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Peer-Review Record

Spin-Orbit Angular Momentum Conversion in Metamaterials and Metasurfaces

Quantum Rep. 2019, 1(1), 91-106; https://doi.org/10.3390/quantum1010010

by Graciana Puentes^1,2

Reviewer 1: Anonymous

Reviewer 2: Anonymous

Reviewer 3: Anonymous

Quantum Rep. 2019, 1(1), 91-106; https://doi.org/10.3390/quantum1010010

Submission received: 28 June 2019 / Revised: 17 July 2019 / Accepted: 19 July 2019 / Published: 25 July 2019

Round 1

Reviewer 1 Report

In this manuscript, the author reviewed the recent progress in the region of metasurfaces and angular momentum, including OAM, SAM and TAM. Indeed, the platform of metasurface provides a new way to generate OAM mode within a planar structure, which grows very fast and shows numerous significant advances. In general, the paper is well organized and solid. Thus there is only one minor comment: (1) Some recent works in microwave region can also be referred to, including: (a) Optics Express, 26(2), 1351-1360, 2018.

Author Response

Response Referee 1

We thank the Referee for reviewing our manuscript and for providing valuable comments. Moreover, we are delighted to hear that the Referee considers that “in general, the paper is well organized and solid.” We also thank the Referee for the helpful suggestion to include some references to recent works in the microwave region. To this end, we have included the following relevant recent References:

[1]- K. Zhang et al., Phase-engineered metalenses to generate converging and non-diffractive vortex beam carrying orbital angular momentum in microwave region, Opt. Exp. 26, 1351 (2018).

[2]-Z. Sabegh, M. Maleki, M. Mahmoudi, Microwave-induced orbital angular momentum transfer, Sci. Rep. 9, 3519 (2019)

[3]-J. Ren and K. Leunga, Generation of microwave orbital angular momentum states using hemispherical dielectric resonator antenna, Appl. Phys. Lett. 112, 131103 (2018)

We hope the Referee will find the revised manuscript acceptable for publication in Quantum Reports.

Author Response File: Author Response.pdf

Reviewer 2 Report

The manuscript entitled as "Spin-orbit angular momentum conversion in metamaterials and metasurfaces" introduced recent advancements in the field of 2D metasurfaces/metamaterials to generate and manipulate spin- and orbital-angular momentum of light through spin-orbit conversion. Different approaches, the summary of basic principles, and current applications were discussed. This review manuscript has a strong potential for a second review after applying the issues and addressing the shortcomings listed below:

1-The author should polish/revise some grammatical mistakes and typos along the manuscript. For instance, ‘In the last decades unprecedented…’, ‘…enable…(too much repetition)’, ‘…manipultation…’, ‘…azymuthal…’, ‘…and is quantized as…’, ‘…manipulation…(too much repetition)’, ‘…techniques…(too much repetition)’, ‘In section 2 we describe…’, ‘…spin angular momentum (SAM)… (no need to use the whole format once the abbreviation is mentioned, which is also valid for other examples like OAM)’, ‘…materials made of subwavelength…’, ‘…stongly…’, ‘…resonance modes…’, ‘Light incident…’, ‘However, a significant limitations of plasmonic metasurfaces (revise the whole statement)’, ‘…which can increases…’, ‘…electric and magnetic fields enhancement’, ‘…can in principle enable highly efficiencient…’, ‘…with state of art..’, ‘As a simple example to illustrate (revise the whole statement)…’, ‘…shifts in metasurfaces, it should be noted…’, ‘…explains in part the recent unrivalled…’, ‘More specific…’, ‘In this experiment a half wave-plate…’, ‘A beam of light circularly polarized…’, ‘Beth meaured torque…(revise the whole statement)’, ‘…laser modes but they were…’, ‘Geometric phase elements and metasurfaces…(revise the whole statement)’, ‘In the next sections we provide…’, ‘…polarization states has been reported…’, ‘…metasurfaces which enable manipulation…’, ‘For this reason the OAM…’, ‘In order to perferm SOC…’, ‘…hability…’, ‘…is a signifcant…’.

2-The manuscript has some problems about the transition between sentences. The author should fix those issues, such as between Line 3-4.

3-For the following statements, corresponding references should be added: ‘It is well known that besides linear momentum…’, ‘…OAM modes have been used to encode…’, ‘2D metamaterials, also known as metasurfaces, is an…’, ‘…such as negative refractive index and invisibility cloaking…’, ‘…unavailable in natural compounds’, ‘…index, and surrounding media’, ‘…generate arbitrary wave fronts’, ‘…power threshold of deformation’, ‘Fano resonances are also observed in pure…’, ‘…which can be exploited in sensing and…’, ‘…light corresponding to orthogonal polarizations’, ‘Up to now, conversion between a linear…’, ‘…with arbitray elliptical…’, ‘…between the different orthogonal channels’.

4-For the following statement, number of examples should be increased: ‘…such as high resistive loss’.

5-The following statement is misleading for the possible readers of this manuscript and it should be revised, since plasmonic antennas are based on metallic structures, not the dielectric ones: ‘Aside from dielectric metasurfaces based on plasmonic antennas…’.

6-The title of Section 2 can be revised, since in its current form, ‘metasurface’ and ‘building blocks’ contains the similar meanings.

7-Section 2 is weak in terms the recent advancements in the field of metamaterials and Fano resonances. The following studies must be properly mentioned and cited within the manuscript: [(1) Photonics 6, 43 (2019); (2) Science 339, 1232009 (2013); (3) Nanoscale 11, 8091-8095 (2019); (4) Science 331, 290-291 (2011); (5) Phys. Rev. B 97, 161405 (2018); (6) Nat. Mater. 13, 139-150 (2014); (7) J. Phys. Chem. C 122, 24304-24308 (2018); (8) Nano Lett. 11, 2142-2144 (2011); (9) Nano Lett. 19, 605-611 (2019); (10) Nat. Mater. 11, 30-33 (2012); (11) Nanoscale DOI: 10.1039/C9NR04312H (2019); (12) Nat. Nanotech. 8, 252-255 (2013); (13) Opt. Mater. 84, 301-306 (2018); (14) Nat. Mater. 9, 707-715 (2010); (15) IEEE J. Lightw. Technol. 35, 4961-4966 (2017)].

8-Related references should be mentioned if the equations/formulas are taken from other sources, such as Equations 1, 2, etc.

9-What is the meaning of (3) in SO(3) (in Line 137)?

10-About the caption of Figure 3: A caption is missed for Figure 3b.

11-For the Figure 5: A reference or a copyright explanation should be added, if the image was taken from other work.

12-It seems Section 5.2 is not related to Section 5. So, the author may want to assign a new section for this discussion section.

Author Response

Response Referee 2

We thank the Referee for carefully reading our manuscript, and for providing several relevant suggestions to improve the overall quality of the paper. We have included all the helpful remarks by this Referee. Below we enclose a response to all the questions and comments, in addition to a list of modifications introduced in the manuscript in response to the valuable comments provided by the Referee. We hope the Referee will find the revised version acceptable for publication in Quantum Reports

We thank the Referee for this valuable comment. We have corrected the several typographic mistakes. These corrections appear in bold letters in the revised manuscript. Moreover, in order to avoid repetition, we have replaced “enable” by “permit, allow, or warrant”, we have replaced “manipulation” by “engineering, or maneuvering” and we have replaced “techniques” by “methods, processes, or approaches”. We have also deleted the expressions “Spin Angular Momentum” and “Orbital Angular Momentum” after introducing the acronyms (SAM) and (OAM). In addition, we have rephrased all the sentences outlined by the Referee. We thank the Referee for the very helpful comments.

2-The manuscript has some problems about the transition between sentences. The author should fix those issues, such as between Line 3-4.

We thank the Referee for this comment, we have removed, or corrected, the connectors that were not appropriate, such as Line 3 to Line 4.

We thank the Referee for this comment. We have added the citations requested by the Referee in the text. These appear in bold letters in the revised version.

4-For the following statement, number of examples should be increased: ‘…such as high resistive loss’.

We thank the Referee for this comment. We have increased the number of examples by adding “dielectric, and high resistive (ohmic) loss”.

We thank the Referee for this comment. We have modified “dielectric” by “metallic” (bold letters), in order to prevent misleading statements.

6-The title of Section 2 can be revised, since in its current form, ‘metasurface’ and ‘building blocks’ contains the similar meanings.

We thank the Referee for this comment. We have revised the title of Section 2, by replacing “building blocks” by “components”.

We thank the Referee for this comments. We have included all the References suggested by the Referee [Ref. 82 to Ref. 97], and their corresponding citation in Section 2. We hope the Referee will fin this updated list of References acceptable.

8-Related references should be mentioned if the equations/formulas are taken from other sources, such as Equations 1, 2, etc.

We thank the Referee for this comment. We have added explicit References for Eq. 1 and Eq. 2 [Ref. 1 and Ref. 85, respectively].

9-What is the meaning of (3) in SO(3) (in Line 137)?

We thank the Referee for this comment. SO(3) refers to the spin-1 matrix operators, the generators of rotations in the canonical momentum representation, as reported in Bliokh et al., Physics Reports 592, 1-38 (2015):

We have included explicit expression spin-1 matrix operators in Eq. 3. Moreover, we have included an explicit reference to Bliokh et al Physics Reports 592, 1-38 (2015) (bold letters).

10-About the caption of Figure 3: A caption is missed for Figure 3b.

We thank the Referee for this comment. We have included the caption for Figure 3 (b) (bold letters).

11-For the Figure 5: A reference or a copyright explanation should be added, if the image was taken from other work.

We thank the Referee for this comment. Figure 5 is not copied, it is original and was realized by the author.

12-It seems Section 5.2 is not related to Section 5. So, the author may want to assign a new section for this discussion section.

We thank the Referee for this comment. We have modified the labels for Section 3, and Section 4 in order to include TAM of light. We have also updated the description of the contents of each Section accordingly, on page 2 first paragraph.

Author Response File: Author Response.pdf

Reviewer 3 Report

This paper addresses some interesting questions concerning the exploitation of metamaterials for the generation of Spin and Orbital Angular Momentum Generation and Conversion

The paper has many references and gives a good overview of the state of the art.

But this paper is more a status report of the field than a scientific work.

The problem is that when dealing with quantum formalism many errors and misspellings appear:

for example

Eq(2): is rather confusing (perhaps due some typo errors), also the electric field E is treated as a quantum state which seems a short-cut with normal quantum theory. Especially in the eigenvalue equation Sz E = sigma E where the electric field is considered the eigenvalue of the angular momentum projection Oz observable. In general the electric field is quantified using the ladder operators a and a+ this is called “second quantification”.

Eq(7): here two distinct orthogonal quantum states |L> and |R> are proportional one to each other by a simple phase factor (exp[i2q phi ]) but in this way it would mean that the two states are the same, this is a contradiction. This shows the poor knowledge of quantum theory. I think the author makes confusion between quantum states and spin observables which are the operators that act on the Bloch sphere.

In conclusion this paper although interesting is very confusing regarding the formalism and the corresponding physical interpretation.

The paper can be accepted only if the scientific explanations are convincing and compatible with standard quantum theory.

Author Response

Response Referee 3

We thank the Referee for his/her relevant remarks and comments, which helped to further improve the quality of the manuscript. Below we enclose a response to the issues raised by this Referee. Moreover we provide a list of modifications introduced in the revised manuscript, in response to the valuable Referee comments.

We thank the Referee for this comment. First of all, let us note there are two levels of quantum formalism for light: (i) the first quantization approach, which deals with operators of dynamical variables acting on classical electromagnetic fields, and (ii) the second quantization approach, which quantizes the fields and makes them quantum operators acting on the Fock states of photons, as the Referee suggests. The description presented in our manuscript is compatible with the first quantization approach, in the sense that the electromagnetic field is treated as a classical variable (i.e., a plane wave). As it is explained in the manuscript, the electric field (E) in Eq. 2 is not a quantum state, but a vectorial representation of the polarization properties of a classical plane wave describing the electric field, similar to a Jones vector in the Jones formalism for polarization of light.

Let us mention that providing a self-consistent separation of the spin and orbital angular momentum (AM) for non-paraxial or non-monochromatic electromagnetic fields is not straightforward, since the quantum-mechanical first-quantization operators of separated spin and orbital AM are inconsistent with the transversality condition for photons. Furthermore, the spin and orbital parts of the conserved AM Noether currents in electromagnetic field theory are not conserved separately.

The discrepancy between quantum operators of spin/orbital AM and the transversality of photons has been partially resolved: It was shown, using both a second quantization approach and a first-quantization approach, that suitably modified quantum-mechanical operators of spin and orbital AM can be made consistent with both field transversality condition and measured expectation values, by introducing a spin-orbit correction term.

This development is not yet a complete solution, however. The quantum-operator approach is based on the Fourier momentum representation and yields only integral expectation values of the spin and orbital AM. In contrast, optical interaction with small particles or atoms requires a proper local description of the spin and orbital AM in terms of densities in real space (see Bliokh, Dressel and Nori, New J. Phys. 16, 093037 (2014), and references therein).

The description presented in our review corresponds to a unified theory of angular momentum of light, based on canonical momentum and spin densities, as developed by K. Bliokh et al. in Physics Reports 592, 1-38 (2015). This description overcomes the abovementioned limitations of the quantum-operator approach. We have further clarified this point in bold letters in the revised manuscript. We have also added an explicit expression of the spin-1 matrix operators in the canonical momentum representation (Eq. 3).

Regarding Eq. (2) in our manuscript, we note that it is equivalent to Eq. (2.4) in Bliokh et al. Physics Reports 2015, additionally expression SzE=+/-E, is equivalent to Eq. (2.5) in Bliokh et al. Physics Reports 2015, and references therein. We consider the notation in our manuscript is based on standard literature, and therefore it is compatible with standard quantum theory. The issue raised by the Referee could possibly be based on a lack of familiarity with the field of spin-orbit coupling of light.

We thank the Referee for this relevant comment. Indeed, in this case there was a typographic mistake. Instead of the symbol “=” we meant to write the mapping-operation symbol indicated by an arrow “->”. We have corrected this typo in Eq. 8 and Eq. 9. Please note once again, that the notation used in Eq. 8 and Eq. 9 is the standard accepted notation in the literature, see for instance Delvin et al. Science 358, 896–901 (2017). Therefore we consider our manuscript is compatible with standard quantum theory.

In conclusion this paper although interesting is very confusing regarding the formalism and the corresponding physical interpretation.

The paper can be accepted only if the scientific explanations are convincing and compatible with standard quantum theory.

We thank the Referee for considering our work of interest. We hope our explanations regarding the standard accepted notation in the field (Bliokh, Dressel and Nori, New J. Phys. 16, 093037 (2014); Bliokh et al., Physics Reports 592, 1-38 (2015); Delvin et al. Science 358, 896–901 (2017) and references therein), is sufficiently clear and convincing, and the manuscript can be accepted for publication in Quantum Reports.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

In its current format, the revised manuscript is suitable for publication in Quantum Reports.

Author Response

Response Referee 2

We thank the Referee for reading the revised manuscript, and for considering that “In its current format, the revised manuscript is suitable for publication in Quantum Reports.” We have further rephrased some of the English expressions in the manuscript in order to further improve the readability of the paper. We thank this Referee once again for the many valuable remarks and suggestions that helped to greatly increase the overall quality of the paper.

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors replied well to my preceding report.

I would still recommend "caution" on overoptimistic conclusions and a little more criticism on what seems up to now only a promising technology.

Also be careful when going into the quantum applications for example the sentence at line 353

"Although classical fields are mainly considered here, the physics of SOC also holds at the single-photon level given the one-to-one mapping between Jones formalism and single-photon polarization description."

in Physics there is no such thing as one-to-one mapping...

Author Response

Response Referee 3

We thank the Referee for the relevant remarks and comments, which helped to further improve the quality of the manuscript. Below we enclose a response to the issues raised by this Referee and we provide a list of modifications introduced in the manuscript in response to the Referee comments. We hope the Referee will find the revised version acceptable for publication in Quantum Reports.

I would still recommend "caution" on overoptimistic conclusions and a little more criticism on what seems up to now only a promising technology.

We thank the Referee for this comment. We have rephrased the Sections “Discussion” and “Conclusions” in order to present a more critical outlook. To this end, we have included the following cautionary remarks in the text (see bold letters):

-“To a great extent”, “to a large extent”, “to some extent”, “by and large”, “on the whole”, “potentially”, “plausibly”, “conceivably”, etc.

Also be careful when going into the quantum applications for example the sentence at line 353

We thank the Referee for this comment. We have removed the phase "given the one-to-one mapping between Jones formalism and single-photon polarization description." as suggested by the Referee.

in Physics there is no such thing as one-to-one mapping...

We thank the Referee for this remark. Let us mention that the sentence ”given the one-to-one mapping between Jones formalism and single-photon polarization description.", refers to the analogy between the description of the polarization state of classical plane wave in the classical Poincare sphere, and the description of the state of a pure two-level quantum system (i.e., a qubit) in the quantum Bloch sphere. We agree with the Referee in that there is no such analogy for other degrees of freedom of light, such as OAM or TAM.

Author Response File: Author Response.pdf

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