Generalized total internal reflection at dynamic interfaces
Bibliographic record
Abstract
Recent research developments in the area of spacetime metamaterial structures and systems have raised new questions as to how the physics of fundamental phenomena is altered in the presence of spacetime modulation. In this context, we present a generalized and comparative description of the phenomenon of total internal reflection (TIR) at different dynamic interfaces. Such interfaces include, beyond the classical interfaces corresponding to the boundaries of moving bodies (moving interface--moving matter systems), interfaces formed by a traveling-wave step modulation of an electromagnetic parameter (e.g., refractive index) (moving interface--stationary matter systems) and fixed interfaces between moving-matter media (stationary interface--moving matter systems). We first resolve the problem using the evanescence of the transmitted wave as the criterion for TIR and applying the conventional technique of relative frame hopping (between the laboratory and rest frames), which results in closed-form formulas for the relevant critical (incidence, reflection, phase refraction, and power refraction) angles. We then introduce the concept of catch-up limit between the dynamic interface and the transmitted wave as an alternative criterion for the critical angle. We use this approach both to analytically verify the critical angle formulas, further validated by full-wave (FDTD) analysis, and to explain the related physics, using Fresnel-Fizeau drag and spacetime frequency transition considerations. These results might find various applications in ultrafast optics, gravity analogs, and quantum processing.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.008 |
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; both teacher heads agree on what is shown here.
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".