Stability of a semiconductor laser with a dispersive extended cavity
Bibliographic record
Abstract
We present a theoretical investigation of the stability properties of semiconductor lasers with strong feedback from dispersive extended cavities. Surprisingly, unstable behavior had been observed experimentally for chirped fiber grating lasers, where the stability of the laser was found to depend upon the orientation of the fiber grating. We reproduce this finding through a linear stability analysis, demonstrating that the presence of both the linewidth enhancement of the semiconductor diode, and a negative curvature of the phase of the external cavity reflection coefficient are necessary for instability to occur. In order to explain the role of the linewidth enhancement and phase curvature, we present a second approach based on more approximate model wherein the field evolution is found to be described by an equation that resembles the nonlinear Schr\"odinger equation (NLSE); the curvature of the phase then corresponds to the dispersion coefficient of a usual NLSE, and the linewidth enhancement factor corresponds to the nonlinear coefficient. We find an unstable regime analogous to the anomalous dispersion regime of the usual NLSE, where the boundary between normal and anomalous dispersion depends upon the width of the reflectivity spectrum. We also find that there is an additional unstable region that arises due to the carrier dynamics, and has no analogy in systems with an instantaneous nonlinearity. Further, for lasers with a negatively chirped grating, we find that oscillation tends to occur on the red side of the reflection spectrum peak.
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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 | 0.000 |
| 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".