Application of the boundary integral equation method to very small wavelength-to-period diffraction problems
Bibliographic record
Abstract
Diffraction from 1D multilayer gratings having arbitrary border profiles including edges is considered for small wavelength-to-period (λ/d) ratios, the most difficult case for any rigorous numerical method. The boundary integral equation theory is so flexible that we can indicate a few areas where it can be modified. In this work, special attention is paid to the main aspects of the Modified Boundary Integral Equation Method for λ/d ≪ 1 as well as to a more general treatment of the energy conservation law applicable to multilayer absorption gratings. Three types of small λ/d problems are known from optical applications: (a) shallow gratings working in the X-ray and extreme ultraviolet ranges, both at near-normal and grazing angles, (b) deep echelle gratings with a steep working facet illuminated along its normal by light of any wavelength, and (c) rough mirrors and gratings in which rough boundaries can be represented by a large-d grating, and which contain a number of random asperities illuminated at any angle and wavelength. Numerical examples of diverse in-plane diffraction problems are presented.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".