Emerging Photonic Principles and Negative Effective Mass: Exploring New Physics in the Tradition of Grothendieck.

Erwin Schrödinger his dynamics constrained to surfaces into an extended conceptual discussion tailored for experimentalists and theorists who prefer high-level physical interpretation over dense calculations can make sense. Because it emphasizes how curvature, topology, and boundary conditions influence localization, scattering, and mode hybridization in surface-constrained systems work. Photonic realizations include patterned waveguides on curved substrates, surface plasmon polaritons guided along curved interfaces, and metamaterial coatings that emulate curvature effects.

Think of experimental recipes: how to fabricate curved photonic architectures (laser writing, nanoimprint lithography), how to excite and probe surface modes, and how to distinguish curvature-induced effects from fabrication-induced disorder. The idea is to also surveys diverse applications: curvature-enabled mode confinement for on-chip delay lines, curvature-assisted dispersion engineering for pulse shaping, and topology-inspired surface channels for robust transport.

Interpretive frameworks are essential for understanding phenomena commonly observed in these systems: curvature-induced bandgaps, enhanced backscattering at curvature singularities, and mode conversion between surface and bulk modes. Practical diagnostic advice includes polarization-resolved spectroscopy, angle-dependent emission studies, and correlation measurements to map coherence properties.

An experimental program to systematically explore surface-constrained quantum analogues is called for: a gradient of curvature across samples, measure mode evolution and lifetimes across the gradient. Perhaps one could compile an open-access dataset to support machine-learning-driven modeling.

Excerpt from: Emerging Photonic Principles and Negative Effective Mass: Exploring New Physics in the Tradition of Grothendieck. by P. De Ceuster

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