Optical-Frequency-Comb Generation Based on Single-Tone Modulation and Four-Wave Mixing Effect in One Single Semiconductor Optical Amplifier

Round 1

Reviewer 1 Report (Previous Reviewer 1)

The authors propose a study on the generation of comb by an SOA under direct modulation current modulation. The injected signal produces sidebands which then lead to even more modes by four-wave-mixing.

I still have an issue with Eq (1), the presence of ASE in the time evolution of A does not appear explicitly . Can the author justify the absence of ASE in the time evolution of the mode generated? This is a serious issue on the validity of the results presented in Section 4.

As mentioned in  a previous review, the direct modulation  is given by Io exp(iωmt). How can Eq. 5 converge since the modulation has a complex component and also a negative part for half a period? This has then
consequence on the equation of the gain and the field amplitude. In other words, what is the dc value of current applied to the SOA?

The variance of the power variation must be included in the paper. It gives information of the amplitude noise of the comb.

I am sure the authors can find some information on the physical limit of power injected in an SOA, the limit of the current modulation magnitude, and an the RF frequency limit.

I found also an experimental paper on comb expansion with SOA (https://doi.org/10.1364/OE.27.016560). This reference should be added to the paper.

Author Response

Dear editor and reviewers:

Thank you very much for your kind consideration of our manuscript. We thank the reviewers for their thoughtful comments and suggestions. Their comments have improved the manuscript effectively. We have studied the comments carefully and made corrections which we hope meet with approval. The main corrections are in the manuscript and the response to the reviewers’ comments are as follows. All changes made in the revised manuscript have been underlined and highlighted in yellow background.

Revision list according to the comments from Reviewer #1:

Q1) I still have an issue with Eq (1), the presence of ASE in the time evolution of A does not appear explicitly. Can the author justify the absence of ASE in the time evolution of the mode generated? This is a serious issue on the validity of the results presented in Section 4.

In the broad-band dynamic model, the influence of ASE has been considered, although the term of ASE does not appear in Eq. (1). Eq. (9) is the traveling wave equations for the ASE spectrum. Eq. (11) is the carrier density rate equation, where the fourth term on the right describes the effect of ASE on the carrier density. The ASE affects the carrier density N and the gain coefficient by Eq. (11), which in turn affects the light wave modes through traveling wave equations. A such theoretical model is widely used in references, such as Ref. [1, 2].

As for the validity of the results presented in Section 4, the proposed OFC generation method is simulated by using Optisystem in this paper. OptiSystem is an innovative, continuously updated, and powerful optical communication design software, which is widely used in the design and research of optical communication systems from device to system level, including SOA and its application research. The results show that Optisystem is reliable. Therefore, the simulation results in Section 4 are credible.

Q2) As mentioned in a previous review, the direct modulation is given by I₀exp(iω_mt). How can Eq. 5 converge since the modulation has a complex component and also a negative part for half a period? This has then consequence on the equation of the gain and the field amplitude. In other words, what is the dc value of current applied to the SOA?

Sorry, this question was not clearly stated last time. Although the modulation has a complex component and also a negative part for half a period, there is no need to worry about whether the carrier density rate equation Eq. (11) converges. There are two steps in the solution to our theoretical model.

The first step is to use Connelly's steady-state model (dN/dt=0) to calculate the carrier concentration distribution in the SOA through iteration as the second step’s initial condition. In this step, the injected current of SOA is a direct current, which is I₀/2. Therefore, Eq. (11) can converge.

The second step is to solve the dynamic carrier density rate equation (dN/dt≠0). The injected current of SOA is I(t). Firstly, we convert the differential equation into a difference equation to find the carrier density in the next period. Afterward, update the carrier density and substitute it into the traveling wave equations to calculate the optical power of each segment. In this step, there is no need to consider convergence.

Q3) The variance of the power variation must be included in the paper. It gives information of the amplitude noise of the comb.

The variances of the power variation have been calculated and added in the revised paper, which can be seen on page 7, line 1 and line 13; page 9, line 10; and page 10, line 4 of the revised paper and have been underlined and highlighted.

Q4) I am sure the authors can find some information on the physical limit of power injected in an SOA, the limit of the current modulation magnitude, and the RF frequency limit.

The limit of the power injected in an SOA is that the input optical power should not be too large. The SOA used in this paper is traveling wave SOA, in which both ends of the semiconductor chip are coated with an anti-reflection film (AR). If the input lightwave is too strong, it will damage the AR film on both ends, causing the SOA to not work properly. In addition, when the input optical power increases to a certain extent, gain saturation in SOA will occur, which makes the growth rate of OFC power decrease with the increase of input optical power. We have added “However, the input optical power should not be too large. If the input lightwave is too strong, it will damage the anti-reflection film on both ends of the semiconductor chip, causing the SOA to not work properly. In addition, when the input optical power increases to a certain extent, gain saturation in SOA will occur, which makes the growth rate of OFC power decrease with the increase of input optical power.” on page 10, line 8 of the revised paper.

The limit of the current modulation magnitude is that the injection current should not be too large. If the injection current is too large, a large amount of heat will be generated in the SOA, which will reduce its working performance and even burn it. It can be seen on page 7, line 15 of the revised paper.

The limit of the RF frequency is that the RF frequency should not be too large. As the RF frequency increases, the interval between the new frequency components produced by single tone modulation increases. Since the FWM effect weakens rapidly with increasing frequency interval, the FWM effect that occurs between new frequency components generated by single tone modulation will become weaker, thereby deteriorating the performance of the OFC. We have added “Since the FWM effect weakens rapidly with increasing frequency interval, the FWM effect that occurs between new frequency components generated by single tone modulation will become weaker, thereby deteriorating the performance of the OFC.” on page 9, line 6 of the revised paper.

Q5) I found also an experimental paper on comb expansion with SOA (https://doi.org/10.1364/OE.27.016560). This reference should be added to the paper.

Thank you for your suggestion. We have added this reference as reference [16] on page 2, line 6 and line 9 of the revised paper.

Thank you very much for your kind attention and I look forward to hearing a favorable reply from you.

Best regards,

Corresponding author: Zeyu Tan

E-mail: [email protected]

Reference

[1] Kyo Inoue, Takaaki Mukai, and Tadashi Saitoh. Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier. Appl. Phys. Lett. 1987, 51(14): 1051~1053

[2] Mukai T, and Saitoh T. Detuning characteristics and conversion efficiency of nearly degenerate four-wave mixing in a 1. 5-μm traveling-wave semiconductor laser amplifier. IEEE J. Quantum Electron. 1990, 26(6): 865~875

[3]   J. L. Wei, A. Hamié, R. P. Gidding, E. Hugues-Salas, X. Zheng, S. Mansoor, J. M. Tang, Adaptively modulated optical OFDM modems utilizing RSOAs as intensity modulators in IMDD SMF transmission systems, Opt. Express 18 (2010) 8556.

[4]   E. Thomas, Z. V. Rizouu, Semiconductor optical amplifier direct modulation with double-stage birefringent fiber loop, Appl. Phys. B 122 (2016) 158.

Reviewer 2 Report (New Reviewer)

In this manuscript entitled “Optical Frequency Comb Generation Based on Single Tone 2 Modulation and Four-wave Mixing Effect in One Single Semiconductor Optical Amplifier”, the authors propose a novel optical frequency comb (OFC) generation scheme based on single tone modulation and four-wave mixing (FWM) effect in one single semiconductor optical amplifier 10 (SOA) modulated by a radio frequency (RF) current. They present a broad-band dynamic model which considers single tone modulation and the FWM effect. I think the topic is of interesting, and the method is helpful for the design of OFC. However, there are minor issues which should be revised before the paper is accepted. My comments and questions are listed as below:

1.       They said “A comprehensive broad-band dynamic model which takes into account single tone modulation and FWM effect”. My question is how to takes into account both single tone modulation and FWM effect? And when do we take into them separately? In simulation Figure 2 (a), the result is achieved when FWM effect is ignored. Therefore, they need to explain the condition or situation that the FWM effect is ignored.

2.       Another big problem is this paper just shows the simulation results. I think they need give more evidence to prove the scheme can be used in the real application.

3.       In page 5, they said “The first term on the right side of equation (5) represents the carrier injection caused 109 by the modulated RF current.” I don’t figure out the presentation in Eq. (5). So is this a typo？

4.       What are the factors limiting the number of comb lines in their scheme? I think they also need to explain it.

Author Response

Dear editor and reviewers:

Thank you very much for your kind consideration of our manuscript. We thank the reviewers for their thoughtful comments and suggestions. Their comments have improved the manuscript effectively. We have studied the comments carefully and made corrections which we hope meet with approval. The main corrections are in the manuscript and the response to the reviewers’ comments are as follows. All changes made in the revised manuscript have been underlined and highlighted in yellow background.

Revision list according to the comments from Reviewer #2:

Q1) They said “A comprehensive broad-band dynamic model which takes into account single tone modulation and FWM effect”. My question is how to takes into account both single tone modulation and FWM effect? And when do we take into them separately? In simulation Figure 2(a), the result is achieved when FWM effect is ignored. Therefore, they need to explain the condition or situation that the FWM effect is ignored.

In our broad-band dynamic model, single tone modulation is taken into account by the first term on the right side of the equation (11). The injected RF current I(t) induces a time-dependent change in the carrier density in the SOA, which in turn changes the gain of the SOA. So the input CW light is directly modulated by the injected RF current. The third term on the right side of the equation (1) represents the FWM effects among lightwaves satisfying the condition of ω_j +ω_l =ω_k+ω_m. Therefore, in the broad-band dynamic model, both single-tone modulation and FWM are considered.

When the injected current of the SOA is an RF signal, single tone modulation occurs in SOA. In simulation Figure 2 (a), the result is achieved by setting the FWM coupling coefficients small so that the FWM term on the right side of equation (1) is approximately zero and the FWM effect can be ignored.

If FWM effect occurs in SOA, multiple lightwaves (at least two lightwaves) and phase matching are required. Because SOA has a linear structure and low dispersion, the phase matching is easily satisfied.

However, in this scheme, if the injected current of SOA is a direct current, single tone modulation does not occur and no new frequencies are generated. Then there is only one beam of light in SOA. Therefore, FWM effect does not occur.

Q2) Another big problem is this paper just shows the simulation results. I think they need give more evidence to prove the scheme can be used in the real application.

   Thank you for your valuable suggestions. As you said, the experimental data will greatly enhance the credibility and value of this work. We are sorry for the lack of this experimental condition, so it is difficult to supplement the experiment. However, although it is a simulation study based on models from previous papers, the results can also be proved credible.

On the one hand, the proposed OFC generation method is simulated by using Optisystem in this paper. OptiSystem is an innovative, continuously updated, and powerful optical communication design software, which is widely used in the design and research of optical communication systems from device to system level, including SOA and its application research. The results show that Optisystem is reliable, and the simulation results are credible.

On the other hand, direct modulation of SOA has been experimentally reported in the literature [3, 4]. FWM effect in SOA, in which new frequencies can be generated, is also widely experimentally investigated. Therefore, it is experimentally feasible to realize OFC using the single tone modulation and the FWM effect in SOA.

Q3) In page 5, they said “The first term on the right side of equation (5) represents the carrier injection caused by the modulated RF current.” I don’t figure out the presentation in Eq. (5). So is this a typo？

Thank you for reminding. Yes, It is a typo. We have already changed it into Eq. 11 and checked our paper again.

Q4) What are the factors limiting the number of comb lines in their scheme? I think they also need to explain it.

In this scheme, the factors limiting the number of comb lines are mainly the amplitude and the frequency of the injected RF modulation current.

Although the number of comb lines of the optical comb increases with the increase of the amplitude of the injection current, as shown in Fig. 3 in the paper, the injection current should not be too large, because a large amount of heat will be generated in the SOA, which will reduce the SOA’s working performance and even burn the SOA.

Although by appropriately tuning the modulation current frequency, an OFC with a tunable frequency interval within a certain range can be realized. However, as is shown in Fig. 4, with the increase of the modulation current frequency, the number of comb lines of the OFC decreases from 43 to 19, and the power variation of the OFC deteriorates from 8.82 dB to 17.07 dB. To avoid the degradation of SOA performance, the increase of the frequency of the RF modulation should be limited.

So we have added “The number of comb lines is limited by the amplitude and the frequency of the injected RF modulation current.” to the conclusion on page 6, line 18 of the revised paper.

Thank you very much for your kind attention and I look forward to hearing a favorable reply from you.

Best regards,

Corresponding author: Zeyu Tan

E-mail: [email protected]

Reference

[1] Kyo Inoue, Takaaki Mukai, and Tadashi Saitoh. Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier. Appl. Phys. Lett. 1987, 51(14): 1051~1053

[2] Mukai T, and Saitoh T. Detuning characteristics and conversion efficiency of nearly degenerate four-wave mixing in a 1. 5-μm traveling-wave semiconductor laser amplifier. IEEE J. Quantum Electron. 1990, 26(6): 865~875

[3]   J. L. Wei, A. Hamié, R. P. Gidding, E. Hugues-Salas, X. Zheng, S. Mansoor, J. M. Tang, Adaptively modulated optical OFDM modems utilizing RSOAs as intensity modulators in IMDD SMF transmission systems, Opt. Express 18 (2010) 8556.

[4]   E. Thomas, Z. V. Rizouu, Semiconductor optical amplifier direct modulation with double-stage birefringent fiber loop, Appl. Phys. B 122 (2016) 158.

Reviewer 3 Report (New Reviewer)

In this paper the authors propose, describe and simulate a novel optical frequency comb (OFC) generation scheme based on single tone modulation and four-wave mixing (FWM) effect in single tone modulation and four-wave mixing (FWM) effect in one single semiconductor optical amplifier (one single semiconductor optical amplifier (SOA) modulated by a radio frequency (RF) current. The proposed design  is novel and can advance the knowledge in the relevant research field. Nevertheless they are some points that need clarification and improvement in order for the paper to be accepted. More specifically:

1) I propose authors to clarify how a FWM and a single tone modulation gives a OFC theoretically.

2) The language of the paper needs improvement.

Author Response

Dear editor and reviewers:

Thank you very much for your kind consideration of our manuscript. We thank the reviewers for their thoughtful comments and suggestions. Their comments have improved the manuscript effectively. We have studied the comments carefully and made corrections which we hope meet with approval. The main corrections are in the manuscript and the response to the reviewers’ comments are as follows. All changes made in the revised manuscript have been underlined and highlighted in yellow background.

Revision list according to the comments from Reviewer #3:

Q1) I propose authors to clarify how a FWM and a single tone modulation gives an OFC theoretically.

In this scheme, only one single continuous-wave (CW) light with angular frequency ω_c is input into an SOA, whose injection current is a sinusoidal RF signal I(t) with angular frequency ω_m. The polarization direction of the input optical carrier is controlled by a polarization controller to excite the TE mode in the SOA. The injected RF current causes a change in the carrier density of the SOA, which in turn changes the gain of the SOA. Therefore, the input CW light is directly modulated by the injected RF current to generate several new frequency components which have the same polarization direction with the input at frequency ω_c+nω_m, where n = ±1, ±2, ±3 .... Meanwhile, the FWM effect will occur among these equally spaced lightwaves, resulting in additional new frequency components with the same adjacent frequency interval ω_m. Therefore, the combination of single tone modulation and FWM generates a large number of new frequency components. The optical spectrum produced by single tone modulation has a Gaussian distribution, and the FWM effect can make the power difference between frequency components smaller. Thus, an OFC with frequency interval ω_m can be achieved using this scheme.

To make our theory clear, we have added some explanations on page 3, which have been underlined and highlighted.

Q2) The language of the paper needs improvement.

We have checked our paper carefully, and improved our language.

Thank you very much for your kind attention and I look forward to hearing a favorable reply from you.

Best regards,

Corresponding author: Zeyu Tan

E-mail: [email protected]

Reference

[1] Kyo Inoue, Takaaki Mukai, and Tadashi Saitoh. Nearly degenerate four-wave mixing in a traveling-wave semiconductor laser amplifier. Appl. Phys. Lett. 1987, 51(14): 1051~1053

[2] Mukai T, and Saitoh T. Detuning characteristics and conversion efficiency of nearly degenerate four-wave mixing in a 1. 5-μm traveling-wave semiconductor laser amplifier. IEEE J. Quantum Electron. 1990, 26(6): 865~875

[3]   J. L. Wei, A. Hamié, R. P. Gidding, E. Hugues-Salas, X. Zheng, S. Mansoor, J. M. Tang, Adaptively modulated optical OFDM modems utilizing RSOAs as intensity modulators in IMDD SMF transmission systems, Opt. Express 18 (2010) 8556.

[4]   E. Thomas, Z. V. Rizouu, Semiconductor optical amplifier direct modulation with double-stage birefringent fiber loop, Appl. Phys. B 122 (2016) 158.

Round 2

Reviewer 1 Report (Previous Reviewer 1)

I am satisfied with the corrections made by the authors. I would be even more satisfied if they are included in their revised submission. I think the explanations you made on my Q1 and Q2 queries, bring clarity and credibility to your paper.

Author Response

Dear editor and reviewers:

Thank you very much for your kind consideration of our manuscript. We thank the reviewers for their thoughtful comments and suggestions. Their comments have improved the manuscript effectively. We have studied the comments carefully and made corrections which we hope meet with approval. The main corrections are in the manuscript and the response to the reviewers’ comments are as follows. All changes made in the revised manuscript have been underlined and highlighted in yellow background.

Revision list according to the comments from Reviewer #1:

Q1) I am satisfied with the corrections made by the authors. I would be even more satisfied if they are included in their revised submission. I think the explanations you made on my Q1 and Q2 queries, bring clarity and credibility to your paper.

Thank you for your good comments. The explanations of Q1 and Q2 have been added on page 6, line 11.

Best regards,

Corresponding author: Zeyu Tan

E-mail: [email protected]

Author Response File: Author Response.pdf

Reviewer 2 Report (New Reviewer)

I have carefully checked the revised manuscript. All comments I posed are answered. I think they have explained the questions well, so the revised manuscript can be accepted at this time.

Author Response

Dear editor and reviewers:

Thank you very much for your kind consideration of our manuscript. We thank the reviewers for their thoughtful comments and suggestions. Their comments have improved the manuscript effectively. We have studied the comments carefully and made corrections which we hope meet with approval. The main corrections are in the manuscript and the response to the reviewers’ comments are as follows. All changes made in the revised manuscript have been underlined and highlighted in yellow background.

Revision list according to the comments from Reviewer #2:

Q1) I have carefully checked the revised manuscript. All comments I posed are answered. I think they have explained the questions well, so the revised manuscript can be accepted at this time.

Thank you for your good comments.

Best regards,

Corresponding author: Zeyu Tan

E-mail: [email protected]

Author Response File: Author Response.pdf

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

The authors are presenting a paper on the simulation of an SOA under optical injection and direct current modulation. With this scheme, they propose to produce an optical comb.

I have some issues with the model proposed:

1) The term of amplified spontaneous emission does not appear in Eq. 1). How can the authors guarantee that the modes will not be affected by the amplified spontaneous emission?

2) The carrier dependence of the gain does not appear in Eq 2). It is through fc and fv. I suggest the authors include the expression of fc and fv with the carrier dependence.

3) The modulation expression is given by I0 exp(iωmt). How can Eq. 5 converge since the modulation has a complex component and also a negative part for half a period? This has then consequence on the equation of the gain and the field amplitude.

3) The reader will need a simulation of the ASE spectrum (no modulation no injection) and a simulation without FWM but injection and modulation of SOA. Through the paper there is no proof of FWM.

4) In Section 4, how can the authors be sure of the value of the power variation since Eq. 1 does not include the ASE.

5) The variance of the power variation should be also included in their assessment.

6) According to the authors is there a limit to the value of I? Is there a limit to the power injected? What is the limit of the RF modulation?

Reviewer 2 Report

The authors present a method for optical comb generation based on RF modulation over an SOA with CW light input for amplification. The comb line number is as large as 43 with 10GHz RF tone modulation. This result is very much attractive given the very simple realization and very effective comb generation performance. However, it is a simulation study based on models from previous papers, which makes the results somehow questionable. For example, the principle of FWM between carrier and the sideband tones generated by the RF modulation of the carrier is not reasonable. And the SOA amplification can hardly goes to 10GHz for modulation due to the carrier dynamics. And certain length of the SOA is needed for the nonlinear process including the so called FWM, but also SPM, meaning that certain requirements of SOA have to be satisfied. Generally, I think there are too many concers regarding the principle and simulation resutls cannot clear those concerns. It is highly useful work if it can really work. I suggest the authors try to prove it experimentally and then resubmit.