标题： 亥姆霍兹方程的辐射共振与薄二维波导检测 显示英文标题

标题： Radiating Resonances for the Helmholtz Equation and Thin 2D Waveguide Detection

摘要： 我们研究了二维空间中亥姆霍兹方程在具有高折射率对比的无限长波导存在时的辐射共振。通过问题的格林函数的适当渐近分析，我们描述了这些辐射共振何时出现，并利用这些共振来识别波导的厚度、位置和折射率。我们提出了一种合适的数值重建算法，该算法需要观测包含第一个辐射共振的多频段范围。 显示英文摘要

摘要： We investigate the radiating resonances for the Helmholtz equation in the two dimensional space in the presence of an unbounded waveguide with a high contrast index of refraction. Using a suitable asymptotic analysis of the Green's function of the problem, we describe when these radiating resonances appear, and we exploit these resonances to identify the thickness, location, and index of refraction of the waveguide. We propose a suitable numerical reconstruction algorithm that requires observations in a multifrequency range containing the first radiating resonance.