Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides

摘要: We derive a sufficient condition for the existence of indexguided modes in very general class dielectric waveguides, including photonic-crystal fibers (arbitrary periodic claddings, such as “holey fibers”), anisotropic materials, and waveguides with periodicity along propagation direction. This provides rigorous guarantee cutoff-free index-guided any structure where core is formed by increasing index refraction (e.g. removing hole). It also weaker guidance cases refractive increased “on average” (precisely defined). The proof based on simple variational method, inspired analogous proofs localization two-dimensional attractive potentials quantum mechanics.