Selection Rules of Linear and Nonlinear Polarization-Selective Absorption in Optically Dressed Matter

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The manuscript ID photonics-3149349 has been devoted to study some characteristics exhibited by linear and nonlinear optical absorption sensitive to polarization in particular optically dressed matter. Please see below some points to the authors:

1. A graphical abstract could be included in the introduction in order to easily visualize the methodology and main findings that can be highlighted to improve the potential impact of this research.
2. The authors state that “transition between Floquet bands (absorption/ emission) is allowed only for linearly polarized probes that are in phase with the dressing field, for any nonlinearity order” However the influence of linear and nonlinear behavior in materials exhibiting second-order nonlinearity is for specific symmetry of materials while third-order nonlinearity is for any material. Please clarify.
3. It should be discussed how is the influence of the two-photon absorption over the main findings for resonance and off-resonance conditions. Both cases are possible for different specific wavelengths.
4. Why equation 7 does not clearly includes the nonlinear polarization component. Please clarify.
5. The main results should be confronted with updated publications in the topic of nonlinear polarization-selective absorption in optically dressed matter.
6. Coexistance of different physical mechanisms of optical absorption can be present in nonlinear materials. The authors are invited to discuss, you can see for instance: https://doi.org/10.1364/JOSAB.35.001295
7. Perspectives of this work should be included in order that the conclusions can be a base for future search. You can see for instance: https://pubs.acs.org/doi/10.1021/acs.jpclett.4c00837#
8. Please verify that all the parameters and variables are declared in the text and with limited values justified if it is the case.
9. Equations must be numbered at the right side.
10. The citations presented in collective form could be split in order to better present and justify the importance of each reference selected for the study of the topic of this research.

Comments on the Quality of English Language

A proofreading is suggested

Author Response

Reviewer 1

1. A graphical abstract could be included in the introduction in order to easily visualize the methodology and main findings that can be highlighted to improve the potential impact of this research.

Thank you for your advice. Following your suggestion, we will submit Figure 1 as a graphical abstract.

2. The authors state that “transition between Floquet bands (absorption/ emission) is allowed only for linearly polarized probes that are in phase with the dressing field, for any nonlinearity order” However the influence of linear and nonlinear behavior in materials exhibiting second-order nonlinearity is for specific symmetry of materials while third-order nonlinearity is for any material. Please clarify.

Thank you. Indeed, the original sentence   did not convey the message clearly enough.

Our selection rules are based on dynamical symmetries which include information about both the spatial and temporal symmetries of the system. The utility of this approach is that it reveals selection rules that might not be evident when using the (spatial) symmetry properties of the nonlinear susceptibility tensor.

For example, in the sentence you have cited, we refer to a situation where an optical transition is only allowed for particular phases of the probe field. This limitation is imposed by the temporal part of the symmetry of the light-matter system and cannot be predicted solely from the spatial symmetries of the material system.

To avoid any potential confusion and to ensure that the message is accurately communicated, we have revised the sentence to make it clearer and more straightforward. The revised manuscript reads:

“For a Hamiltonian with time-reversal (T) symmetry, we find that transitions between Floquet bands (absorption/emission) of linearly polarized probes are allowed only when the electric field is in phase with the dressing field, regardless of the interaction's nonlinearity order. “

3. It should be discussed how is the influence of the two-photon absorption over the main findings for resonance and off-resonance conditions. Both cases are possible for different specific wavelengths.

Thank you. In principle, the Flouqet formalism apply to any material system with the appropriate symmetry properties, regardless of whether the system is resonant with the dressing/ probe field.

To ensure this point is clear, we have added additional sentences that further clarify and emphasize the universality of our approach. The revised manuscript reads (page 5):

 “Additionally, the presented formalism is general, provided that the light includes enough optical cycles to account for the Flouqet formalism. Notably, on-resonance interaction requires significantly larger number of optical cycles “

Why equation 7 does not clearly includes the nonlinear polarization component. Please clarify.

Thank you. The expression in Equation 7:              

where E is the emitted electric field and may also be replaced by the nonlinear polarization . So Eq 7 indeed includes the nonlinear polarization component. We have clarified this in the revised manuscript (page 4):

“Where E is the emitted electric field and may also be replaced by the nonlinear polarization .“

4. The main results should be confronted with updated publications in the topic of nonlinear polarization-selective absorption in optically dressed matter.

Thank you. At the fourth paragraph of our manuscript, we provide a detailed comparison of our results with those reported in the article titled 'Dynamical Symmetries and Symmetry-Protected Selection Rules in Periodically Driven Quantum Systems.'.

That paper directly addresses the topic of 'nonlinear polarization-selective absorption in optically dressed matter. We find our expressions reduce to previously derived expression in the appropriate conditions, and therefore, agreement between our work and previous works.

 

5. Coexistance of different physical mechanisms of optical absorption can be present in nonlinear materials. The authors are invited to discuss, you can see for instance: https://doi.org/10.1364/JOSAB.35.001295

Thank you. We have included a note on the various physical mechanisms of optical absorption at the beginning of the paper and cite this paper at the sentence (page 5): “. It is important to note that our work is based solely on symmetry arguments, independent of the specific molecular structure or the various physical mechanisms of optical absorption[1]”. Additionally, we have clarified that our work is intended to be general and applicable to any specific mechanism.

6. Perspectives of this work should be included in order that the conclusions can be a base for future search. You can see for instance: https://pubs.acs.org/doi/10.1021/acs.jpclett.4c00837#

Thank you for your feedback. We have included a discussion in the conclusion outlining the foundation for future research.

Thank you, the suggested paper is indeed very relevant for future work in ‘Floquet Engineering’. We have cited it in the revised manuscript. We add the sentence (page 6): “Our selection rules can serve as a guide for further research on nonlinear absorption in complex geometries[2]”

7. Please verify that all the parameters and variables are declared in the text and with limited values justified if it is the case.

Thank you for your remark. Following your comment, we

have identified that the parameter Ω was not defined in the text. We have now corrected this oversight. Additionally, we have made sure that all other parameters and variables are clearly defined and explained throughout the paper to avoid any ambiguity.

8. Equations must be numbered on the right side.

We have changed the numbering as you advised.

9. The citations presented in collective form could be split in order to better present and justify the importance of each reference selected for the study of the topic of this research.

We have updated the citations as you advised.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The presented manuscript “Selection Rules of Linear and Nonlinear Polarization-selective Absorption in Optically Dressed Matter” by Michael Feldman, Matan Even Tzur, and Oren Cohen is devoted to a theoretical study of how the symmetries of laser-dressed matter determine selection rules and its absorption spectrum.

 

This paper is intended to advance the existing knowledge in the crucial area of floquet engineering and optically dressed states in innovative low-dimensional materials and surfaces.  

 

Therefore, I believe that this paper should be accepted for publication in Photonics provided that the authors address the following comments.

 

Did I get it right that the consideration was mainly done for the dipole molecules which mainly consist of two spatially separated charges?  Please explain in more detail for which molecules or materials and their phase states this method could be applied.

 

Please explain in more detail what our-of-plane polarization means? Is it a type of a circularly polarized light? Could the direction of light polarization be not perpendicular to the direction of its group velocity? This really needs to be explained in more details to make this paper clearer for the readers. 

 

It would be also important and beneficial to the readership if the authors could discuss some recent relevant findings on Floquet engineering of tilted and gapped Dirac bandstructure, and Floquet modification of the bandgaps and energy spectrum in flat-band materials.

Comments on the Quality of English Language

Certain improvement of the word usage and formulations is needed in some places, such as "determine selection rules that determine its absorption spectrum"

Author Response

Referee 2

The presented manuscript “Selection Rules of Linear and Nonlinear Polarization-selective Absorption in Optically Dressed Matter” by Michael Feldman, Matan Even Tzur, and Oren Cohen is devoted to a theoretical study of how the symmetries of laser-dressed matter determine selection rules and its absorption spectrum.

 

This paper is intended to advance the existing knowledge in the crucial area of floquet engineering and optically dressed states in innovative low-dimensional materials and surfaces.  

 

Therefore, I believe that this paper should be accepted for publication in Photonics provided that the authors address the following comments.

 

Did I get it right that the consideration was mainly done for the dipole molecules which mainly consist of two spatially separated charges?  Please explain in more detail for which molecules or materials and their phase states this method could be applied.

 

Thank you. Our work is applicable to any molecule that possesses one of the symmetries tabulated by Floquet Group Theory[3] , regardless of the specific structural details of the molecule. Additionally, in our example, we use the electric dipole interaction and the dipole moment of the benzene molecule. (Eq. 1) . To enhance clarity on this aspect, we have added additional sentences to provide a more thorough explanation and ensure that the general applicability of our results is well understood. The revised manuscript reads (page 5):

“It is important to note that our work is based solely on symmetry arguments, independent of the specific molecular structure or the various physical mechanisms of optical absorption. Additionally, the presented formalism is general, provided that the light includes enough optical cycles to account for the Flouqet formalism. Notably, on-resonance interaction requires significantly larger number of optical cycles.”

 

Please explain in more detail what our-of-plane polarization means? Is it a type of a circularly polarized light? Could the direction of light polarization be not perpendicular to the direction of its group velocity? This really needs to be explained in more details to make this paper clearer for the readers. 

Thak you. You are correct that the orientation of the field was not clearly presented. We have addressed this issue by providing a detailed clarification in the paper regarding the orientations of both the driving and probe fields, as well as the molecule orientation. This additional information aims to ensure that all aspects of the field and molecule orientations are explicitly and comprehensively explained. According to feedback from our colleagues, the revised paper is significantly easier to read and conveys the message much more smoothly. The revised manuscript reads (page 2):

“The k-vector of the driving field is in z direction   while the probe beam k-vector is in y-direction   and it is linearly polarized in z-direction.. the time dependent Hamiltonian of the system is given by.”,” As a generalization, the polarization of the prob can also account for the absorption of in-plane (the molecule XY plane) probes”

Certain improvement of the word usage and formulations is needed in some places, such as "determine selection rules that determine its absorption spectrum"

We have reviewed the paper and improved the English throughout. Specifically, we have revised the phrase 'determine selection rules that determine its absorption spectrum' to 'determine the selection rules that influence its absorption spectrum.'

Bibliography

[1]          Torres-Torres, Carlos, et al., “Coexistence of two-photon absorption and saturable absorption in ion-implanted platinum nanoparticles in silica plates.,” JOSA B 356 2018 1295-1300.

[2]          B. Gu, “Generalized Optical Sum Rules for Light-Dressed Matter,” J. Phys. Chem. Lett., vol. 15, no. 21, pp. 5580–5585, May 2024, doi: 10.1021/acs.jpclett.4c00837.

[3]          O. Neufeld, D. Podolsky, and O. Cohen, “Floquet group theory and its application to selection rules in harmonic generation,” Nat. Commun., vol. 10, no. 1, p. 405, Jan. 2019, doi: 10.1038/s41467-018-07935-y.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have importantly improve their manuscript. The results and analysis are clear and solid. Then, I can recommend this work for publication in present form.

Comments on the Quality of English Language

A proofreading is suggested