Propagating arbitrarily shaped pulses in a nonlinear normally dispersive fiber using moments
Bibliographic record
Abstract
We use the method of moments to calculate the propagation of an arbitrarily shaped pulse in a nonlinear dispersive fiber. By assuming that the pulse is linearly chirped, we are able to determine analytically the evolution of the second order moments (representing the duration, bandwidth and chirp of the pulse) along propagation regardless of the initial pulse shape. The evolution of the moments is given by an implicit equation and several invariants. These invariants allow an easy estimation of the different pulse parameters. The linear chirp approximation implies that the arbitrary pulse shape remains invariant along propagation but allows to calculate the propagation in both dispersion regimes from the same solution. The solution show an oscillatory behavior in the anomalous dispersion regime and a monotonic behavior in the normal dispersion regime. In both regimes the calculations are compared to numerical split-step simulations and are shown to agree for propagation over many dispersion and nonlinear lengths. While this method describes well the evolution of the pulse duration, bandwidth and chirp, we need to proceed differently to find the evolution of the pulse shape. From these propagation equations for the moments, we derive an approximate implicit solution describing the propagation of a Gaussian pulse in the normal dispersion regime. This approximate solution describes the pulse shaping toward a parabola that the pulse undergoes along propagation. A good agreement is found between the pulse obtained from numerically solving the implicit equation and the split-step propagation of the same pulse. Numerically solving the implicit analytical function describing the pulse is much faster than using purely numerical simulations, which becomes time consuming for highly chirped pulses with large bandwidths over long propagation distances. These and other results suggest that pulse shaping along propagation is only adequately modeled by implicit functions.
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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 | 0.001 |
| Open science | 0.001 | 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".