Study of Field Enhancement in the Subnanometer Gap of Plasmonic Dimers Accounting for the Surface Quantum Effect
Round 1
Reviewer 1 Report
The author studied the surface quantum effect of plasmonic Au dimers. The calculation method is improved and influence of diameter, gap, and aspect ratio are investigated. Finally, some interesting phenomenon is obtained, such as the reduction of enhacement factor inside gap and blue shift of plasmonic peak. This work is well-written and interesting. I believe it can be published after some revision.
1) As known, the dielectric environment is also important to the plasmonics. What's the dielectric environment is used in this work? It would be better if the author can investigated the influence of dielectric environment to the gold dimers or add some comment about it.
2) Unfortunately, experimental data is lack, which make this work not so convincing. I suggest to compare the calculation results with some experimental results in literatures. For example, as far as I know, ion implantation has been used for the interparticle spacing manipulation. The author can make some comment.
3) The writing formation of novelties mentioned in the conclusion part looks strange to me. It's true that it will make the novelties more clear to readers by listing one by one. However, I think the expression of novelty should be integrated into the text rather than deliberately highlighted.
Author Response
Please, see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
In this paper, the authors investigated the influence of surface quantum effects on the optical properties of plasma dimers composed of two identical gold nanoparticles with small gaps. It is shown that the quantum surface effect leads to a blue shift and damping of the corresponding plasmon resonance. This effect becomes more substantial when the constituent particles are elongated, and the gap size shrinks to sub-nanometer values. In this case, the difference in the results obtained using the surface response functions and the local response approximation can be up to four times and is accompanied by a spectral blue shift of 10 nm. I believe that publication of the manuscript may be considered only after the following issues have been resolved.
1. In this article, the authors mentioned a lot of formulas, and the authors need to provide corresponding numbers for these formulas.
2. When the spacing between nanoparticles is very small, there will be a strong electric field enhancement effect between the particles. The author needs to provide corresponding electric field diagrams.
3. The introduction can be improved. The articles related to some applications of Nanoplasmonics should be added such as Results in Physics 48, 2023, 106420; Micromachines 2023, 14, 953; Optics Express, 30(20), 35554-35566, 2022; Electronics 2023, 12(12), 2655.
4. The English expression of the whole article needs to be further improved.
Minor editing of English language required
Author Response
Please, see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
The authors present an investigation of the influence of surface quantum effects on the optical characteristics of a plasmonic dimer composed of two identical gold nanoparticles with a subnanometer gap. Using a semiclassical theory based on mesoscopic boundary conditions and surface response functions, the extinction cross-section and field enhancement factor are calculated for various particle elongations and gap sizes. The study demonstrates the impact of surface quantum effects. Specifically, with smaller gap sizes and elongated particles, deviations up to four times from local response predictions are observed, leading to a blue spectral shift of 10 nm. This is attributed to an electron cloud spill-in, resulting in a decrease in plasmon resonance amplitude and a shift to shorter wavelengths. The author gave a very comprehensive discussion of related works. However, the following questions need to be addressed to improve the novelty of the paper.
1. How are the results of surface response function (SRF) compared with GNOR as shown in the author's previous work reference [32]? Is there any way to combine both methods to see how well it accounts for the quantum effects? It would be helpful if the author could shed some light on this.
2. The authors also listed the main difference between the studies [43] and their cases. How much difference are the results compared to the reference [43] because of the consideration of Landau damping? It is important to show that the improvement in the paper is nontrivial.
3. If jellium nanoparticles are considered using the presented theory, would it reproduce the red-shift and broadening because of the spill out of electrons?
4. The construction of the discrete sources relies on fitting the transmission condition. Can the author offer more details about this process either in the main text or in the methods?
Author Response
Please, see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have perfectly answered my first question.
For the second question, I still believe comparsion with experimental results is necessary. As the author said, there may be no literatures with both of the experimental results and simulation considering mesoscopic conditions. However, I think the author can still compare their simulation results with experimental results in literatures to prove that, if one consider mesoscopic condition in simulation, a more accurate results can be obtained. It is not necessary to find papers with both experimental results and mesoscopic condition based simulation results. Or does the author mean the mesoscopic condition should not be used in some cases of nanodimers? Only in this way, the experimental results in literature can not be compared.
For my third comment, the author didn't do any changing. Although I still feel strange for the formation, it is acceptable for me.
Overall, the manuscirpt can be published in present version. But I highly recommended the authors to reconsider adding some literatures with experimental results.
Author Response
Dear Reviewer!
We would like to thank you for your helpful recommendations. Below we provide our responses to your comments.
- The authors have perfectly answered my first question.
- For the second question, I still believe comparsion with experimental results is necessary. As the author said, there may be no literatures with both of the experimental results and simulation considering mesoscopic conditions. However, I think the author can still compare their simulation results with experimental results in literatures to prove that, if one consider mesoscopic condition in simulation, a more accurate results can be obtained. It is not necessary to find papers with both experimental results and mesoscopic condition based simulation results. Or does the author mean the mesoscopic condition should not be used in some cases of nanodimers? Only in this way, the experimental results in literature can not be compared.
Answer. Indeed, there are publications discussing experimental results on dimers or optical antennas. However, most of the experimental results are devoted to nanodimers with sizes exceeding 10–20 nm, where the contribution of quantum effects can be insignificant. In addition, most publications consider the dimers located on a substrate, but the existing implementation of the discrete source method is not intended for studying nanostructures located near the substrate. Nevertheless, following your recommendations, we have added some references to articles containing experimental results related to nanodimers in the text of our manuscript:
- Zhou, X.; Deeb, C.; Kostcheev, S.; Wiederrecht, G. P.; Adam, P.-M.; Béal, J.; Plain, J.; Gosztola, D. J.; Grand, J.; Félidj, N.; Wang, H.; Vial, A.; Bachelot, R. Selective Functionalization of the Nanogap of a Plasmonic Dimer. ACS Photonics 2014, 2 (1), 121–129. https://doi.org/10.1021/ph500331c.
- Scholl, J. A.; Garcı́a-Etxarri, A.; Koh, A. L.; Dionne, J. A. Observation of Quantum Tunneling between Two Plasmonic Nanoparticles. Nano Letters 2013, 13 (2), 564–569. https://doi.org/10.1021/nl304078v.
In addition, we mentioned that some experimental results can be found in the articles [17,19].
- For my third comment, the author didn't do any changing. Although I still feel strange for the formation, it is acceptable for me.
The writing formation of novelties mentioned in the conclusion part looks strange to me. It's true that it will make the novelties more clear to readers by listing one by one. However, I think the expression of novelty should be integrated into the text rather than deliberately highlighted.
Answer. We formulated the novelties in both ways - integrated them into the main text (lines #156-158, and #271-274) and highlighted them in the conclusions section (lines #450-461).
- Overall, the manuscirpt can be published in present version. But I highly recommended the authors to reconsider adding some literatures with experimental results.
Answer. We have included some new references that are mentioned above.
With the very best wishes,
Authors
Yu. Eremin, V. Lopushenko.
Reviewer 2 Report
Accept in present form.
Author Response
Dear Reviewer,
We would like to thank you for the helpful comments and positive report!
With the very best wishes,
Authors
Yu. Eremin, V. Lopushenko.
Reviewer 3 Report
The authors have responded to my comments and I recommend the acceptance of the manuscript in its current form.
Author Response
Dear Reviewer,
We would like to thank you for the helpful comments and positive report!
With the very best wishes,
Authors
Yu. Eremin, V. Lopushenko.
