OPTICAL MODES OF A DISPERSIVE PERIODIC NANOSTRUCTURE
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Bibliographic record
Abstract
We show that the optical modes of a periodic nanostruc- ture with frequency dependent dielectric constant (i.e., a dispersive optical nanostructure), in general can be written as an ordinary eigen- value problem of a \dielectric function operator, for each distinct sym- metry representation of the periodic nanostructure. For a frequency dependence in the form of polynomial rational function, the problem translates to a polynomial eigenvalue equation in the frequency of the mode. The resulting problem can be solved using the basis functions of a dielectric backbone structure, which has a frequency independent dielectric constant. Rapid convergence is achieved when the basis func- tions are selected to be the modes of a dielectric backbone structure that minimizes the frequency perturbation of the dielectric function of the optical nanostructure. In particular, using a two dimensional photonic crystal constructed with a polar crystal as an example, we demonstrate that, remarkable simple cubic equations are su-cient to obtain accurate descriptions of eigenfrequencies.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 it