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arXiv · 0803.2850

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

Karen K. Y. Lee·Yehuda Avniel·Steven G. Johnson
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Abstract

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.

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Karen K. Y. Lee, Yehuda Avniel, Steven G. Johnson. 2008-03-19. Rigorous sufficient conditions for index-guided mode in microstructured dielectric waveguides. https://doi.org/10.1364/oe.16.009261

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