Student Presenter(s): Andrew Wong
Faculty Mentor: Vitaly Katsnelson
School/College: Engineering and Computing Sciences, Manhattan

We analyze a technique to produce a focused wave inside a layered material with access to only one side. Generating a focused wave is important because it can localize flaws and imperfections within the material and distinguish them from the desired properties of a material. In many practical situations, only access to one side of the material is available, so inspection consists of sending incident sound pulses into it and measuring the resulting reflected pulses. The one-sided access, combined with imperfections within the material, pose a challenge to focused wave generation. The main problem we analyze is, given single-sided access only, ‘how does one focus sound to a point at a specified time within a one-dimensional layered medium with an unknown velocity profile?’ James Rose proposes an algorithm to generate an incident pulse that focuses at a specific point in the material at a specific time after propagation into it. We have developed a computer simulation that implements Rose’s algorithm for single-sided focusing and generates a focused wave using single-sided measurements. The program simulates the movement of a one-dimensional wave in the form of a contour plot that shows changes in its speed and amplitude as it passes through interfaces. The program visualizes multiple iterations of Rose’s algorithm and shows the generation of a focused wave. We have shown mathematically that in certain cases, an infinite number of iterations will generate a focused wave.