Electromagnetic mode density at the band edge of a 1D graded periodic dielectric structure

Abstract

Analytical expressions are derived for electromagnetic mode density in 1D periodic dielectric structures consisting of dielectric slabs of different dielectric constants. Firstly, the Maxwell's equation is solved for a dielectric scatterer block that contains two dielectric slabs of different dielectric constants, and then it is solved for a dielectric scatterer block that contains three dielectric slabs of different dielectric constants. Finally, a generalized expression for the dielectric scatterer block, containing n dielectric slabs of different dielectric constants, is written. The dependence of the photonic band gap upon the dielectric contrast, dimensions of the unit cell, and number of periods is investigated. The various properties of mode density at the band edge are discussed for both the quarter-wave stack as well as the generalized case. © 2004 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2005.