Theory of the interference tunability of second harmonic generation for two-dimensional materials in layered structures
Bibliographic record
Abstract
We theoretically study how the intensity of second harmonic generation (SHG) for a sheet of two-dimensional (2D) material is controlled by an underlying layered structure. By utilizing the transfer matrix method with the inclusion of a nonlinear sheet current to describe the response of the 2D material, an explicit expression for the intensity of upward propagating second harmonic (SH) light is obtained, and the effects of the layered structure can be identified by a structure factor β , defined as the ratio of SH intensity from such a structure to that from a freely suspended 2D material. Our results show that the influence of a layered structure on the SHG intensity arises from interference effects of both the fundamental light and the SH light; the value of the structure factor is 0 ≤ β ≤ 64. Furthermore, when the incident light is pulsed, the interference effects are partially canceled due to the existence of many wave vectors and frequencies, and the cancellation becomes severe for thick films, small beam spots, and short pulses. For a specific structure of 2D material/dielectric film/substrate, the thickness of the dielectric film can effectively tune the value of β in an interval [ β min , β max ], and detailed discussions are performed for the thicknesses when these two extreme values can be obtained. When there is optical loss or the substrate is not perfectly reflective, the extreme value of β max or β min cannot reach 64 or 0. A large β max requires two conditions to be fulfilled: (1) the substrate should be highly reflective, and (2) the refractive indices of the dielectric film at the fundamental and the SH frequencies should differ. Our results indicate how practical substrate structures can be used to achieve high SH signals, and the simple expression we give for the SH enhancement will be useful in characterizing the nonlinear susceptibility of 2D materials.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".