Transmission of Vortex Solitons in Three-Dimensional χ(2) Helical-Periodically Poled Ferroelectric Crystals
Round 1
Reviewer 1 Report
The work presented for review is carried out very correctly and my general assessment is positive, so I recommend its publication with very slight changes.
In the first place, I would like to point out that
the most original aspect of the work, the inclusion
of terms of spiral polarization, should be treated
in more depth, for example in eq. 3.
Another possible aspect to improve would be the appearance of Table 1, the ampersand "&" does not seem very appropriate for use in the table.
Finally, some discussion could be introduced
about the result obtained in Fig.6 and the
possible causes of it.
Author Response
The work presented for review is carried out very correctly and my general assessment is positive, so I recommend its publication with very slight changes.
In the first place, I would like to point out that the most original aspect of the work, the inclusion of terms of spiral polarization, should be treated in more depth, for example in eq. 3.
Response: We add more descriptions to explain the meaning of Eq. (3), like “It is evident that this Fourier series expansion provides a specific representation of the helical periodic polarization structure in cylindrical coordinates (r, θ, z) The phase factor Ï•d, serves as a modulation phase factor, where the magnitude of the index, n, determines the degree of distortion in the ferroelectric crystal. Through this phase-twisted modulation, a helical periodic polarized ferroelectric crystal can be formed.”
Another possible aspect to improve would be the appearance of Table 1, the ampersand "&" does not seem very appropriate for use in the table.
Response: The ampersand "&" in Table 1 is replaced by “,”.
Finally, some discussion could be introduced about the result obtained in Fig.6 and the possible causes of it.
Response: Discussions of “For larger input powers, spatial solitons exhibit stronger nonlinear effects, leading to enhanced self-focusing and beam convergence. This results in the gradual contraction of the soliton during propagation, accompanied by an increase in its energy density. Consequently, the nonlinear effects are further intensified. As a consequence, the soliton experiences stronger nonlinear interactions, such as self-phase modulation and self-phase modulation-induced optical pumping, which distort the soliton and reduce its propagation distance. Thus, as the input power increases, the stable propagation distance of the soliton decreases.” are added before the last sentence of the section 3 to explain the possible causes of the Fig. 6.
Reviewer 2 Report
In this MS the authors examine vortex solitons in helical-periodically poled quadratic crystals. In particular, they use a spiral periodic polarization in a ferroelectric cystal to embed the topological charge of the quadratic crystal. They show that such a structure stabilized quadratic two-component vortex solitons. I find that this paper is interesting and can be published provided that the authors respond to the following comments:
1. The authors do not perform linear stability analysis of their numerical solutions but they rely on direct numerical simulations. However, since there might be some slowly growing instabilities, I think that it is important to introduce random perturbation to they numerical solutions [Figure 1]. Then they should check that the solutions remain stable for much larger propagation distances.
2. In Fig. 3 the VK criterion is applied (d \beta/d P>0). Did the authors check that the solutions are stable everywhere along this curve by direct numerical simulations?
2. For vortex-antivortex states [Fig. 4] it is stated that “vortex-antivortex states can stably exist”. However, in Fig. 6 we see the stable propagation distance as a function of the power. Thus, the solutions are not actually stable but they have slowly growing instabilities. This should be clarified everywhere in the main text of the paper.
The English Language of the MS is acceptable.
Author Response
In this MS the authors examine vortex solitons in helical-periodically poled quadratic crystals. In particular, they use a spiral periodic polarization in a ferroelectric crystal to embed the topological charge of the quadratic crystal. They show that such a structure stabilized quadratic two-component vortex solitons. I find that this paper is interesting and can be published provided that the authors respond to the following comments:
- The authors do not perform linear stability analysis of their numerical solutions but they rely on direct numerical simulations. However, since there might be some slowly growing instabilities, I think that it is important to introduce random perturbation to they numerical solutions [Figure 1]. Then they should check that the solutions remain stable for much larger propagation distances.
Response: That is a very important suggestion for us to verify the validity of our work. We introduce random perturbation to all the numerical solutions by adding 0.1% noise. The solutions remain stable. But the stable propagation distance reduce to approximate 3.6 cm other than the original 10 cm. For a stable transmission of 3.6 cm, our conclusion is remained the same as when there is no perturbation. Because 3.6 cm is still a value that long enough for most commercially available crystals. Sentence of “The random perturbation noise of direct simulation is 0.1%.” is added to every figure caption and the corresponding place on the main content. And “The stable propagation length is 10 cm” is replaced by “The approximate stable propagation distance is 3.6 cm” in line 168.
- In Fig. 3 the VK criterion is applied (d \beta/d P>0). Did the authors check that the solutions are stable everywhere along this curve by direct numerical simulations?
Response: Yes, we get this conclusion by direct numerical simulations at everywhere along this curve. To emphasize this we add “This conclusion is verified by direct numerical simulations at everywhere along this curve.”
- For vortex-antivortex states [Fig. 4] it is stated that “vortex-antivortex states can stably exist”. However, in Fig. 6 we see the stable propagation distance as a function of the power. Thus, the solutions are not actually stable but they have slowly growing instabilities. This should be clarified everywhere in the main text of the paper.
Response: We agree with this. We use the word “stable” carefully and replace it to “robust” or “quasi-stable” instead. For example, in the last 4th sentence of the introduction part, “Simulation results show that stable vortex optical solitons can be formed in realistic parameter space.” is changed to “Simulation results show that quasi-stable vortex optical solitons can be formed in realistic parameter space.”. To clarify this, we add discussions of “The stable propagation distance as a function of the power. For larger input powers, spatial solitons exhibit stronger nonlinear effects, leading to enhanced self-focusing and beam convergence. This results in the gradual contraction of the soliton during propagation, accompanied by an increase in its energy density. Consequently, the nonlinear effects are further intensified. As a consequence, the soliton experiences stronger nonlinear interactions, such as self-phase modulation and self-phase modulation-induced optical pumping, which distort the soliton and reduce its propagation distance. Thus, as the input power increases, the stable propagation distance of the soliton decreases.” before the last sentence of the section 3.
Reviewer 3 Report
The manuscript entitled "Transmission of vortex solitons in three-dimensional χ2 helical-periodically poled ferroelectric crystals" is a valid research work with appropriate level of novelty and originality. The manuscript is devoted to vortex solitons containing fundamental-frequency and second-harmonic waves which can be stably propagate over a distance in a quadratic (χ(2)) LiNbO3 ferroelectric crystal possessing a special kind of helical-periodically poled structure. The topic of the manuscript fits well the scope of the journal. The introduction section clearly describes the state of the art in the specific field of the research, which is well-substantiated by the relevant references including the recent ones. The technical quality of the manuscript is high. The presented results are described and treated correctly. The conclusion section clearly substantiated by the obtained results. The results presented in this manuscript definitely goes beyond the state of the art and should have definite impact on the specific field of the research. With pleasure I can recommend this manuscript for publication as it is.
Author Response
The manuscript entitled "Transmission of vortex solitons in three-dimensional χ2 helical-periodically poled ferroelectric crystals" is a valid research work with appropriate level of novelty and originality. The manuscript is devoted to vortex solitons containing fundamental-frequency and second-harmonic waves which can be stably propagate over a distance in a quadratic (χ(2)) LiNbO3 ferroelectric crystal possessing a special kind of helical-periodically poled structure. The topic of the manuscript fits well the scope of the journal. The introduction section clearly describes the state of the art in the specific field of the research, which is well-substantiated by the relevant references including the recent ones. The technical quality of the manuscript is high. The presented results are described and treated correctly. The conclusion section clearly substantiated by the obtained results. The results presented in this manuscript definitely goes beyond the state of the art and should have definite impact on the specific field of the research. With pleasure I can recommend this manuscript for publication as it is.
Response: Thank you so much for the comment. We still work hard to improve our work during revision. More discussion and details of description are added or revised. We hope to present a quality work to Photonics magazine.
Reviewer 4 Report
1. The summary should be improved, it is very confusing.
2. Other references that highlight the work must be added in the introduction.
3. Give a better description of the results
Major corrections must be made in the English language so that it is understood
Author Response
- The summary should be improved, it is very confusing.
Response: In the conclusion part, the structure is rearranged and some descriptions are revised. We hope to improve the logicality of this part. The abstract is also revised.
- Other references that highlight the work must be added in the introduction.
Response: 9 references that highlight the work are added in the introduction.
- Give a better description of the results
Response: Thank you so much for the comment. More discussion and details of description are added or revised. Such as, we add discussions of “For larger input powers, spatial solitons exhibit stronger nonlinear effects, leading to enhanced self-focusing and beam convergence. This results in the gradual contraction of the soliton during propagation, accompanied by an increase in its energy density. Consequently, the nonlinear effects are further intensified. As a consequence, the soliton experiences stronger nonlinear interactions, such as self-phase modulation and self-phase modulation-induced optical pumping, which distort the soliton and reduce its propagation distance. Thus, as the input power increases, the stable propagation distance of the soliton decreases.” before the last sentence of the section 3.
Comments on the Quality of English Language
Major corrections must be made in the English language so that it is understood
Response: We check carefully through the manuscript and corrected the grammar mistakes. For example, in the 3rd sentence of the 2nd paragraph of the introduction part, “Vortex optical solitons carrying topological charges have various applications” is revised to “There are various applications for vortex optical solitons who carry topological charges”. All revisions to the manuscript are marked up using the “Track Changes” function. Please check the revised manuscript for the changes on the English expressions. We hope the quality of English language is improved greatly in the revised version.
Round 2
Reviewer 4 Report
OK
ok
