Closed-Form Approximations to Solutions of Plasmon Dispersion at a Dielectric/Conductor Interface
Bibliographic record
Abstract
The dispersion equation for surface plasmons (SPs) at a dielectric/conductor interface has been studied extensively with respect to the design of plasmonic devices. A key design requirement is the reduction of damping in the propagating SP polariton wave. Satisfaction of this constraint requires that an “electron gas” in a conducting medium, such as a doped semiconductor, move along the interface at speeds that approximate the polariton wave speed. At these low relative speeds, the efficient exchange of energy between the drifting electrons and a traveling SP polariton may be enabled. The ill-conditioned, eighth-order, complex coefficients dispersion equation derived earlier is dependent upon six parameters that vary over many orders of magnitude. The dispersion equation is also found to be singular in regions of practical interest, and, taken together, these properties have hampered the success of numerical investigations. Therefore, the dispersion equation is analytically investigated here, and closed-form results are found for the parametric dependence of the surface polariton's propagation constant on five dimensionless groups. These new solutions show how compensation of propagation losses without the use of structures can be achieved and provide avenues that guide device design. The closed-form results are used to initialize numerical optimization by providing sufficiently accurate starting points within the parameter space that avoid numerical ill-conditioning.
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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 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".