Structurally Stable Astigmatic Vortex Beams with Super-High Orbital Angular Momentum (ABCD Matrix Approach)
Round 1
Reviewer 1 Report
The ABCD matrix method in the article simplified the mathematical description of astigmatic transformations of structured beams, and through this method, this article showed the spherical lens’ ability to turn a structurally unstable astigmatic structured LG beam into a stable one. I think the results of this article have certain theoretical value. I have the following questions and suggestions:
1. β in Fig. 1 b is not found in the theory section, is it θ in the text?
2. In Fig. 5, there are four graphs with two curves, I thought you should add a legend to make the results clearer and more intuitive.
3. ε and θ, which first appear in formula (4), need to explain what they represent.
I think it can be published after solving the above problems.
Author Response
Responses to reviewer comments are in the PDF file
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In the present paper, higher-order structured Laguerre-Gaussian beams (sLG) are transformed into structurally stable astigmatic sLG beam by using the ABCD matrix approach. The analytical expressions are derived. Based on the obtained analytical formula, the corresponding numerical simulations are performed, and the corresponding analyses are detailed. This research is original and interesting. Furthermore, this study is beneficial for researchers in the field of photonics. Therefore, it can be accepted for publication after addressing the following minor revisions:
1. English expression needs further improvement. Laguerre-Gaussian beams (sLG) beam is incorrect.
2. What is the inherent logic of 2.1 to 2.4? Please explain clearly in the text.
English expression needs further improvement. Laguerre-Gaussian beams (sLG) beam is incorrect.
Author Response
Responses to reviewer comments are in the PDF file
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors employed the ABCD calculation to elucidate the astigmatism induced by cylindrical and spherical lenses in structured light beams. They conducted numerical simulations to analyze the propagation of astigmatic Laguerre-Gaussian modes at various distances. Furthermore, they demonstrated that a spherical lens has the capability to transform a structurally unstable LG beam into a stable one in the far diffraction domain.
To enhance the impact of the paper, it is recommended that the authors perform experimental validation and compare the obtained results with the theoretical predictions.
One noteworthy concern is the inadequacy of the bibliography review conducted by the authors, as several pertinent papers have been omitted. It is imperative that the authors incorporate the following papers related to astigmatism in structured light into the introduction section:
- P. Vaity, J. Banerji, and R. P. Singh, "Measuring the topological charge of an optical vortex using a tilted convex lens," Phys. Lett. A 377, 1154 (2013). [DOI: 10.1016/j.physleta.2013.02.030]
- B. Pinheiro da Silva, D. S. Tasca, E. F. Galvão, and A. Z. Khoury, "Astigmatic tomography of orbital-angular-momentum superpositions," Phys. Rev. A 99, 043820. [DOI: 10.1103/PhysRevA.99.043820]
- B. Pinheiro da Silva, B. A. D. Marques, R. B. Rodrigues, P. H. Souto Ribeiro, and A. Z. Khoury, "Machine-learning recognition of light orbital-angular-momentum superpositions," Phys. Rev. A 103, 063704. [DOI: 10.1103/PhysRevA.103.063704]
- Wagner Tavares Buono et al. "Eigenmodes of aberrated systems: the tilted lens," Optics (2022, Vol. 24, p. 125602).
- Atirach Ritboon. "The effect of astigmatism induced by refraction on the orbital angular momentum of light" Optics (2020, Vol. 22, p. 075201).
Upon addressing these recommendations and enhancing the bibliography review, I am inclined to recommend the paper for publication.
Author Response
Responses to reviewer comments are in the PDF file
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
I agree with the modifications.
