Bessel beams: a unified and extended perspective
Bibliographic record
Abstract
We present a unified and extended perspective of Bessel beams, irrespective of their orbital angular momentum (OAM)—zero, integer or noninteger—and mode—scalar or vectorial, and LSE/LSM or TE/TM in the latter case. The unification is based on the integral superposition of constituent waves along the angular-spectrum cone of the beam, and enables us to describe, compute, relate, and implement all Bessel beams, and even other types of beams, in a universal fashion. We first establish the integral superposition theory. Then, we demonstrate the existence of noninteger-OAM TE/TM Bessel beams, compare the LSE/LSM and TE/TM modes, and establish useful mathematical relations between them. We also provide an original description of the position of the noninteger-OAM singularity in terms of the initial phase of the constituent waves. Finally, we introduce a general technique for generating Bessel beams using an adequate superposition of properly tuned sources. This global perspective and theoretical extension may be useful in applications such as spectroscopy, microscopy, and optical/quantum force manipulations.
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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) | 0.000 | 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 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".