Modeling of Pulse Propagation in Layered Structures With Resonant Nonlinearities Using a Generalized Time-Domain Transfer Matrix Method
Bibliographic record
Abstract
We introduce a generalized time-domain transfer- matrix (TDTM) method, the only method to our knowledge that is capable of modeling high-index-contrast layered structures with dispersion and slow resonant nonlinearities. In this method transfer matrix is implemented in the time domain, either by switching between time and frequency domains using Fourier transform and its inverse operation, or by replacing the frequency variable (ω) with its temporal operator (-i (d/dt)). This approach allows us to implement the transfer matrix method (which can easily incorporate dispersion, is analytical in nature, and requires less computation time) in the time domain, where we can incorporate nonlinearity of various kinds, instantaneous (such as Kerr nonlinearity), or slow resonant nonlinearity (such as carrier-induced nonlinearity). This generalized TDTM method is capable of incorporate non-analytical forms of dispersion and of nonlinearity, making it a versatile tool for modeling optical devices where dispersion and nonlinearities are obtained phenomenologically. We also provide a few numerical examples to compare our method with the standard finite-difference time- domain (FDTD) method, as well as to examine the range of validity of our method. For pico-second and longer pulses, our results agree with the FDTD simulation results to within 1% and the computation time of our method is more than 100 fold reduced compared to that of FDTD for the longest pulse we used.
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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 | 0.001 | 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".