Localized light orbitals: Basis states for three-dimensional photonic crystal microscale circuits
Bibliographic record
Abstract
We demonstrate the utility of three-dimensional (3D) optical Wannier functions (WF's) for quantitative description of electromagnetic wave localization and propagation in 3D photonic band gap (PBG) microcircuits. Using these localized ``optical orbitals'' we reconstruct electromagnetic waveguiding in bulk two-dimensional (2D) and 3D PBG materials, 2D-3D PBG heterostructures composed of 3D PBG structures inserted with 2D microchip layers, and 2D membrane photonic crystals. In 3D photonic crystal circuits, the expansion of electromagnetic fields with typically less than 20 maximally localized WF's (MLWF's) simplifies the calculation of electromagnetic phenomena of spectral bandwidth surrounding the PBG and improves computational efficiency, compared to the plane wave expansion and the finite-difference time-domain methods. The MLWF's are defined by a unitary transformation on the extended Bloch mode basis, chosen to minimize a wave function delocalization functional, while retaining symmetries of the underlying Bloch modes. We introduce an effective approach to constructing modified MLWF's in 3D architectures involving surface polarization charges and electromagnetic field discontinuities. These modified optical orbitals are also corrected for Gibbs phenomena arising near sharp dielectric interfaces. We demonstrate the accuracy of our localized light orbital method for recapturing TM and TE modes in idealized 2D photonic crystals and mixed polarization waveguide modes in 3D architectures.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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".