报告人：张海文副研究员

报告题目：Uniqueness in inverse diffraction grating problems with infinitely many plane waves

报告摘要：This talk is concerned with the inverse diffraction problems by a periodic curve with Dirichlet boundary condition in two dimensions. It is proved that the periodic curve can be uniquely determined by the near-field measurement data corresponding to infinitely many incident plane waves with distinct directions at a fixed frequency. Our proof is based on Schiffer's idea which consists of two ingredients: i) the total fields for incident plane waves with distinct directions are linearly independent, and ii) there exist only finitely many linearly independent Dirichlet eigenfunctions in a bounded domain or in a closed waveguide under additional assumptions on the waveguide boundary. Based on the Rayleigh expansion, we prove that the phased near-field data can be uniquely determined by the phaseless near-field data in a bounded domain, with the exception of a finite set of incident angles. Such a phase retrieval result leads to a new uniqueness result for the inverse grating diffraction problem with phaseless near-field data at a fixed frequency. Since the incident direction determines the quasi-periodicity of the boundary value problem, our inverse issues are different from the existing results of [Hittlich & Kirsch, Inverse Problems 13 (1997): 351-361] where fixed-direction plane waves at multiple frequencies were considered.

报告时间：2022年4月22日（周五）9:00-11:00

报告地点：腾讯会议，会议号：105-150-313

报告人简介：张海文，中国科学院数学与系统科学研究院副研究员。2013年博士毕业于中国科学院数学与系统科学研究院。研究方向为声波、弹性波与电磁波反散射问题。2018年获全国反问题年会“曙光青年学术奖”。2019年入选中国科学院数学与系统科学研究院“陈景润未来之星”计划。2021年入选中国科学院“青年创新促进会”会员。在 SIAM J. Appl. Math.、SIAM J. Imaging Sci.、SIAM J. Sci. Comput.、Inverse Problems、J. Comput. Phys. 等学术期刊上发表论文20余篇。