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Sum frequency generation from real-time simulations in two-dimensional crystals
by Mike N. Pionteck, Myrta Grüning, Simone Sanna, Claudio Attaccalite
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Claudio Attaccalite |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2503.07095v1 (pdf) |
| Date submitted: | March 11, 2025, 9:52 a.m. |
| Submitted by: | Attaccalite, Claudio |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Sum frequency generation (SFG) and difference frequency generation (DFG) are second order nonlinear processes where two lasers with frequencies ω1 and ω2 combine to produce a response at frequency ω=ω1±ω2 . Compared with other nonlinear responses such as second-harmonic generation, SFG and DFG allow for tunability over a larger range. Moreover, the optical response can be enhanced by selecting the two laser frequencies in order to match specific electron-hole transitions. Here, we propose a first-principles framework based on the real-time solution of an effective Schr\"odinger equation to calculate the SFG and DFG in various systems, such as bulk materials, 2D materials, and molecules. Within this framework, one can select from various levels of theory for the effective one-particle Hamiltonian to account for local-field effects and electron-hole interactions. To assess the approach, we calculate the SFG and DFG of two-dimensional crystals, h-BN and MoS2 monolayers, both within the independent-particle picture and including many-body effects. Additionally, we demonstrate that our approach can also extract higher-order response functions, such as field-induced second-harmonic generation. We provide an example using bilayer h-BN.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1- Presents a clear methodological advance that should allow calculation of high-order susceptibilities in shorter time.
2- Gives clear examples of relevant applications of the method.
Report
The manuscript presents method development for ab-initio description of non-linear sum frequency generation and difference frequency generation with two lasers. The relevant quantity is a susceptibility that has to be extracted from polarizations. These are in turn calculated via a time-dependent simulation that runs an effective model, which is based on ab-initio methods (like GW).
I am probably not close enough to field to have noticed it if the
authors should have failed to reference important papers that should have been discussed. I did find the chosen references to be helpful and to the point.
The methodological step forward introduced here is the extraction of the polarization via a singular-value decomposition
or via a least-squares fit instead of a Fourier transform. The latter, which had been used before, naturally tends to need very large simulation times given that the time needs to capture the periodicity of both involved frequencies. It appears, however, that the new approaches can extract the same information from much shorter simulation times.
The method is then applied to two cases h-BN and MoS_2, and in both cases, as single-particle and an interacting description are used and compared. In the case of h-BN, results differ quite significantly once interactions are included: The (ω1,ω2) pairs with maximal susceptibility are at different values and of much higher intensity. This is explained as a resonance with excitons. For MoS2, the impact of correlations is less striking, although features in the frequency dependent heat map become sharper when interactions are included. Finally, a simulation is also run from field-induced second-harmonic generation, a third-order effect.
The method indeed appears to be valuable and to permit a simulation of interesting processes with realistic cases with acceptable computational effort. It is 'incremental', but that is not negative: it clearly builds on earlier work and takes it one (plausible) step further. This makes it the presentation of a useful tool that may also help others who have to deal with extracting frequency-dependent information from time-dependent data.
Also, the applications that the authors discuss are well motivated and illustrative. On sees that it is nice to be able to include electron-hole interactions, at least in some materials. They also
suggest that the method can indeed be practically useful for understanding experimental data.
The criterion "Detail a groundbreaking theoretical/experimental/computational discovery" can
be considered as fulfilled, and one cane hope for "Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work".
Requested changes
On the whole, I also found the paper to be well written and understandable, however, I have a few comments below.
1- The discussion of the problem that the necessary period is
technically finite for any two rational frequencies, but can become rather long, is maybe too elaborate: I am fairly sure that most readers would also understand this point if it were dealt with a bit more briskly.
2- I would probably have structured the discussion of ω1≈ω2 a bit differently: I would have started by noting that it is hard for the Fourier-transform approach (so that readers know right away that this is not some new problem introduced here). Then, say that it is still hard now (for technically slightly different reasons). (This suggestions is optional.)
3- I would have liked to learn a bit more about which of the two
'shortcuts' introduced here (SVD or least squares) is better in which situations: Figure 3 tells us that both work, but not why one should choose one or the other. This is my biggest issue that I think should really be addressed. Knowing more about this would make the paper more valuable to other researchers.
4- I was wondering whether experimental data are available, to which the authors could directly compare, or whether the results presented are pure predictions.
5- Also, please proof read once more, I think that the sentence that introduces Ref.[11] on the first page is missing its verb. Also, to continue nitpicking, the references are not formatted fully
consistently ("Phyis. Rev." vs. "Physical Review" and such details).
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Author: Claudio Attaccalite on 2025-05-02 [id 5439]
(in reply to Report 1 on 2025-04-24)Dear Editor,
We thank the referee for providing careful attention to the manuscript, for his/her many helpful comments and the recommendation for publication in SciPost Physics. We have made minor revisions and address the referee’s comments below.
We have condensed the discussion about the period.
We thank the referee for this helpful remark. We have introduced this paragraph as suggested by the referee.
For the systems we have tested, we do not see any differences between SVD and least square optimization in terms of efficiency and results. This is due to the fact that we are dealing with a linear problem. Note, however, that although at convergence the two methods should give the same result, there is the possibility of getting caught in local minima, which we did not notice in our case anyway. For a nonlinear problem SVD and the least square optimization do not necessarily provide the same results.
In the manuscript we studied two systems hBN and MoS2. The first one is used more as a proof of principle of our methodology, because due to its large band gap experiments are quite difficult. On the other hand, MoS2 is active in the visible range and experiments are available. In this manuscript there is already a discussion on the comparison of SFG/DFG, but we catch the occasion to add more references and enlarge the discussion, see changes in Sec. ~5.2.
We thank the referee for this remark, we proof read our manuscript again, and fixed all abbreviations in the references.