Laser resonator with a defective Jones matrix designed with the polar decomposition theorem
Bibliographic record
Abstract
The polar decomposition theorem (PDT) makes it possible to express any Jones matrix as a combination of a pure polarizer and a pure retarder. We establish the relations that these two elements must have to produce a defective Jones matrix, where two polarization eigenstates coalesce into a single state to create an exceptional point (EP). We present a laser resonator whose structure directly derives from the PDT and whose round-trip Jones matrix, J RT , becomes defective for some values of the control parameters. We show conditions wherein J RT commutes with the time-reversal ( T ) operator. J RT transitions from exact T symmetry, where the eigenvectors of the Jones matrix and the time reversal operator are shared and eigenvalues are real, to broken T symmetry, where eigenvectors are distinct, and eigenvalues are a pair of complex conjugates. The EP, located at the boundary between the two regimes, is characterized by a local maximum in the round-trip mode loss and a dip in the degree of polarization of the eigenstates.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| 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 source (direct Gemma or distilled Codex), 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".