ABSTRACT
Scattering in 1D PhCs ....................................................................................................... 12 2.1.4 Disorder and Inverted Photonic Band Structure .......................................................... 17 2.1.5 Extra-Narrow Bragg Bands Created by Disorder ......................................................... 19 2.1.6 Conclusions ........................................................................................................................ 20 Acknowledgments ........................................................................................................................ 21 References ....................................................................................................................................... 21
which can give rise to localization of light.1 By the time the concept of PhC was introduced in 1987,1,2 signicant advances had been made in understanding classical wave propagation in disordered structures.3 In the case of innite 1D structures, any solution of the corresponding wave equation is localized. That means the solution decreases on average exponentially with the distance from a bounded area of disordered structure. In the case of a long-enough disordered 1D sample, a transmission spectrum consists of a set of narrow bands with transmittivity up to one, which is superimposed on a background with vanishing transmission (Figure 2.1.1). Such a quasi-discrete state with high transparency corresponds to a large concentration of energy in randomly arranged areas inside a disordered structure. The formal analogy between problems of electron localization in random structures and bound state in a shallow potential well has been revealed in the study by Economou and Soukoulis.4 Following this approach, one can describe a disordered structure as a well (area of wave localization) bounded on both sides by potential barriers5 (for details see Chapter 2.4).
