Cavity Formation and Light Propagation in Partially Ordered and Completely Random One-Dimensional Systems

We study light transport in ordered, partially ordered, and completely random one-dimensional (1-D) systems. In a periodic structure, there are three types of passbands with different origins. When disorder is introduced to a periodic system, the passbands change differently, depending on their origins. The transmissivity and decay length in the passbands near the band edges decrease drastically. The stopbands are widened. The introduction of randomness to a periodic structure enhances light localization in frequency regions in which it is delocalized in a periodic structure. In a completely random system, a resonant cavity is formed by two stacks of multiple layers which serve as two highly reflective broadband mirrors. We calculate the size and the quality factor of 1-D random cavities. With an increase in the degree of disorder, the lasing threshold in such a cavity first decreases, then increases. The lasing frequency spreads from the band edge toward the stopband center.