| _version_ | 1866901717211152384 |
|---|---|
| author | 王有福 |
| author_facet | 王有福 |
| contents | <p>Stable transmission or propagation windows are widely observed in hybrid mode systems, including polaritonic and photonic crystal structures. Conventional explanations attribute these windows to local extrema, such as minimum residue or maximum group index. However, such pointwise descriptions fail to account for variations in window width.</p> <p> </p> <p>In this work, we introduce a platform integral framework based on the residue landscape Z_R(\theta). Instead of focusing on local minima, we define a global measure of low-residue and low-gradient regions:</p> <p> </p> <p>P^*=\int \exp(-Z_R/\langle Z_R\rangle)\cdot \exp(-|\partial_\theta Z_R|/\langle|\partial_\theta Z_R|\rangle)\, d\theta</p> <p> </p> <p>Using Hopfield coefficient data from polariton systems, we show that P^* correlates with stable window width and correctly predicts the ordering of observed configurations.</p> <p> </p> <p>This leads to a structural conclusion: the minimum residue determines the mode center, while the integrated weight of low-residue plateaus governs the window width.</p> <p> </p> <p>We further outline a mapping of this mechanism to slow-light photonic crystal systems, suggesting a platform-based description of window formation beyond local extremum models.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20039115 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Platform Integral Governs Stable Window Formation in Hybrid Modes 王有福 * hybrid modes * polariton * slow light * platform integral * residue landscape * flatband * stability window * mode structure * photonic crystal * Hopfield coefficients <p>Stable transmission or propagation windows are widely observed in hybrid mode systems, including polaritonic and photonic crystal structures. Conventional explanations attribute these windows to local extrema, such as minimum residue or maximum group index. However, such pointwise descriptions fail to account for variations in window width.</p> <p> </p> <p>In this work, we introduce a platform integral framework based on the residue landscape Z_R(\theta). Instead of focusing on local minima, we define a global measure of low-residue and low-gradient regions:</p> <p> </p> <p>P^*=\int \exp(-Z_R/\langle Z_R\rangle)\cdot \exp(-|\partial_\theta Z_R|/\langle|\partial_\theta Z_R|\rangle)\, d\theta</p> <p> </p> <p>Using Hopfield coefficient data from polariton systems, we show that P^* correlates with stable window width and correctly predicts the ordering of observed configurations.</p> <p> </p> <p>This leads to a structural conclusion: the minimum residue determines the mode center, while the integrated weight of low-residue plateaus governs the window width.</p> <p> </p> <p>We further outline a mapping of this mechanism to slow-light photonic crystal systems, suggesting a platform-based description of window formation beyond local extremum models.</p> |
| title | Platform Integral Governs Stable Window Formation in Hybrid Modes |
| topic | * hybrid modes * polariton * slow light * platform integral * residue landscape * flatband * stability window * mode structure * photonic crystal * Hopfield coefficients |
| url | https://doi.org/10.5281/zenodo.20039115 |