Hidden fractals in light transmission through disordered multilayer photonic systems

摘要

The growth process of multilayer systems is not completely deterministic. There exist factors that limit the accuracy with which the widths of the single layers, and their roughness, can be achieved. For example, in Molecular Beam Epitaxy, the temperature of the source materials cannot be changed infinitely fast. Likewise, the shutters have a finite response time. Finally, there exist impurities and temperature gradients in the substrate's surface. For these reasons, it is interesting to study the effect of disorder on the properties of layered photonic systems. In this theoretical work, we consider waves within a band of frequencies, and calculate the total transmission through a disordered layered structure. We generate deviations away from the perfectly ordered structure: each interface is located around the "perfect" position with a probability distribution with width W. A given growth process, is characterized by W'and by the available number of positions, N We then calculate the length, L, of the curve Transmission vs Wor a given N Finally, we plot log(L) vs log(N) and find a straight line. The fractal dimension is found to be 2.