Bibliographic record
Abstract
In this PhD Thesis, we theoretically and numerically investigate novel aspects of light propagation in three-dimensional (3D) photonic band gap crystals that open up new opportunities to tune the interaction between light and matter. We also develop highly accurate nonreflecting boundary conditions for a mixed DG discretization of the Maxwell equations on finite size computational domains. Photonic crystals are a class of nanostructures with a periodically varying refractive index in space. Three-dimensional photonic crystals can have a 3D photonic band gap: due to wave interference, light is not allowed to exist within the crystal. A 3D band gap offers new opportunities to tailor the interaction between light and matter. We explore for the first time the propagation of light in a 3D cavity superlattice inside a 3D photonic band gap crystal. Each cavity acts as a "cage" for light due to the surrounding band gap. In a superlattice with closely spaced cavities, the light sometimes "escapes" and hops to one of the neighboring cavities. We calculate the coupling coefficients that describe the hopping transport. We observe for one of the modes of light propagation that light hops only in the Cartesian directions. This cannot be readily inferred from radiation patterns, due to higher-dimensional wave interference. We also study time-resolved propagation patterns in a 3D cavity superlattice, and the effects of disorder on the density of states (DOS) in 3D photonic band gap crystals. Mixed discontinuous Galerkin (DG) finite element methods are well suited to solve the Maxwell equations in complex structures, as they allow to efficiently capture singularities at dielectric corners and interfaces and also provide a spectrum of electric field solutions that is free of spurious modes. In this PhD Thesis, we combine a mixed DG discretization with nonreflecting boundary conditions. The boundary conditions are obtained by applying the well-known Hagstrom-Warburton nonreflecting boundary conditions separately to the tangential components of the electric field. The discretized Hagstrom-Warburton boundary conditions successfully describe unboundedness with only small spurious reflections that are accurately predicted by an estimate. These new nonreflecting boundary conditions will allow accurate computations of the behavior of light in finite structures.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 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".