Enhancement of Self-Collimation via Nonlinear Symmetry Breaking in Hexagonal Photonic Crystals

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript presents a study on enhancing the self-collimation (SC) effect in photonic crystals (PCs) through optical nonlinearity. The authors employ both the Plane Wave Expansion (PWE) method and Finite-Difference Time-Domain (FDTD) simulations to investigate the nonlinear SC behavior, reporting improved propagation and higher transmission. While the topic is interesting and relevant, there are several critical issues that must be addressed before the manuscript can be considered for publication:

1.Use of PWE Method in Nonlinear Systems:
It is unclear how the Equifrequency Contours (EFCs) of a nonlinear system are obtained using the PWE method, which is traditionally valid only for linear, periodic structures with well-defined eigenvalue problems. In systems with Kerr-type nonlinearity, the refractive index becomes intensity-dependent, breaking the assumptions of linear eigenmode analysis.

The authors should clarify whether the nonlinear PC is approximated as a linear PC with an effective refractive index shift. If this approximation is used, the potential inaccuracies should be discussed, and its impact on the EFC results (e.g., Fig. 3) should be assessed. The physical meaning of these EFCs in the context of nonlinearity remains ambiguous and should be explained.

2.Description of the Nonlinear Mechanism:
More details should be provided regarding how the nonlinear effect (Kerr nonlinearity) is realized in the system: How is the Kerr effect induced in practice? Where and how is the pump beam introduced to achieve the required nonlinear index modulation? Are there any practical considerations or constraints on the pump intensity or material properties?

3.Consistency Between FDTD and PWE Approaches:
The FDTD method is capable of simulating nonlinear systems directly, but it is not clear how the results from FDTD simulations are compared with those obtained via PWE analysis. Are both methods treating nonlinearity in the same way (e.g., as a static index change)? If so, this treatment may not capture the full dynamics of Kerr nonlinearity. The authors should discuss whether the results from these two methods are consistent and how the validity of comparisons is ensured.

4.Field Distribution Results:
The manuscript would benefit from the inclusion of field distributions associated with the SC modes: In particular, the field distribution corresponding to the SC modes shown in Fig. 3 (presumably obtained via PWE) should be presented. For Fig. 4, the field distribution should also be provided to demonstrate the beam profile. This can be done by showing Ez field snapshots, preferably with zoomed-in views to highlight the SC behavior.

5.Justification for Using Nonlinearity:
While the use of Kerr nonlinearity is central to the paper, the manuscript does not adequately justify why this approach is preferred over simpler methods such as changing the material composition or geometry of the PC to modify the EFCs. 
The authors should clarify what specific advantages Kerr nonlinearity provides for enhancing SC performance. Is the nonlinear response tunable in ways that material design is not? A comparison with conventional (linear) tuning strategies would strengthen the argument for nonlinearity-based design.

The authors are encouraged to address the above points in detail and revise the manuscript accordingly. Clarifying these theoretical and methodological aspects will significantly improve the scientific rigor and clarity of the work.

Author Response

"Please see the attachment."

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Reviewer comments:

In the present study, the author investigates how introducing Kerr-type nonlinearity and symmetry (nonlinear) reduction in hexagonal photonic crystals (PCs) can enhance self-collimation (SC), a phenomenon where light propagates without dispersion. The study employs a low-symmetry hexagonal photonic crystal (LSHPC) made of nonlinear LiNbO₃ rods. The symmetry of the PC is reduced by introducing auxiliary rods with varied radii. Plane-Wave Expansion (PWE) and Finite-Difference Time-Domain (FDTD) are used to simulate self-collimation characteristics, transmission spectrum, group velocity dispersion and third-order dispersion. The results demonstrate that by increasing the nonlinear index, the EFCs are significantly flattened, thereby enhancing self-collimation. Also, beam confinement is improved through symmetry-lowering perturbations that enable all-angle self-collimation.

The work is interesting and can be implemented in various photonic devices. However, several concerns need to be addressed before the manuscript can be considered for publication in the Journal of Photonics. The reviewer’s comments and suggestions are as follows:

1. The author described how lowering the symmetry of a photonic crystal can be useful for various applications, anisotropic propagation, the slow light effect, mode decomposition, etc. However, the manuscript should also address how symmetry reduction impacts the complete photonic bandgap. In particular, the author should clarify whether lowering the symmetry leads to a diminished or incomplete photonic bandgap.
2. It is important to present a comparison of the photonic bandgap with and without the inclusion of Kerr-type nonlinearity in the LSHPC structure. This would help illustrate the effect of nonlinearity on the band structure.
3. Self-collimation can also be achieved in photonic crystals with high symmetry. Therefore, the author should justify the choice of a low-symmetry lattice for enhancing self-collimation. Is this choice motivated by design advantages, or are there fabrication constraints associated with high-symmetry lattices?
4. The manuscript should explain how the incorporation of Kerr-type optical nonlinearity enables dynamic tunability of the self-collimation effect in photonic crystals.
5. The following sentence appears to be repeated in the manuscript: “Also, all-angle self-collimation was obtained. Low-index material was preferred, and the upper bands were studied.” Please revise to eliminate redundancy.
6. For further context on enhanced self-collimation through high-index nanoparticles, the author is encouraged to reference the following study: Khatun, N., Sridurai, V., & Nair, G. G. (2023). Nanoscale, 15(44), 17808–17817.
7. Is the reported 6.5% relative bandwidth significantly better than existing results in the literature?

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

In this manuscript, the authors propose the use of a low-symmetry hexagonal photonic crystal (LSHPC) composed of LiNbO₃ nonlinear rods that include Kerr-type nonlinearity to improve self-alignment, transmission spectrum, group velocity dispersion (GVD), and third-order dispersion (TOD). The low-symmetry hexagonal photonic crystal structure consists of rods in the air.
As an overall recommendation, the reviewer feels the manuscript in present form is not suitable for publication. The main concern is the lack of novelty. However, the manuscript can be reconsidered pending some revisions and modifications as follows:
1.    Given that symmetry breaking causes more optical noise in nonlinear systems, add the effects of this noise on the system performance in the paper.
2.    It is recommended to compare the results of other methods for analyzing and simulating optical structures, such as the Monte Carlo simulation and the Green's function method, with the current methods, and incorporate them into the manuscript.
3.    It is mentioned that Figure 7 shows the field propagation in the optimized NLLSHPC.  But there is no optimization method or algorithm for the proposed structure? Please clarify.
4.    Please compare and analyze the enhancement of self-alignment achieved through nonlinear transformations, such as SHG and THG, with the current method.
5.    Given the existence of materials such as AlGaAs and GaAs with high nonlinear coefficients, explain the reason for using LiNbO₃ nonlinear rods.
6.    The authors should investigate the performance of the proposed method in mitigating phase fluctuations or instabilities in the optical response of the system under small design changes.
7.    Although the results are based on the simulations, the important parameters of the manuscript, such as operating bandwidth and self-alignment, should be compared and validated with the experimental results.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript presents a study on enhancing the self-collimation effect in photonic crystals through optical nonlinearity. Both the theoretical analysis and methodological approach are sound, and the manuscript is recommended for publication.

Author Response

Author's Reply to the Review Report (Reviewer 1)

Comments and Suggestions for Authors

Reviewer comment:

The manuscript presents a study on enhancing the self-collimation effect in photonic crystals through optical nonlinearity. Both the theoretical analysis and methodological approach are sound, and the manuscript is recommended for publication.

 

Response to Comment:

I sincerely thank the Reviewer for taking the time to evaluate my manuscript and for the positive assessment. I truly appreciate your recognition of the theoretical and methodological contributions of my study. Your encouraging feedback is highly motivating and greatly valued.

 

 

 

 

 

 

 

Reviewer 2 Report

Comments and Suggestions for Authors

The author has addressed all reviewer comments. The manuscript is now suitable for publication in the Journal of Photonics.

Author Response

Author's Reply to the Review Report (Reviewer 2)

 

Comments and Suggestions for Authors

Reviewer comments:

The author has addressed all reviewer comments. The manuscript is now suitable for publication in the Journal of Photonics.

 

Response to Comment:

I sincerely thank the Reviewer for taking the time to evaluate my manuscript and for the positive assessment. I truly appreciate your recognition of the theoretical and methodological contributions of my study. Your encouraging feedback is highly motivating and greatly valued.

 

Reviewer 3 Report

Comments and Suggestions for Authors

In the revised version, the main part of comments is considered and addressed. However, the main concern regarding the novelty is yet remine. As mentioned, "This study is based on the low-symmetry structure used in reference [29]." It is recommended to highlight the novelty in the manuscript. Also, the position of MONITOR in the "low-symmetry hexagonal photonic crystal (LSHPC) structure; Figure 2" should be corrected, because the detector is not in the LSHPC.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf