Dynamics of the Frequency Shifts in Semiconductor Lasers under the Injection of a Frequency Comb
Round 1
Reviewer 1 Report
The paper "Dynamics of the frequency shifts in semiconductor lasers under the injection of a frequency comb" presents some results on frequency locking of a semiconductor laser with a frequency comb is injected into the laser. Locking regimes are studied for varying detuning frequencies, injection currents and comb line spacing. Different regions of locking/frequency pulling and pushing are identified. It is shown that the spacing between comb lines strongly affects the locking bandwidth. The results are interesting for the specialists in the field and may be useful for telecommunication applications.
The paper can be accepted after some issues are addressed.
1) It is not clear if the laser cavity resonances are taken into account. What is the value of the laser cavity inter-modal spacing? How it is compared to the tuning range and the comb spacing?
2) It is stated that "the frequency comb spacing has a crucial role on the locking map of semiconductor laser ". Is there any characteristic frequency or time scale in the system to which the comb spacing should be compared to say if it is small or large?
3) Not all parameters and abbreviations are defined in the text. For example, line 63, what is "master signals MLm"? Are they comb lines?
4) Clarification of some sentences is needed.
For example, line 81: " The SL is injected with the frequency comb (with the spacing ∆ = 0.2 GHz) and the central peak (f3) is swapped in frequency and injection level" must be rewritten.
Line 184: " the spacing of the come increases". Should be "comb"?
Overall, the paper can be accepted after revision.
Author Response
We would like first to thank the reviewer for his valuable comments and here is our response:
1) It is not clear if the laser cavity resonances are taken into account. What is the value of the laser cavity inter-modal spacing? How it is compared to the tuning range and the comb spacing?
Answer: In fact, our parameters are all obtained through experimental characterization as mentioned in the manuscript and listed in Table 1. The mode spacing in our laser is estimated to be 0.3 nm and this value is used to calculate the differential gain mentioned in the table, which is used in our simulation. However, since the laser is assumed to be a single mode DFB laser, this mode spacing can be considered in low injection current (near threshold) or in other words in the Amplified Spontaneous Emission (ASE) region. Now, since the injection current in our case is far above threshold (twice the threshold current as listed in the table), the effect of mode spacing can be neglected.
This idea is explained and added in the manuscript at line 126.
2) It is stated that "the frequency comb spacing has a crucial role on the locking map of semiconductor laser ". Is there any characteristic frequency or time scale in the system to which the comb spacing should be compared to say if it is small or large?
Answer: As mentioned before, since the SL is a single mode laser, the only way is to compare it with frequency detuning (the difference between the SL peak and the central frequency of the comb.
3) Not all parameters and abbreviations are defined in the text. For example, line 63, what is "master signals MLm"? Are they comb lines?
Answer: You probably did not notice what we have written in line 61:(m represents the order of the frequency in the comb (m=1,2,3,4,5)). We have checked again the rest of the parameters.
4) Clarification of some sentences is needed.
For example, line 81: " The SL is injected with the frequency comb (with the spacing ∆ = 0.2 GHz) and the central peak (f3) is swapped in frequency and injection level" must be rewritten.
Answer: we have rewritten the sentence to read:
The master frequency comb MLm (with the spacing ∆ = 0.2 GHz) is injected inside the cavity of the SL. It's central peak (f3) is then swapped from -20 GHz to +20 GHz at each injection level (from 0 – 0.7) to draw the map shown in Figure 2.
Line 184: " the spacing of the come increases". Should be "comb"?
Answer: Corrected.
Reviewer 2 Report
In the manuscript, the authors build the model based upon Lang’s approach, and numerically investigate the effect of the injection of a frequency comb (master laser, ML) on the frequency shifts of a semiconductor laser (slave laser, SL). Results show that the injection level, spacing of the comb and frequency detuning can affect the frequency shift of the slave laser, and the spacing of the comb have an influence on the locking bandwidth. These analytical results may be instructive to the experiment with a frequency comb injection. The manuscript can be considered for publication if the following comments can be well addressed.
1. Line 62: “△ωmt-φ0(t)” refers to phase difference. It would be clearer to use △φm rather than △tm to represent this variable.
2. Line 66: The injection strength Km appears without suddenly and it is not mentioned in any equations before. It can be better to replace “Em/E0(t)” by “Km/(P)1/2” in equation (2). Otherwise, it would be confusing for the readers.
3. Line 68: The power of each comb line is assumed to be the same. But in reality, the comb lines are not in a same power level. I wonder how it would affect the numerical results. Besides, I also wonder how the number of the comb lines influences the numerical results.
4. As demonstrated in section “Materials and Methods”, the number of the comb lines is 5 and the power of each comb line is equal. However, it seems that the number of comb lines is bigger than 5 and the power is different. Please add some explanations.
5. Line 70: it should be 15 GHz rather than -15 GHz.
Author Response
We would like first to thank reviewer for their valuable comments and here is our response:
1- Line 62: “△ωmt-φ0(t)” refers to phase difference. It would be clearer to use △φm rather than △tm to represent this variable.
Answer: Sure, we have changed that in the equations as well.
2-Line 66: The injection strength Km appears without suddenly and it is not mentioned in any equations before. It can be better to replace “Em/E0(t)” by “Km/(P)1/2” in equation (2). Otherwise, it would be confusing for the readers.
Answer: K is the injection level and is not used in running the rate equations. It is defined to draw the injection locking map. Eos is the electric field of the free-running SL, while Eo is the the electric field of the injected SL.
3- Line 68: The power of each comb line is assumed to be the same. But in reality, the comb lines are not in a same power level. I wonder how it would affect the numerical results. Besides, I also wonder how the number of the comb lines influences the numerical results.
Answer: In terms of the inequality in comb lines power in reality, we believe that needs experimental investigation or one may slightly vary the power of the lines and see the effect. This can be the future work. The same thing is said for the the effect of changing the number of comb lines to be investigated in the future.
We have added this in the conclusion.
4- As demonstrated in section “Materials and Methods”, the number of the comb lines is 5 and the power of each comb line is equal. However, it seems that the number of comb lines is bigger than 5 and the power is different. Please add some explanations.
Answer: We have added a sentence (line 117) to explain this :
"However, due to the gain inside the cavity, the comb number and power largely altered according to their position relative to the SL peak."
5- Line 70: it should be 15 GHz rather than -15 GHz.
Answer: Corrected
Round 2
Reviewer 2 Report
The authors have revised manuscript by considering my previous comments. I recommend its publication now.
