Tight-binding method modelling of photonic crystal waveguides

• Published in: Optical and quantum electronics Vol. 34; no. 5-6; pp. 445 - 454
• Main Authors: LE VASSOR D'YERVILLE, M, MONGE, D, CASSAGNE, D, ALBERT, J. P
• Format: Conference Proceeding Journal Article
• Language: English
• Published: Dordrecht Springer 01.05.2002; Springer Nature B.V
• Subjects: Applied sciences; Binding; Circuit properties; Crystal defects; Electric, optical and optoelectronic circuits; Electronics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Integrated optics. Optical fibers and wave guides; Mathematical models; Modelling; Optical and optoelectronic circuits; Optical materials; Optics; Photonic bandgap materials; Photonic crystals; Physics; Plane waves; Solid state physics; Waveguides; Photonic band gap; Tight binding approximation; Photonic crystal; Dielectric materials; Digital simulation; Two dimensional structure; Theoretical study; Optical materials; Wannier functions; TM mode; Optical waveguides
• ISSN: 0306-8919; 1572-817X
• DOI: 10.1007/BF02892609

We present here a tight-binding-like modelling of two-dimensional (2D) photonic crystals (PCs). Adopted from solid-state physics, the concept of generalized Wannier functions is used to construct a localized state basis that allows a parameter-free ab initio study of defects in PCs. We demonstrate here for a 2D triangular lattice of dielectric rods in air, the existence of this localized basis and the possibility to study large scale complex dielectric structures deviating from periodicity. Specific numerical simulations on a split waveguide embedded in this triangular lattice are performed, and they demonstrate the superiority of this method over plane wave based techniques.