Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides.
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.
Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA. kylkaren@mit.edu
Karen K
KK
Lee
Yehuda
Y
Avniel
Steven G
SG
Johnson
D003198:Computer Simulation; D004867:Equipment Design; D019544:Equipment Failure Analysis; D008027:Light; D008962:Models, Theoretical; D012031:Refractometry / Q000379:methods*; D012542:Scattering, Radiation