Photonic bands and gap maps in a photonic crystal slab

• Published in: IEEE journal of quantum electronics Vol. 38; no. 7; pp. 891 - 898
• Main Authors: Andreani, L.C., Agio, M.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-07-2002; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Bands; Dielectric constant; Lattice vibration; Lattices; Magnetic fields; Mathematical analysis; Optical refraction; Optical scattering; Optical waveguides; Photonic crystals; Photonics; Planar waveguides; Reflectivity; Slabs; Waveguides
• ISSN: 0018-9197; 1558-1713
• DOI: 10.1109/JQE.2002.1017603

The photonic bands of a two-dimensional (2-D) lattice patterned in a planar waveguide are calculated by expanding the magnetic field on the basis of waveguide modes. The method yields both the truly guided modes of the structure as well as the quasi-guided modes (or guided resonances) which lie above the light line in the first Brillouin zone. Representative results for the photonic bands are shown in the cases of strong- and weak-confinement waveguides patterned with a triangular lattice of holes. The gap maps as a function of hole radius are calculated and show significant differences with respect to the ideal 2-D case. A comparison of the photonic bands with those extracted from the calculated surface reflectance shows very good agreement, thereby indicating the reliability of the approach.