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Rigorous sufficient conditions for index-guided modes in microstructured dielectric waveguides
Karen K Lee1, Yehuda Avniel, Steven G Johnson
1Research Laboratory of Electronics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA. kylkaren@mit.edu
Optics Express
|June 26, 2008
Summary
We established a condition guaranteeing index-guided modes in diverse dielectric waveguides, ensuring cutoff-free propagation in structures with increased refractive index cores. This applies to photonic-crystal fibers and anisotropic materials.
Area of Science:
- Optics and Photonics
- Materials Science
Background:
- Dielectric waveguides are crucial for light manipulation.
- Understanding mode guidance is essential for device design.
- Existing theories often lack generality for complex structures.
Purpose of the Study:
- To derive a general condition for index-guided modes.
- To provide a rigorous guarantee of cutoff-free modes.
- To cover a broad range of dielectric waveguide types.
Main Methods:
- Derivation of a sufficient condition for mode existence.
- Application of a variational method.
- Inspiration from quantum mechanics localization proofs.
Main Results:
- A general condition for index-guided modes is derived.
- Rigorous guarantee of cutoff-free modes for increased refractive index cores.
- Weaker guidance guarantee for "on average" increased refractive index.
Conclusions:
- The derived condition ensures reliable mode guidance in complex waveguides.
- Applicable to photonic-crystal fibers, anisotropic materials, and periodic waveguides.
- The variational method offers a powerful tool for waveguide analysis.
