Immittance matching for multidimensional opensystem photonic crystals
Abstract
An electromagnetic (EM) Bloch wave propagating in a photonic crystal (PC) is characterized by the immittance (impedance and admittance) of the wave. The immittance is used to investigate transmission and reflection at a surface or an interface of the PC. In particular, the general properties of immittance are useful for clarifying the wave propagation characteristics. We give a general proof that the immittance of EM Bloch waves on a plane in infinite one and twodimensional (2D) PCs is real when the plane is a reflection plane of the PC and the Bloch wave vector is perpendicular to the plane. We also show that the purereal feature of immittance on a reflection plane for an infinite threedimensional PC is good approximation based on the numerical calculations. The analytical proof indicates that the method used for immittance matching is extremely simplified since only the real part of the immittance function is needed for analysis without numerical verification. As an application of the proof, we describe a method based on immittance matching for qualitatively evaluating the reflection at the surface of a semiinfinite 2D PC, at the interface between a semiinfinite slab waveguide (WG) and a semiinfinite 2D PC linedefect WG, and at the interface between a semiinfinite channel WG and a semiinfinite 2D PC slab linedefect WG.
 Publication:

Physical Review B
 Pub Date:
 October 2003
 DOI:
 10.1103/PhysRevB.68.155115
 arXiv:
 arXiv:condmat/0306260
 Bibcode:
 2003PhRvB..68o5115U
 Keywords:

 42.70.Qs;
 42.79.Gn;
 Photonic bandgap materials;
 Optical waveguides and couplers;
 Condensed Matter  Materials Science
 EPrint:
 8 pages, 6 figures