An Integro-Differential Equation Formulation for the Ideal Veselago Lens
Bibliographic record
Abstract
The 2-D problem of finding the electric field for a line-source illuminating a lossless Veselago lens (VL) is cast as an integro-differential equation (IDE). The integral corresponds to a surface integral of the total tangential magnetic field on the boundaries of the lens. The IDE is obtained using an incident/scattered-field decomposition such that the VL is considered to be the scatterer. The new formulation is applied in five distinct regions: the illuminating-source region on the left side of the lens, two regions within the lens separated by a power-transfer plane, and two regions to the right of the lens, also separated by a power-transfer plane. The formulation is shown to be consistent with previously derived analytic expressions for the fields. In addition, the new IDE formulation provides a physically intuitive picture of the focusing behavior of the lens, specifically, showing how the induced contrast sources at the boundaries determine the resulting focused field. It is shown how the line integral contributions to the scattered field on the left side of the lens are zero, and how the scattered field produces the expected focus point singularities on the interior and far-side of the lens.
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How this classification was reachedexpand
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 | 0.001 | 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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".