Analytic Sinusoidal Steady-State Electromagnetic Field Expressions for the Ideal Veselago Lens
Bibliographic record
Abstract
Analytic expressions for the sinusoidal steady-state electromagnetic field associated with an ideal Veselago lens illuminated by either a line-source (2D case) or an electric dipole point-source (3D case) are obtained based on power flow considerations and the imposition of appropriate boundary conditions. The fields are written in terms of the standard free-space Green’s function except that both incoming and outgoing waves are utilized. Expressions for the Poynting vector are also provided. Some components of the field suffer a complex-conjugate discontinuity across two <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">power-transfer singularity planes</i> , one within the lens and one through the external focus point, so named because all the power generated by the point-source transfers through a singular point on each plane. The internal <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">power-transfer singular point</i> and the illuminating point-source are equidistant from the first lens boundary, whereas the external singular point, i.e., the focus point, and the internal singular point are equidistant from the second lens boundary. These singularities represent different physical properties than the traditional source or sink singularities. The new interpretation based on the concise analytic field expressions clears up the physically objectionable interpretation of these singularities as representing new sources of energy: no new sources of energy exist in our representations.
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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 | 0.000 | 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) | 0.000 | 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".