Review Reports

Round 1

Reviewer 1 Report

This manuscript studies the cross-spectral density (CSD) distributions of a partially coherent Laguerre-Gaussian (PCLG) vortex beam transmitting through a couple of CLs with varying angles. The TC of PCLG with different coherence could be determined when the included angle of CLs rotated from 90° to 0°. This manuscript is instructive and could be considered for publication after the following issues have been addressed.

1) Reference 1 is lost in the Introduction section.

2) The authors should explain the concept of cross-spectral density in more detail, because this term appears repeatedly in the manuscript.

3) The authors claim that the relationship between the number of bright stripes and the TC is N=2|l|+1 in Line 127, but from the simulated results in the third and fourth columns of Figure 1, this statement does not seem to be very appropriate. To make the reader more intuitive about the results, it is recommended to mark the number of bright stripes on the graph.

4) It is proposed in Line 158 that the relationship between TC and stripes is clearer when the angle near 30° (with σ_g=0.4ω₀, l=±2). I think the relationship between the included angle of CLs and the visibility of the stripes can be further investigated to reveal the specific relationship between the σ_g and CL’s angle. For an example, the optimal included angle depending on the degree of coherence is given. 

Author Response

Thank you for your suggestions. Please refer to the attachment for specific responses.

Author Response File: Author Response.docx

Reviewer 2 Report

The authors in the manuscript entitled “Topological charge measurement of a partially coherent vortex beam using dual-cylindrical-lens with arbitrary angle”, provided a general scheme for the TC measurement of PCLG vortex beam covering situations of coherence from very low to very high. The quantitative relationship between the sign and magnitude of TC and the CSD amplitude and phase after propagating through a dual-cylindrical-lens with adjustable angles were thoroughly studied, which were demonstrated both in theory and experiment. This work has potential applications in free-space and turbulence-atmosphere optical communications.

However, there are still some aspects that can be improved. This manuscript can be published with considering to the following suggestions.

1.          In line 51, please confirm whether the references and statements are consistent in “diffraction measurement [18], interferometry [19-21], …”. It seems that it should be “interferometry [18], diffraction measurement [19-21], …”. Besides, in addition to Reference 9, all other references were studied before 2021, so it is necessary to keep abreast of research trends and add some references for the latest advances and applications.

2.          It is recommended to add a schematic diagram in the “Theory” Section, indicating the coordinates and parameters involved in the theoretical formula, as well as the corresponding transformation process, etc.

3.          In the “Simulation results” Section, whether the different sizes of parameters z₀, s, and z affect the simulation results, and whether there are any points needing attention when selecting their values.

4.          In line 126-128, “The relationship between the number of bright stripes and TC is N = 2|l|+1. In addition, the number of singularities or dislocations is twice of the TC magnitude, i.e., M = 2|l|.”. It seems hard to find the difference between Fig. 1(b) and Fig. 1(c). It is necessary to mark their differences in the figures. In addition, please qualitatively explain this quantitative relationship.

5.          In the Part “4.2. Experimental results and discussions”, there is only the experimental results with medium coherence width (σ_g = 0.4?₀). In order to better demonstrate the consistency between theory and experiment, the experimental results with low and high coherence widths should be added.

Author Response

Thank you for your suggestions. Please refer to the attachment for specific responses.

Author Response File: Author Response.docx

Reviewer 3 Report

The authors develop and analysis of the vortex beam information like TC and CSD amplitude and phase of partially coherent LG beams. Both the numerical simulations and the experiments are correctly developed and confirm the interest of the methods in particular when varying the beam coherence with the rotating disk. I outline the following points to clarify and complete informations on the present form of the paper :

- Mention the incident beam polarizations on the SLM in Fig 1. Characteristics of the used SLM, number of pixels and size.  

- The physical significance of the CL angle to apply for low or high coherence is not well explained . How the amplitude of the pertubation values may affect the quality of the results in case of low and high coherence. 

- Simulation and experimental results are limited to low l values +1 or l+2 + 3 . What is the evolution of the quality of simulation and of experimental results when the l value is increased as is the case in applications to communications and encryption. 

- Is there a clear reason for good results of phase distribution and TC evaluation at an CL angle of 30°. 

To conclude the manuscript is of interest in terms of novel methods for LG vortex beam characterization. However it is recommended to consider the above comments and questions before being accepted for publication in the journal. 

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 4 Report

Generally speaking, the authors forgot to mention that the measurement of the magnitude and sign of the topological charge of polychromatic vortex beams using a single cylindrical lens was predicted and experimentally investigated back in 2009 in the article doi.org/10.1364/OE.17.023374. The theory of this problem for simple monochromatic beams using a single cylindrical lens was developed in the article doi.org/10.1364/AO.56.004095, and for a more general case - in the article doi.org/10.1364/AO.396557. Obviously, the extension of this problem to the case of partial coherence should rely on the use of the cross-spectral density function. Therefore, before setting the problem in this article, the author should discuss in detail these articles and justify the need to use a second cylindrical lens.

 

It seems that the theoretical section 2 breaks off without revealing the main thing - the relationship between the number of bright stripes of the intensity pattern and the topological charge. This formula appears suddenly in Section 3. Then why do we need a theoretical section if we can restrict ourselves to the intensity picture..., without explanations?

 

Page 4 at the top after the formula for the TC. The authors should explain why they use the term “dislocation” if it is defined exclusively for monochromatic scalar fields. If this is the line of singularities of the correlation function, then this should be explained with appropriate references.

 

The authors should explain in detail in detail the mysterious phrase “With the increasing of coherence, the stripes in CSD amplitude disappear but singularities still maintain”  The following phrases turn out to be no less mysterious without corresponding theoretical explanations.

 

In addition, it is necessary to explain in detail the need to use the convolution method if, in fact, there is no corresponding theory at all. This is an elementary disrespect for readers.

Author Response

Thank you for your suggestions. Please refer to the attachment for specific responses.

Author Response File: Author Response.pdf

Reviewer 5 Report

In this work, the authors theoretically and experimentally studied the CSD distributions of a PCLG vortex beam transmitting through a couple of CLs with varying angles. When the CLs are placed vertically, the orientation of CSD magnitude can be used to distinguish the sign of TC. I see the acceptance of the article after making the following modifications.

 

My suggested corrections are as follows:

 [1]- The quantitative relationship between the TC and CSD phase distribution is studied, thus in turn determining the magnitude and the sign of TC for the PCLG vortex beam. This research has potential applications in free space and turbulent-atmospheric optical communications. The performance and limitations of the PCLG model in free space optics should be discussed more to improve the innovation of your work.

 

[2]- The atmospheric turbulence effects and noises in a free-space optical aren't seriously discussed for PCLG vortex beams in free-space and a non-axisymmetric ABCD optical system is given.

 

 

 

[3]- The explanations unclear for the quantitative relationships for the CSD amplitude and phase of the PCLG vortex beam based on the CSD amplitude or phase distributions can help us determine the magnitude and sign of TC in the PCLG vortex beam.

 

 

[4]- The self-reference holography method was introduced to realize the measurement of the CSD amplitude and phase [34,25]. The target plane is the output plane of the dual-CL system, where a transmission function ?(?) was introduced. Here, ?(?) is a square window function that is used to limit the field of view (FOV). Then, a Fourier lens was used to focus the beam on the recording plane where the intensity can be expressed as

?0(?)=∬?(?1,?2)?(?1)?∗(?2)×exp[−i2??(?1−?2)]??1??2,

The equation is not clear. Please cite it.

 

[5]- The validation and realization to verify the effectiveness of the proposed scheme need a better and more detailed explanation. The self-reference holography method was introduced to realize the measurement of the CSD amplitude and phase [34,25]. The comparison is required for the previous works.

 

[6]- A lot of grammatical mistakes are there.

 

[7]- The conclusion is inaccurate. It must contain a reflection of all results, contributions, and improved values. The level of deformation and according to the distorted intensity profiles of the vortex beams of the atmospheric air, you can determine this system and require more accurate and analyze all the levels of OAM deformation effect of the new model in the work of this.

 

[8]- The calculations of the refractive index structure (Cn^2) value are important and must provide all conditions for atmospheric turbulence for the potential applications in free space and turbulent-atmospheric optical communications. The analysis and the calculation of the distortion vortex beam of the OAM mode after the transmission in the turbulence FSO medium for all the different turbulence in the weak, moderate, and strong. How to restore the distorted intensity profiles of the vortex beams after transmitting through atmospheric turbulence? the inter-channel crosstalk when there is receiver angular error for OAM-vortex beam communications and CSD/ systems. The authors have not considered the background radiation effect.

[9]- The abstract of the manuscript should describe the main issues addressed by the researchers, the proposed technique, and a summary of the results. The abstract is not formatted properly and should be revised and rewritten.

 

[10]- References should be improved to be more applicable and practical -- these are some references that may be useful and important for work.

(a)- https://doi.org/10.3390/photonics8100445

(b)- http://dx.doi.org/10.1088/1402-4896/ab03a2

(c)- Miao Dong, XingYuan Lu, Chengliang Zhao, Yangjian Cai, and Yuanjie (d)- Yang, "Measuring topological charge of partially coherent elegant Laguerre-Gaussian beam," Opt. Express 26, 33035-33043 (2018)

(e)- https://doi.org/10.1109/ACCESS.2019.2924531

(f)- https://doi.org/10.3390/mi13101709

 

[11]- Some problems are not clarified for the influences of CLs angles on CSD distributions. What is the reason that the number of stripes or rings in CSD amplitude (Fig. 4a-f) has no obvious relationship to TC? In comparison, the number of ‘dumbbell piece and handle’ in the phase pattern. How to achieve this for the angle gradually decreases from 90° to 0, the singularities 153 in CSD amplitude gradually evolve into stripes. Why the angle is around 30°, the relationship in the phase is more obvious than that in the amplitude pattern, although the amplitude has been shown in the log scale.

 

[12]- The manuscript includes several typos and grammatical mistakes.

 

[13]- References need to be updated with the addition of more references on this approach more applicable.

 

[14]- There are too abbreviations. Please try to reduce the abbreviations so that the paper is clearer and better for readers.

Author Response

Thank you for your suggestions. Please refer to the attachment for specific responses.

Author Response File: Author Response.docx

Reviewer 6 Report

Comments for author File: Comments.pdf

Author Response

Thank you for your suggestions. Please refer to the attachment for specific responses.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

The authors have responded with some details to the questions of the review. Several points are thus developed and precised in the text. Also several pertinent references are included. To conclude the quality of the revised manuscript is now well suited for publication in the journal. 

Reviewer 4 Report

The authors have only partially implemented my recommendations. But this time I will not object to the publication of the manuscript

Reviewer 6 Report

The authors have addressed my comments and concerns, and I support the publication in Photonics.