Reflection of waves from disordered surfaces

The transmission of waves through disordered media has received much attention in the context of electrical conduction, and numerous techniques have been brought to bear on the problem. Here the authors focus on the reflection coefficient, a closely related quantity. The change in reflectivity on adding a new element to a disordered chain can be calculated by a recursion formula. This in turn suggests a novel formulation of the problem in terms of transfer matrices. These new matrices can be calculated explicitly and, although in principle of infinite dimensions, can be approximated by a truncated form. Using this tool they show how some problems can be solved exactly and how an accurate perturbation expansion can be made for others.