated in the caption of Figure 1. In the attached article, we have also highlighted this change.

3. " In Eq. (1), write the names of all three segments L_k ."

Response: We agree with this suggestion. We have explained all the components involved after eq1. This added content has been highlighted on page 3, lines 71-72 of the attached article.

4. "As the Eqs. (8) and (9) are written directly, so include the reference from where these are taken."

Response: We agree with this suggestion. We have inserted relevant literature references on page 4, lines 97-99 of the new article and highlighted it in the attached article.

5. "On page 4, in line no. 93, the text “The center wavelength frequency” should be corrected."
Response: We are very sorry for our incorrect writing and it is rectified on page 4, line 99. In the attached article, we have also highlighted this change.

6. " Please mention somewhere the value of frequency spacing between two successive longitudinal modes of laser."

Response: We are very sorry for our forgetting. The the value of frequency spacing have been annotated in the caption of Figure 2. In the attached article, we have also highlighted this change.

7. "In Fig. 1, at the same temperature, two bistable modes differ slightly in wavelength, but consists of dramatically different powers. Can you explain physical reason behind it?"

Response: This is a good question, which can help us understand the dynamics behind the laser output mode. Referring to Opt. Express 2014,22(8143–8149),the dynamic equation for output power is

t is time. R is spontaneous emission rate. γ is cavity loss rate. g is linear gain. θ is differential gain coefficient. N₀ is the average inversion available for lasing. g_Bogatov is Bogatov gain. It will approach zero after lasing. When lasing, even if R,g and θN₀ are almost the same, due to the presence of FP, low power modes also require much greater static attenuation. This result in its significantly smaller lasing modes.

8. "On page 5, line no. 158, it is written that with the increase of temperature, the curve of FP and grating shifts blue, and the comb shifts red. Why an increase in temperature cause blue shift in optical comb, not red shift?"

Response: This is a good question, which can help us understand the material characteristics of different components. FP and grating are composed of quartz. The refractive index of quartz has a negative temperature drift coefficient. The optical comb is dominated by gain chips, which are compounds of three to five groups and have a positive temperature drift coefficient. The optical comb is dominated by gain chips, which are made of IIIV group compounds with a positive temperature drift coefficient. As a result, an increase in temperature cause blue shift in optical comb.

9. "In the text Fig. 2a is explained in detail, however, Fig.2b is not detailed enough. I suggest to elaborate the description of it more."

Response: We agree with this suggestion. We have added more detail in the caption of Figure 2 on page 6 and highlighted it in the attached article.

10. "On page 6, line no 179-180, it is assumed that the upper surface of the temperature controller always maintains a constant value. However, in practice it may not be true.
How the nonuniformity in temperature may affect the outcomes? As nonuniformity in temperature may change heating and cooling time. I suggest to add description of it."

Response: We agree with the idea of "it is assumed that the upper surface of the temperature controller always maintains a constant value. However, in practice it may not be true." But here, our understanding is as follows. Figures 3b is intended to illustrate " the thermal stability time of the gain chip is in the order of 10^-3 seconds under conventional pump current injection." Figures 3c and d are both intended to illustrate "the thermal balance time of the FP is as long as 3 seconds approximately." The existence of temperature gradients does not affect the thermal equilibrium time of the device itself. The purpose of Figure 3 is to illustrate the intrinsic thermal equilibrium time of the component. In practice, there may be temperature deviations, and temperature control drives may also experience oscillations. However, due to the extremely fast thermal balance speed of the chip, these disturbance factors often appear relatively slow. Therefore, these factors do not affect the inference of three-step process sequences, but only exacerbate jitter and instability.

11. "The results are presented for a fixed bandwidth of FP. If you change its value (small or large), how the outcome may change?"

Response: This is a good question, which can help us understand the filtering effect of FP. The half height width of the FP curve determines the width of the allowed mode interval. When the value increases or decreases, the range of the single stable mode of the thermal tuning curve will also change accordingly. Specifically, when the changes are moderate and there are not many modes that allow competition, the interval length of a single stable mode will show a positive correlation with the half width of the FP curve. However, when there are too many variables and too many allowed modes, the single mode lasing will be very unstable. A slight temperature disturbance can change the output mode.

12. "In the manuscript, nowhere, the role of strength of feedback is explained. I suggest to add details about it. How the variation in feedback strength may change the mode dynamics? It’s an important point to include it."

Response: We appreciate it very much for this good suggestion. According to your ideas. We have added descriptions of dynamics to our Configuration and Methods section. We highlighted this modification on page 4-5, line 122-148, in the attached article.

Thank you again for reviewing our paper. Best wishes！

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have adequately dealt with my remarks in the first review report and included the Bogatov effect in their paper. It can now be accepted as is.

Reviewer 4 Report

Authors have answered most of the comments, so manuscript can now be accepted for publication.