Title

Highly Localized Wannier Functions For The Efficient Modeling Of Photonic Crystal Circuits

Keywords

Devices; Integrated Optics; Numerical methods; Photonic Crystals; Wannier functions

Abstract

We present a novel approach for the accurate and efficient modeling of photonic crystal-based integrated optical circuits. Within this approach, the electromagnetic field is expanded into an orthogonal basis of highly localized Wannier functions, which reduces Maxwell's equations to low-rank eigenvalue problems (for defect mode and waveguide dispersion calculations) or to sparse systems of linear equations (for transmission/reflection calculations through/from functional elements). We illustrate the construction of Wannier functions as well as, the subsequent determination of defect modes, waveguide dispersion relations, and the characterization of functional elements for realistic two-dimensional photonic crystal structures consisting of square and triangular lattices of air pores in a high-index matrix. Moreover, on the basis of our Wannier function calculations we suggest a novel type of broad-band integrated photonic crystal circuits based on the infiltration of low-index materials such as liquid crystals or polymers into individual pores of these systems. We illustrate this concept through the design of several functional elements such as bends, beam splitters, and waveguide crossings.

Publication Date

7-21-2005

Publication Title

Proceedings of SPIE - The International Society for Optical Engineering

Volume

5733

Number of Pages

324-335

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1117/12.591137

Socpus ID

21844472510 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/21844472510

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