Abstract: We present an analytical model based on scalar-wave approximation to study the stop bands of face-centered-cubic photonic crystals with dielectric spheres at lattice sites. An analytical expression is obtained for the normalized stop band widths along the  and  directions as a function of volume fraction and relative dielectric contrast. These calculations enable us to map out the dielectric constants and volume fractions which results in overlapping L and X stop bands. From this map, it is possible to extract the optimum volume fraction that results in the widest overlapping stop band for a given dielectric contrast. We find that the relation between the optimum volume fraction and the dielectric contrast can be approximated by a simple power-law behavior for fcc photonic crystals.
(Copyright) 1996 The American Physical Society.
Rct Date:(Received 18 March 1996; revised 14 June 1996)
PACS:Type: T-Theoretical. Format KR-Conference. Year: 96. Class nos. 42.70.Qs; 78.20.Ci; 81.10.Aj; 84.90.&a
Keywords:Number: 8. COMPOSITE MATERIALS; FCC LATTICES; OPTICAL MATERIALS; DIELECTRIC PROPERTIES; BAND STRUCTURE; SCALAR FIELDS; WAVE PROPAGATION; MATHEMATICAL MODELS