Bibliographic record
Abstract
In this chapter we summarize the beam propagation method (BPM). The method is widely used for the numerical solution of the Helmholtz equation and also for the numerical solution to the nonlinear Schroedinger equation (to be discussed in Chapter 15 dealing with solitons). It is the most powerful technique for studying the propagation of light in integrated optics. The method was originally introduced by Feit and Fleck in the late 1970s [1]. The BPM was initially based on FFT algorithm. Later on it has been extended to finite-difference based BPM schemes (FD-BPM) and finite-element BPM (FE-BPM) and many others. The main characteristics [2] of FD-BPM are the ability to simulate structures with large index discontinuity, less memory and time consumption in modelling complex structures, the possibility to incorporate wide-angle and full vector algorithms and the ability to incorporate transparent boundary conditions. There is a large number of algorithms available in the literature and almost all of them are based on the concept of a propagator. Propagators are mathematical ‘objects’ which propagate fields from one space coordinate to another. An example of the system where propagation takes place, known as an optical waveguide, is shown in Fig. 12.1. It splits input optical signal into two arms, see also Fig. 12.2. The role of BPM is to determine field profile along the waveguide knowing the distribution of refractive index over the whole waveguide.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.037 | 0.016 |
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 source (direct Gemma or distilled Codex), 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".