Physics – Optics
Scientific paper
2008-03-19
Optics Express Vol. 16, Issue 13, pp. 9261-9275 (2008)
Physics
Optics
15 pages
Scientific paper
10.1364/OE.16.009261
We derive a sufficient condition for the existence of index-guided modes in a very general class of dielectric waveguides, including photonic-crystal fibers (arbitrary periodic claddings, such as ``holey fibers''), anisotropic materials, and waveguides with periodicity along the propagation direction. This condition provides a rigorous guarantee of cutoff-free index-guided modes in any such structure where the core is formed by increasing the index of refraction (e.g. removing a hole). It also provides a weaker guarantee of guidance in cases where the refractive index is increased ``on average'' (precisely defined). The proof is based on a simple variational method, inspired by analogous proofs of localization for two-dimensional attractive potentials in quantum mechanics.
Avniel Yehuda
Johnson Steven G.
Lee Karen K. Y.
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