Optimal design of minimally reflective coatings

The problem of determining coatings on a flat surface that produces the least amount of wave reflection when it is struck by a known incident pulse is investigated. A departure from previous work on this subject is that the problem is formulated in the time domain, leading to a more intuitive understanding of the wave cancellation phenomenon. The model problem considered in this work is that of a scalar, plane wave propagation. The resulting optimization problem is analyzed in the regime where impedance contrasts between the coatings are small. We show that the problem may be illposed, depending on the nature of the incident pulse. We propose a regularization strategy and an efficient computational scheme for solving the optimization problem. The design problem is further studied in several numerical experiments.