One-dimensional description of cylindrically symmetric laser beams: application to Bessel-type nondiffracting beams
Bibliographic record
Abstract
We introduce a new representation of coherent laser beams that are usually described in circular cylindrical coordinates. This representation is based on the decomposition of a laser beam of a given azimuthal order into beams exhibiting Cartesian symmetry. These beams, which we call constituent waves, diffract along only one of their transverse dimensions and propagate noncollinearly with the propagation axis. A cylindrically symmetric laser beam is then considered a coherent superposition of constituent waves and is represented by an integral over an angular variable. Such a representation allows for the introduction of the propagation factor M2, defined in terms of one-dimensional root-mean-square (rms) quantities, in the treatment of two-dimensional beams. The representation naturally leads to the definition of a new rms parameter that we call the quality factor Q. It is shown that the quality factor defines in quantitative terms the nondiffracting character of a laser beam. The representation is first applied to characterize Laguerre-Gauss beams in terms of these one-dimensional rms parameters. This analysis reveals an asymptotic link between Laguerre-Gauss beams and one-dimensional Hermite-Gauss beams in the limit of high azimuthal orders. The representation is also applied to Bessel-Gauss beams and demonstrates the geometrical and one-dimensional characters of the Bessel-Gauss beams that propagate in a nondiffracting regime. By using two separate rms parameters, Q and M2, our approach gives an alternative way to describe laser beam propagation that is especially well suited to characterize Bessel-type nondiffracting beams.
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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 | 0.001 |
| 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".