One-dimensional photonic crystals – multilayer stacks
Bibliographic record
Abstract
In this chapter, we will consider reflective properties of planar multilayers, and guidance by multilayer waveguides. We will first introduce a transfer-matrix method to find electromagnetic solutions for a system with an arbitrary number of planar dielectric layers. We will then investigate the reflection properties of a single dielectric interface. Next, we will solve the problems of reflection from a multilayer stack, guidance inside a dielectric stack (planar waveguides), and finally, propagation perpendicular to an infinitely periodic multilayer stack. We will then describe omnidirectional reflectors that reflect radiation completely for all angles of incidence and all states of polarization. Next, we will discuss bulk and surface defect states of a multilayer. We will conclude by describing guidance in the low-refractive-index core waveguides. Figure 3.1 presents a schematic of a planar multilayer. Each stack j = [1 … N ] is characterized by its thickness d j and an index of refraction n j . The indices of the first and last half spaces (claddings) are denoted n 0 and n N+1 . The positions of the interfaces (except for j = 0) along the axis ẑ are labeled z j , j = [1 … N + 1], whereas z 0 can be chosen arbitrarily inside of a first half space. In the following, we assume that the incoming plane wave has a propagation vector k confined to the xz plane. The planar multilayer possesses mirror symmetry with respect to the mirror plane xz .
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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 | 0.000 | 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 | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".