Geometric Representation of Vector Vortex Beams: The Total Angular Momentum-Conserving Poincaré Sphere and Its Braid Clusters

Round 1

Reviewer 1 Report

In this paper, the Total Angular Momentum-Conserving Poincaré sphere (TAM-C PS), a new framework for effectively characterizing diverse vector vortex beams, is presented. Comparing with the existing Poincaré sphere, the TAM-C PS offers a more generalized approach and clearer physical interpretation. It represents the first clear and unified approach to express multiple Poincaré spheres within a single framework. Broadly speaking, the investigation of the TAM-C PS is interesting.

1. The efficacy of the total angular momentum-conserving Poincaré sphereand presented in this work should be verified experimentally.

2. The curves with black and blue colors seem to be similar in Fig. 3 and Fig. 4. It’s hard to distinguish them visually. Please modify them.

3. In Fig. 4, the blue line is corresponding to the PS-OAM. However, the authors describe that the blue line represents HyOPs in the lines 185. The author should check if the statement is correct.

4. How to calculate the geometric phase during cyclic evolutions for the TAM-C PS framework? And comparing to the existing Poincaré sphere, where is the facilitation of the geometric phase calculation for the TAM-C PS framework reflected? Time complexity? Space complexity or something else?

Minor editing of English language is required.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

By linking the poles of different TAM-C PSs, the authors constructed TAM-C PS braid clusters that provide a comprehensive framework for the representation and characterization of vector vortex beams under the paraxial approximation. 

However:

1)Vector vortex beams are usually used in scattering materials.

2)Vector vortex beam shall be expanded during the propagation process.

3)There is no experiment.

4)The interactions between vector vortex beam and materials are more important.

English should be further improved.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

1. The explanation about the calculation of the geometric phase during cyclic evolutions for the TAM-C PS framework is not clear.

2. The present results lack experimental verification.

3. The authors didn’t explain and stress the modification of the abstract part. 

Moderate editing of English language required.

Author Response

Please see the attachment thank you!

Author Response File: Author Response.docx

Reviewer 2 Report

It is not complicated for the authors to do the related experiments. They should provide experimental resluts to support the corresponding viewpoints.

Author Response

Please see the attachment thank you!

Author Response File: Author Response.docx

Round 3

Reviewer 1 Report

The article has been revised as requested and can be considered for publication.

The article has been revised as requested and can be considered for publication.

Author Response

Dear reviewer,

I made some modifications in the conclusion. The part in red font is what I have revised this time.

According to the feedback from this review, I have removed the revision marks made in the first and second rounds of review.

Thank you for your time and assistance!

Best wishes

Reviewer 2 Report

Nothing

Author Response

Dear reviewer,

I made some modifications in the conclusion. The part in red font is what I have revised this time.

According to the feedback from this review, I have removed the revision marks made in the first and second rounds of review.

Thank you for your time and assistance!

Best wishes