Peer review of: Stimulated plasmon polariton scattering (2020)

RR2

     Decision on manuscript NCOMMS-19- 04521A
       Message:
      Dear Dr Wolff,
Please allow me to apologize for the delay in getting a decision to you. The reviewers needed more time to submit their report due to busy schedules. Your manuscript entitled "Stimulated plasmon polariton scattering" has now been seen by 2 referees, whose comments are appended below. In the light of their collective advice advice I regret to inform you that we cannot publish your manuscript in Nature Communications.
You will see that reviewer #3 raises quite substantial concerns regarding feasibility of the observation. While I realize this is a theoretical work, it is clear that we cannot proceed without substantial work detailing how this phenomenon could be observed and unfortunately, these reservations are sufficiently important to preclude publication of this study in Nature Communications. We have also written to reviewer #2 in confidence regarding the concerns of #3, and they have agreed that these concerns are important. Given the collective feedback, we feel it is best at this stage for you to seek publication elsewhere.
If you opted into the journal hosting details of a preprint version of your manuscript via a link on our dedicated website (https://nature-research-under- consideration.nature.com), please note that we will now remove these details as your manuscript is no longer under consideration at Nature Communications. For more information, please refer to our FAQ page at https://nature-research-under- consideration.nature.com/posts/19641-frequently-asked-questions
I am so sorry that we cannot be more positive on this occasion and thank you for the opportunity to consider your work.
Best regards, Lina
Dr Lina Persechini
Associate Editor & Team Manager Nature Communications Lina.Persechini@nature.com
Reviewers' comments:
Reviewer #2 (Remarks to the Author):
I'm satisfied with the changes that the authors have made to address the queries posed. In particular, I'm grateful that the authors have now included in-depth supplementary information. The supplementary information answers numerous technical questions and addresses all of my prior concerns regarding the reproducibility of their results.
With this additional information and the revisions that they have made the manuscript, I feel strongly that this paper should be accepted in nature communications. This manuscript explores some intriguing new ideas, and I think it will definitely spur a great deal of interest at the intersection between nonlinear optics and two-dimensional electronic materials.
Reviewer #3 (Remarks to the Author):
The authors put forward an idea of „stimulated plasmon polariton scattering“
  
            (SPPS), to use in 2D materials like graphene, for studying fundamental physics and for some applications. The idea of SPPS is similar to the stimulated Brillouin scattering (SBS) phenomenon known in nonlinear optics. The authors claim that SPPS power gain in the proposed experiments and structures can be sufficiently large under achievable experimental conditions. The paper is theoretical.
In my opinion, it is quite possible that the idea is interesting and the proposed effects may work indeed. But I have not found in the paper clear evidences that the observation of the proposed effects is realistic.
There exists a very large difference between the SBS and the proposed SPPS phenomena. The propagation length of sound waves in liquids and solids can be as large as kilometers, while the propagation length of 2D plasmons in 2D materials is as small as just a few microns. Therefore the authors had to clearly show that the nonlinearity of the plasmon-light interaction is so large that it can overcome the strong damping of plasma waves in the system. This is the most important point and this had to be done with all details to convince the reader that the idea is realistic indeed. I have not found details in the authors’ arguments and their conclusions are not convincing at all.
Let me illustrate said above by some examples.
1. In Figure 1 the authors show schematic of the SPPS experiment: a rectangular dielectric optical waveguide is covered by a graphene sheet and the nonlinear plasmon-light interaction should lead to the desired effect. The general idea is clear but there are some questions to its practical realization. In particular, we read “A weak THz signal is injected through the bias contact (blue) and amplified along the waveguide”. How the THz wave propagating in free space (wavelength ~ hundred of μm) will be injected into the waveguide with dimensions ~ 200 nm? I believe that a lot of energy will be lost on the interface between the tens-of-μm THz antenna and sub-μm optical waveguides. This issue is not discussed in the paper.
2. In Figure 2(a) the authors suggest two possible realizations of the device. Now we see two dielectric waveguides instead of one from Figure 1. Why two waveguides are better than one? In my opinion, if the graphene sheet lies on the waveguide the light-plasmon interaction (the integral in Eq. (2)) will be larger than when a piece of graphene hangs over the gap of 150 nm width (sheet position 2); this hanging piece of graphene will contribute to the plasmon damping and will work against the desired effect. The sheet position 1 causes even more questions. The optical field is mainly concentrated inside the waveguides and substantially decreases in the gap between the waveguides which is seen from the authors’ CONSOL calculations. Placing graphene between the two waveguides will reduce the interaction again as compared to the structure in Figure 1. Why the authors chose the two-waveguide structure is not discussed in the paper. If my intuitive arguments are wrong and the authors did perform calculations of the field distributions in and around the waveguides and found the best positions for the graphene sheets indeed, why these calculations are not shown and not discussed in detail in the paper?
3. It seems that the difference between positions 1 and 2 is in the dielectric constant of the environment, ε=1 in the position 1 and ε=(1+ε_substrate)/2 in the position 2: due to this difference the plasmon frequency and the quality factor are higher in the position 1 than in the position 2 (unfortunately I have to guess here since the authors did not explain this point). However in typical experiments graphene lies on a substrate. If the authors imply just freely hanging graphene in the position 1 I am wondering how this can be practically realized in a real device? If in the position 1 graphene lies on a substrate than the advantage of this geometry (ε=1) disappears.
4. In Figure 2(a) the waveguide material is assumed to be Si. But Si is a semiconductor often doped by some amount of impurities. This will lead to an additional damping of 2D plasmons and maybe to a damping of the optical modes.
  
            The propagation of optical modes in the Si waveguides is also not explained. The only information that the effective index equals 1.37 is insufficient; moreover this number seems to be too low for Si waveguide (the dielectric constant of Si is 11.7). Usually experimentalists use dielectric materials for the waveguides like silicon oxide or silicon nitride. Why semiconducting silicon is supposed to be used for SPPS in this work?
5. The authors assume to change the Fermi level from ~0.01 eV up to ~2 eV (Figure 2(b)). But, firstly, it is unrealistic to push the Fermi level in graphene above ~0.4 eV, therefore the very high quality factors and very broad frequency ranges “achieved” at Fermi energies up to ~2 eV should be reduced by several times or even by an order of magnitude in realistic structures. Secondly, changing the Fermi level assumes that graphene lies on a SiO2/doped Si substrate and E_F is varied by the gate voltage applied between graphene and Si. But then, if the hanging graphene is assumed to be in the sheet position 1, all left plots drawn in Figures 2(b,c) are useless.
6. If graphene lies on a SiO2/doped Si substrate (in order to control E_F) what is the 2D plasmon spectrum in this paper? As far as I understand (I have to guess again since the authors do not discuss this point) the authors assume the square- root dispersion of 2D plasmons, ω^2~q; this can also be seen from the sketch in Figure 1(a). But in the graphene-dielectric-metal (or heavily doped semiconductor) system the spectrum of 2D plasmons is linear, ω^2~q^2d at qd<1, where d is the dielectric thickness. If to take this fact into account the plasmon frequency and the quality factor will be further reduced. This important practical issue is not discussed in the paper.
7. The authors give minimal information about how the frequency of 2D plasmons (Stokes shift) and their propagation length (quality factor) are plotted in Figure 2(b). No one formula is given here. They write “The polaritonic damping parameter κ_b depends on E_F. We calculate it from a Drude relaxation rate that was experimentally determined for this type of “vdW-sandwich" [24] and plot it implicitly in Fig. 2b as the polaritonic quality factor =Ω/(2v_b κ_b)”. Why the authors did not give here just two numbers, the relaxation rates for 60 K and 300 K, which they extracted from [24]? Why should I or other readers read the long paper [24] only in order to find numbers which the authors used in their paper? I have found the number of 1.6 ps for graphene at 60 K and could get a figure similar (but not identical, again due to the lack of information) to that shown in Figure 2(b) but I still have no idea how the authors plotted the curves for 300 K. Why should the readers guess what the authors’ thoughts were and not just read what they really did?
8. It is unclear at all how the authors calculated the SPPS gain (2) and plotted the corresponding Figures 2(b,c). The value Q in (2) depends on the overlap integral and the nonlinear susceptibility χ^(2). In the SBS effect the interaction takes place in the whole (3D) volume of the waveguide. In the considered here SPPS effect the integration goes over a much smaller volume (over just a 2D plane if χ^(2) is due to the nonlinearity of graphene). Here the authors had to show that, in spite of the thin interaction area the resulting gain is sufficient to overcome losses. But no results of such analysis are shown. Then, what is the value of χ^(2), where it comes from, how it depends on Fermi energy? No specific formula for χ^(2) is given in the paper. Figures 2(b,c) show that the gain very essentially depends on the Fermi energy, with a broad maximum at E_F~0.07 eV and with strongly oscillating, resonant features around 0.4-0.5 eV. What are the physical reasons for these features? Which analytical formulas for χ^(2) demonstrate these feature? What is their physical meaning? The paper does not contain answers to these questions. Moreover, it seems that the authors do not know themselves which nonlinearity they are going to use in the proposed phenomenon. Just after Eq. (2) they write that “χ^(2) is the nonlinear susceptibility tensor describing all suitable second-order nonlinearities in the system”. What are these “all suitable nonlinearities”, are they due to graphene or to the waveguide material? Since the gain is plotted as a function of Fermi energy in graphene and, especially, the resonances are seen at E_F~0.4 eV=ћω/2, this seems to suggest
  
            that the nonlinearity comes from graphene. But in the Supplementary Note the authors write that the waveguide should at least partially be composed of a nonlinear material such as lithium niobate. What does it mean “partially composed” ? Do the authors have specific suggestions how the waveguide should be filled by the nonlinear lithium niobate? Are there specific calculations of the gain made with the LiNb-filled waveguide? Do these calculations show that the gain can be sufficiently high to make the whole story meaningful? Does all this mean that the plots shown in Figure 2 make no sense anymore?
9. In the next sentence from the Supplementary Note the authors write: “... we could not obtain an appreciable SPPS-gain based on this effect alone. The problem is that the polaritonic mode does not penetrate the waveguide enough to lead to a sufficient nonlinear mode overlap”. This is just the central question of the whole story, why this important point is discussed somewhere in the Supplementary Note and not in the main text? Does this negative result mean that the SPPS cannot be actually realized? Does it make sense then to publish this paper?
10. In the next sentence from the Supplementary Note we read “We do, however, emphasize that this approach might prove very useful for the excitation of polaritons in materials other than graphene“. But if, suddenly, the authors decide to replace graphene by other 2D materials, does this mean that all calculations and plots shown in Figure 2 make no sense anymore (they were done using specific properties, like σ(ω), of graphene)? For any other 2D material with a parabolic spectrum all specific results (plasma frequency and damping, nonlinear parameters, etc.) will be different.
11. Finally a couple of minor points:
(a) in the literature there exist several publications on the second order nonlinear response of graphene which are quite relevant for the discussed effect; not all of them are cited. Several publications of the Belyanin’s group treated the plasmon- light nonlinear interaction in a much more comprehensive and quantitative way: PRL 112, 055501 (2014), Phys. Rev. B 93, 235422 (2016), Phys. Rev. B 94, 195442 (2016). The paper of the Sipe group, Scientific Reports 7, 43843 (2017), also treated the discussed nonlinearity and gave detailed derivations and quantitative results. In my opinion, the present paper does not add anything useful and new to these studies;
(b) the term “plasmon polariton” supposes that 2D plasmons strongly interact with light, i.e. the square-root dispersion ω~sqrt(q) is close to the light line ω=cq. In the present work the 2D plasmon frequency is always much smaller than the light frequency with the same q. Therefore the term “plasmon” (instead of plasmon polariton) and SPS (instead of SPPS) would be more relevant.
Summary: since the damping of 2D plasmons is many orders of magnitude larger than the damping of sound waves, the feasibility of SPPS had to be studied and clearly demonstrated in much more details than it is done in the paper. Personally I do not believe that the SPPS phenomenon will ever work in structures with graphene or any other 2D materials and I did not find in the paper convincing arguments that the proposed effect can be observed indeed. The paper is very badly written: the authors carefully hide from the reader details of the theory rather than explain what and how they did.
I do not recommend this manuscript for publication.