Continuous-wave stability and multipulse structures in a universal complex Ginzburg–Landau model for passively mode-locked lasers with a saturable absorber
Bibliographic record
Abstract
The stability of continuous waves and the dynamics of multipulse structures are studied theoretically for a generic model of passively mode-locked fiber lasers with arbitrary nonlinearity. The model is characterized by a complex Ginzburg–Landau equation with a nonlinear term <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>I</mml:mi> <mml:mi>m</mml:mi> </mml:msup> </mml:mrow> <mml:mspace width="negativethinmathspace"/> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mspace width="negativethinmathspace"/> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi mathvariant="normal">Γ</mml:mi> <mml:mi>I</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mo stretchy="false">)</mml:mo> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>I</mml:mi> </mml:math> is the field intensity, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>m</mml:mi> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>n</mml:mi> </mml:math> are real numbers, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Γ</mml:mi> </mml:math> is the saturation power. Fixed-point solutions of the governing equations reveal an interesting loci of singular points in the amplitude-frequency plane consisting of zero, one, or two fixed points, depending on the values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>m</mml:mi> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>n</mml:mi> </mml:math> . The continuous-wave stability is analyzed within the framework of the modulational-instability theory, and the results demonstrate a bifurcation in the continuous-wave amplitude growth rate and propagation constant characteristic of multiperiodic wave structures. In the full nonlinear regime, these multiperiodic wave structures turn out to be multipulse trains, unveiled via numerical simulations of the model nonlinear equation, the rich variety of which is highlighted by considering different combinations of values for the pair ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>m</mml:mi> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>n</mml:mi> </mml:math> ). The results are consistent with previous analyses of the dynamics of multipulse structures in several contexts of passively mode-locked lasers with a saturable absorber, as well as with predictions about the existence of multipulse structures and bound-state solitons in optical fibers with strong optical nonlinearity, such as cubic-quintic and saturable nonlinearities.
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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 | 0.001 |
| 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".