Vectorial Manipulation of High-Resolution Focusing Optical Field through a Scattering Medium
Round 1
Reviewer 1 Report
In this manuscript, the authors measure the vector transmission matrix(VTM) of a scattering medium with the vector basis of orthogonally circular polarizations, the incident wavefronts are modulated through the calculation with the VTM to create a desired high-resolution optical field through a scattering medium. The theoretical and experimental results show that the constructed high-resolution optical field of single point, three points and vector optical field can be realized by a frosted glass with spatially-variant states of polarization. The results are interesting and will benefit the subject area. There are some issues should be addressed before acceptance.
1. The authors should provide a detailed explanation of the generation of two orthogonally circular polarizations by the functioning of the experiment set.
2. The corresponding comparison between the proposed method and other related works should be discussed for justification of the proposed method.
3. There is a conflict presentation between expression of Eq. (3) and the statement above Eq. (3) “ the VTM for an isotropic scattering medium usually has the property of Tll = 0 and Trr = 0”.
4. The English should be improved.
Author Response
In this manuscript, the authors measure the vector transmission matrix(VTM) of a scattering medium with the vector basis of orthogonally circular polarizations, the incident wavefronts are modulated through the calculation with the VTM to create a desired high-resolution optical field through a scattering medium. The theoretical and experimental results show that the constructed high-resolution optical field of single point, three points and vector optical field can be realized by a frosted glass with spatially-variant states of polarization. The results are interesting and will benefit the subject area. There are some issues should be addressed before acceptance.
1. The authors should provide a detailed explanation of the generation of two orthogonally circular polarizations by the functioning of the experiment set.
Response 1:
We thank the reviewer very much for the helpful comment.
We have modified figure 1 to clearly indicate the generation of two orthogonally circular polarizations. The double hole filter has been added in front of the λ/4 wave plate in figure 1, and a detailed explanation for the generation of two orthogonal circular polarizations using our experimental system has been provided in lines 107-111 in the revised manuscript:
“The +1 orders of the x-axis and y-axis on the spectrum plane after reflecting by the SLM are extracted by a double-hole filter, and are converted into left-hand and right-hand circular polarizations through the λ/4 wave plates close to each hole, and generate the required vector beams through the collinear superposition of the left-hand and right-hand circular polarizations by G.”
2. The corresponding comparison between the proposed method and other related works should be discussed for justification of the proposed method.
Response 2:
We thank the reviewer very much for the helpful comment.
The corresponding discussions about other related works have been added in lines 48-64 in the revised manuscript:
“Although the measurement of VTM of a scattering medium and polarization control in a single focus point by the experimental system has been explored[27, 28], the measurement processes of VTM are relatively complicated. The generation of multiple focal spots and vector beams with spatially varying states of polarization after passing through a scattering medium has been theoretically demonstrated [29]. More recently, the generation of vector beams with a scattering medium by one single scalar transmission matrix has been proposed[30]. However, the simultaneous vector manipulation of the states of polarization in both azimuthal and radial directions after passing through a scattering medium needs further exploitation, especially for the input optical field with different orthogonal polarizations such as left- and right- circular polarizations.
In this work, we present a simple and reliable method to manipulate the spatial distribution of polarization state in both azimuthal and radial directions in the focusing high-resolution optical field (points and vector beams) after passing through a scattering medium., In particular, the input optical field with a vector beam by special polarization superposition of orthogonally circular polarizations can provide a feasibility of achieving such vectorial manipulation process.”
3. There is a conflict presentation between expression of Eq. (3) and the statement above Eq. (3) “ the VTM for an isotropic scattering medium usually has the property of Tll= 0 and Trr = 0”.
Response 3:
We apologize the typo, and the expression “Tll = 0 and Trr = 0” has been revised as “Trl = 0 and Tlr = 0” in the revised manuscript.
4. The English should be improved.
Response 4:
Thank you for the comment. We have read the manuscript carefully and improved the English as much as possible.
Reviewer 2 Report
Comments for author File: 
Comments.docx
Author Response
In this work, the authors study the manipulation of the polarization states of the light transmitted through a scattering medium. The vector transmission matrix of a scattering medium is measured with the vector basis of orthogonally circular polarizations by the two-dimensional holographic grating combined with the 4-steps phase shifting method. The focusing high-resolution single point, multiply points and vector beams with spatial distributions of polarization are theoretically and experimentally demonstrated. The experimental results confirm the theoretical predictions. This work can be accepted after minor revisions.
1. In this work, the vector transmission matrix for an isotropic scattering medium are measured, however, according to the description of Eq. (6), there are typo “Tll = 0 and Trr = 0”, they should be revised as “Tlr= 0 and Trl = 0”. In addition, the authors should state the property of the vector transmission matrix for an anisotropic scattering medium, and the advantage of using the orthogonally circular polarizations.
Response 1:
We thank the reviewer very much for the helpful comment.
We apologize the typo, and the expression “Tll = 0 and Trr = 0” has been revised as “Trl = 0 and Tlr = 0” in the revised manuscript.
The statement for vector transmission matrix (VTM) for an anisotropic scattering medium and an isotropic scattering medium has been added in lines 86 - 92 on page 2 in the revised manuscript:
“For highly polarization-sensitive anisotropic scattering media such as ZnO scattering layers, the polarization state of the input field is scattered and perturbed. The components Tll , Tlr , Trl andTrr in the VTM should totally considered [28]. On the otherhand, for an isotropic scattering medium such as the frosted glass used in this work, the components of the VTM for the isotropic scattering medium usually have the properties of Trl = 0 and Tlr = 0[34].”
In addition, the comparison between using the orthogonally circular polarizations and orthogonally linear polarizations has been added in the Section Discusion in the revised manuscript:
“In addition, comared to the input vector optical field with the superpositiom of orthogonally linear polarization, our experiment results indicate that the focusing optical field after passing through a scattering medium with the orthogogally circular polarizations have an advantage on the robustness of the polarization state and field distributions. Figure 6 shows the comparison of focusing optical field between the input vector beams with orthogonally linear and circular polarizations, the vector optical field constructed by the orthogonally linear polarizations can be expressed as [37]. Although the memory effect has been observed in the backscattering geometry of light interacting with a random medium [31, 32, 40], however, the underlying physics for the difference between the circular and linear polarizations passing through a scattering medium, need be further exploited.”
2. For the focusing high-resolution single point and multiply points in Fig. 2, can the polarization distribution be plotted in the first plotted as Figs. 3 and 4? so that the polarization distribution can be better descripted intuitively.
Response 2:
The plots for the corresponding polarization distribution of the focusing high-resolution single point and multiple points have been added in figure 2 in the revised manuscript.
3. As an isotropic scattering medium, the fabrication of the frosted glass of 220 mesh in this work should be introduced.
Response 3:
The scattering medium used in this work is frosted glass which is bought from Lbtek company. We have added the statement and introduction for frosted glass in lines 104-105 on page 3 in the revised manuscript:,
“frosted glass of 220 mesh, LBTEK, DW105-220,, The glass sheet is polished and sanded to obtain the frosted glass[35] ”
Reviewer 3 Report
The optical vector field in scattering media is an important and interesting topic. The manuscript, "Vectorial manipulation of high-resolution focusing optical field through a scattering medium," constructed high-resolution optical field with spatially-variant states of polarization through scattering media. The experimental results agree with the theoretical ones. This manuscript can be accepted for publication if the following questions are addressed.
1. The motivation cannot be seen clearly in the Introduction. It should be presented straightforwardly so that the readers can understand the difference and advancement of the the present work with those in the literature.
2. There are some grammar errors, such as:
Line 36: "... during the propagation of vector beams...during the vector beam propagation..."
Line 78: "...in this work, the components..."
Line 152: "3. Results analysis"
3. There are some differences between experimental and theoretical results for the intensity distributions of vector beams in Fig.3 and Fig4. The petals in the experimental results are farther away from each other than those in the theoretical ones (like Fig.4 in APPLIED PHYSICS LETTERS 98, 201101 (2011)). The reason may be that the propagation distances in the theoretical calculations are shorter than the real ones in the experiments. It is well known that the petal-like pattern of the vector beam always separate during propagation (like like Fig.5 and Fig.8 in OPTICS EXPRESS 24, 21177 (2016)). The authors may revise their theoretical results correspondingly.
Author Response
The optical vector field in scattering media is an important and interesting topic. The manuscript, "Vectorial manipulation of high-resolution focusing optical field through a scattering medium," constructed high-resolution optical field with spatially-variant states of polarization through scattering media. The experimental results agree with the theoretical ones. This manuscript can be accepted for publication if the following questions are addressed.
1. The motivation cannot be seen clearly in the Introduction. It should be presented straightforwardly so that the readers can understand the difference and advancement of the the present work with those in the literature.
Response 1:
We thank the reviewer very much for the helpful comment.
The corresponding statements about motivation of this work and introduction of other work have been added in lines 48-64 on page 2 in the revised manuscript:
“Although the measurement of VTM of a scattering medium and polarization control in a single focus point by the experimental system has been explored[27, 28], the measurement processes of VTM are relatively complicated. The generation of multiple focal spots and vector beams with spatially varying states of polarization after passing through a scattering medium has been theoretically demonstrated [29]. More recently, the generation of vector beams with a scattering medium by one single scalar transmission matrix has been proposed[30]. However, the simultaneous vector manipulation the states of polarization in both azimuthal and radial directions after passing through a scattering medium need further exploited, especially for the input optical field with different orthogonal polarizations such as left- and right- circular polarizations.
In this work, we present a simple and reliable method to manipulate the spatial distribution of polarization state in both azimuthal and radial directions in the focusing high-resolution optical field (points and vector beams) after passing through a scattering medium., In particular, the input optical field with a vector beam by special polarization superposition of orthogogally circular polarizations can provide a feasibility of achieving such vectorial manipulation process.”
2. There are some grammar errors, such as:
Line 36: "... during the propagation of vector beams...during the vector beam propagation..."
Line 78: "...in this work, the components..."
Line 152: "3. Results analysis"
Response 2:
Thanks for your comments, we have corrected the grammar errors in the revised manuscript.
3. There are some differences between experimental and theoretical results for the intensity distributions of vector beams in Fig.3 and Fig4. The petals in the experimental results are farther away from each other than those in the theoretical ones (like Fig.4 in APPLIED PHYSICS LETTERS 98, 201101 (2011)). The reason may be that the propagation distances in the theoretical calculations are shorter than the real ones in the experiments. It is well known that the petal-like pattern of the vector beam always separate during propagation (like Fig.5 and Fig.8 in OPTICS EXPRESS 24, 21177 (2016)). The authors may revise their theoretical results correspondingly.
Response 3:
We appreciate the reviewers' comments.
We have carefully checked the experimental and theoretical results, and found the propagation distances in the theoretical calculations are shorter than that in the experiments, as you judged. The plots of the theoretical results in Figs. 3 and 4 have been revised with the same propagation distances as that in the experiment.
Reviewer 4 Report
Please see attached for my detailed review report. Good luck!
Comments for author File: 
Comments.pdf
Author Response
The manuscript titled "Vectorial manipulation of high-resolution focusing optical field through a scattering medium" has discussed and demonstrated the manipulation and customization of polarization stages through a random media using vectorial beam of circular polarization as basis. The idea of using vector transmission matrix is not very new. Nevertheless, the paper does a good job in terms of demonstrating the feasibility of achieving such manipulation process through this special polarization decomposition. In my opinion, this paper might be published for its value as a technical note for other people in this field. However, it would be very critical to amend and polish the paper with logical flows. I have several concerns regarding the structure of the paper. I would like the authors to consider these comments before the paper is official accepted. See detailed comments below.
Main remarks:
- My major concern regarding the value of the paper is why the authors choose circular polarization light as their basis. The authors mentioned that the reason is to make use of the polarization memory effect (Ref 31-32). If this is true, this would certainly enhance the value of the paper. However, as far as I known, the "polarization memory effect" is a phenomenon that has only been observed in the back-scattering geometry of light interacting with random media. This is discussed in Ref 31-32 as well.There are not similar mechanisms that have been observed or proposed in transmission geometry. If the authors insists that circular polarization has stronger memory effect, they should provide experimental proof by comparing the optimized focusing of light using circular polarization basis with linear polarization basis.
Response 1:
We thank the reviewer very much for the helpful comment.
After analyzing the theoretical and experimental results carefully, we can not determine it is memory effect of circular polarization that result in the difference between the circular and linear polarizations passing through a scattering medium. The statements about the reason to make use of the polarization memory effect in the text have been removed in the revised manuscript:
“ The results can be attributed to the circular polarization light can maintain its original polarization property better than the linearly polarized light during propagating through turbid medium (the memory effect of the circular polarization)[31,32]” has been removed.
The corresponding statement and discussion about the difference between the circular and linear polarizations passing through a scattering medium have been added in the Discussion Section:
“In addition, compared to the input vector optical field with the superpositiom of orthogonally linear polarization, our experiment results indicate that the focusing optical field after passing through a scattering medium with the orthogonally circular polarizations have an advantage on the robustness of the polarization state and field distributions. Figure 6 shows the comparison of the focusing optical field between the input vector beams with orthogonally linear and circular polarizations. Although the memory effect has been observed in the backscattering geometry of light interacting with a random medium [31, 32, 40], however, the underlying physics for the difference between the circular and linear polarizations passing through a scattering medium, need to be further exploited.”
In addition, the comparison between the experimental results for the intensity distributions of vector beam constructed using orthogonally linear polarizations and orthogonally circular polarizations have been added in Discussion Section in the revised manuscript as figure 6.
2. The authors provide "simulation" results in figure 3-5 and said that the experimental results agree with the simulation very well. I have a hard time trying to figure out the details involved in such "simulation". The fact that not specular patterns are generated makes me wonder this is a numerical calculation using analytical solutions, not a "simulation". This means, no scattering is involved in the "simulation". This should be mentioned somewhere in the paper to avoid confusion, if this understanding is correct. Some details on this "simulation" should be given.
Response 2:
We thank the reviewer very much for the comment.
The theoretical results are obtained by using a scattering VTM with a random phase distribution to simulate a scattering medium as adopted in Ref.[29].
We apologize for the unclear description in the text, and the corresponding details involved in the simulation experiment have been added in lines 216-218 on page 6 in the revised manuscript:
“Noted that hereafter a scattering VTM with random phase distribution is adopted to simulate a scattering medium for the theoretical calculations[29].”.
3. The authors mentioned in Line 246-248 that, the focusing effect is 10 times better than "traditional lens". I did not get the meaning of such comparison (as well as the data shown in Figure 5 (a)). The authors should compare the case (i) VTM results showed in Figure 5 (b) and (c) with case (ii) light through the system without scattering media. For me it is not clear what is the meaning of doing a "focusing effect" comparison.
Response 3:
We are very grateful to the reviewer for the helpful comment.
We strongly agree with your suggestion to compare the case (i) VTM results shown in Figure 5 (b) and (c) with case (ii) light through the system without scattering media. However, in this work, the beam has been expanded 10× by the lenses L1 and L2, the size of the vector light field without passing a scattering medium is relatively large and beyond the size cannot be captured directly by our experimental CMOS camera. Therefore, we compare the case (i) VTM results shown in Figure 5 (b) with case (ii) light without passing through the scattering medium but focused by the lens with a focal length of 10cm.
In addition, figure 5 has been further improved in the revised manuscript to more clearly describe the results.
Minor remarks:
1. The authors should double check their reference numbers. I noticed that the references numbers in line 220 should be 31-32, not 29-30. It is very likely that the numbers are messed up.
Response 4:
Thanks for the comment. The errors in the reference numbers have been revised.
2. Double hole filter should be added in figure 1.
Response 5:
The double hole filter(F) and the λ/4 wave plate have been clearly plotted in figure 1 in the revised manuscript.
3. Scale bar in Figure 5 (c) should also be added, even if they are different from Figure 5 (a) and (b). The numbers can be given in the figure.
Response 6:
The scale bar has been added in figure 5(c), and specific value of the scale are given in figure 5(a), 5(b) and 5(c) in the revised manuscript.
Round 2
Reviewer 4 Report
I have gone through the paper thoroughly, along with the replies from the authors to reviewers. I do find that authors have spent a significant amount of time in improving the quality of the work and clearness of their presentation. My only recommendation for the authors would be to spend more time for the English (spell and grammar) during the proof stage. There are still some that can be spotted. For instance, in Line 284: should be "superposition".
Other than that, I am happy to recommend the publication of this paper on Photonics.
