Optical bistability involving photonic crystal microcavities and Fano line shapes
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Bibliographic record
Abstract
The reflectivity of a single-channel waveguide mode upon resonantly coupling to a Kerr-active nonlinear resonant cavity is calculated analytically, including the effects of two-photon absorption. The resonant reflectivity takes the form of a Fano resonance because the solution includes linear reflections from perturbations downstream of the localized cavity. Instead of using a Hamiltonian formulation of the scattering problem, an intuitive set of basis states is used to expand the Green's function of the electric field wave equation. All resulting overlap functions describing the linear coupling between guided and localized states, and the nonlinear renormalization of the material's refractive index, are in terms of well-defined physical quantities. Although derived in the context of photonic crystal-based waveguides and cavities, the treatment is valid for any low-loss waveguide-resonator geometry that satisfies specific weak coupling criteria. For a cavity consisting of Al0.18Ga0.82As, hosting a localized mode at 1.55 microm with a Q of 4000 and a mode volume of 0.055 microm(3), we predict the onset of bistable reflection at incident powers of approximately 40 mW. The downstream reflections lead to hysteresis loops in the reflectivity that are topologically distinct from conventional Lorentzian-derived loops characteristic of isolated Fabry-Perot cavities. We provide a stability argument that reveals the unstable branches of these unique hysteresis loops, and we illustrate some of the rich bistable behaviors that can be engineered with such downstream sources.
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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) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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 it