Dynamics of Fractional Vortex Beams at Fraunhofer Diffraction Zone

Round 1

Reviewer 1 Report

In this manuscript, the authors studied the dynamics of fractional vortex beams at Fraunhofer diffraction zone. Follows the ref. [10], this work shows a complete picture of the behavior of the phase singularities of non-integer fractional vortex beams in the Fraunhofer diffraction region and have found the original beam waist results to be a key factor for the beam profile topology. I think this manuscript may be useful and can be published in “Photonics” after the authors addressed the following comments.

 1.     In Figure 1a, I’ll suggest a topological charge between an odd n to n+1 and then mark the tourist vortex.

2.     In the introduction, some recent literature is missing for the discussion of fractional vortex beam. I suggest some recent references, such as the review paper of fractional vortex [Nanophotonics, 11(2), 241-273, 2022], superhigh-resolution recognition of fractional vortex [Phys. Rev. Lett., 123, 183902, 2019], and metasurface for fractional vortex [Laser Photonics Rev. 15, 2000351, 2021].

3.     The authors should give the reference for the Eq. (1).

4.     The authors should explain in the revised paper how to locate the ‘center’ after propagating to the Fraunhofer diffraction zone, especially for multiple singularities, as the center is important for calculating the distance ‘d’. I also feel confused for the measurement of ‘d0’, which is defined as ‘radius of the beam or the real beam extension’ by the authors. These details should be explained in the revised paper.

5.     The authors discussed the topological charge measurement error in different ranges, <n+0.5 or >n+0.5, where n is integer topological charge. While it seems the method proposed by the authors cannot measure the topological charge between n and n+0.1 (or n+0.15) for small topological charge. As the absolute value of the topological charge increases, the measurable range appears to be smaller. So, the measurable range of the proposed method should be discussed in the paper and mentioned in the conclusion.

6.     Considering a Gaussian beam with finite beam width is one of the highlight of this paper compared with reference 10. The authors also discussed it in figure 3. So, is there any relationship between the beam width and TC’s measurement error and measurable range? It should be discussed in the paper.

7.     For figures: the size, thickness and color of fonts and curves are worth improving. This will help the reader quickly understand the conclusion that the figure wants to express.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The authors have studied the dynamics of optical singularities in fractional charge vortices at the Fraunhofer zone, both theoretically and experimentally. They highlight a possible disagreement in the community on the vortex strength of non-integer optical vortices at the far-field. By changing the beam waist radius, the authors show that the distance between the singularities also varies. The experimental results agree well with the theory, with low error. Hence, I find the manuscript suitable for publication in Photonics.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

All comments are in the attached file

Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The authors answered all my questions.