Spherical Space Bessel-Legendre-Fourier Mode Solver for Electromagnetic Fields
Bibliographic record
Abstract
Controlling and confining light in three dimensions is of significant interest as it represents devices in their entirety with minimal approximations.Localized modes in resonator structures are commonly modelled using the supercell plane wave expansion method, finite element method, or the finite difference time domain.However, these standard techniques are expensive in terms of computational resources when applied to three-dimensional structures.The technique presented in this thesis is a new method for solving Maxwell's vector wave equations for localized modes in three-dimensional spherically resonator structures as well as its application to sensor configurations.The technique requires minimal implementation, provides normalized results, works for finite size and is computationally efficient.The method is such that the structures under test can be arbitrary shape, isotropic, anisotropic, lossless, or lossy.For the structures examined, a modified basis set composed of spherical Bessel, Legendre and Fourier functions (BLF) are used to expand the electric, magnetic, and inverse relative permittivity.These expansions allow for Maxwell's wave equations to be cast as an eigenvalue problem from which the steady state localized modes (not propagating) can be determined from the eigen-frequencies and eigenvectors.This work applies to a number of spherically symmetric structures.Selections of structures whose resonator properties are reported in the literature are used to compare and verify the accuracy of the use of the BLF functions as an expansion basis.
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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 | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.012 | 0.005 |
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".