Joint time-frequency and finite-difference time-domain analysis of precursor fields in dispersive media
Bibliographic record
Abstract
Superluminal group velocities, defined as group velocities exceeding the speed of light in vacuum, c, have been theoretically predicted and experimentally observed in various types of dispersive media, such as passive and active Lorentzian media, one-dimensional photonic crystals, and undersized waveguides. Though superluminal group velocities have been found in these media, it has been suggested that the pulse "front" and associated transient field oscillations, known as the precursors or forerunners, will never travel faster than c, and hence relativistic causality is always preserved. Until now, few rigorous studies of these transient fields in structures exhibiting superluminal group velocities have been performed. In this paper, we present the dynamic evolution of these earliest field oscillations in one-dimensional photonic crystals (1DPC), using finite-difference time-domain (FDTD) techniques in conjunction with joint time-frequency analysis (JTFA). Our study clearly shows that the precursor fields associated with superluminal pulse propagation travel at subluminal speeds, and thus, the arrival of these precursor fields must be associated with the arrival of "genuine information." Our study demonstrates the expected result that abnormal group velocities do not contradict Einstein causality. This work also shows that FDTD analysis and JTFA can be combined to study the dynamic evolution of the transient and steady state pulse propagation in dispersive media.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 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".