The paper is concerned with the reconstruction of a defect in the core of a two-dimensional open waveguide from the scattering data. Since only a finite numbers of modes can propagate without attenuation inside the co...The paper is concerned with the reconstruction of a defect in the core of a two-dimensional open waveguide from the scattering data. Since only a finite numbers of modes can propagate without attenuation inside the core, the problem is similar to the one-dimensional inverse medium problem. In particular, the inverse problem suffers from a lack of uniqueness and is known to be severely ill-posed. To overcome these difficulties, we consider multi-frequency scattering data. The uniqueness of solution to the inverse problem is established from the far field scattering information over an interval of low frequencies.展开更多
基金supported by National Science Foundation of USA(Grant Nos.DMS0908325DMS-0968360 and DMS-1211292)+2 种基金Ofce of Naval Research of USA(ONR)(Grant No.N00014-12-10319)National Natural Science Foundation of China(Grant No.91130004)the grant UJF-MSTIC-Plasmons
文摘The paper is concerned with the reconstruction of a defect in the core of a two-dimensional open waveguide from the scattering data. Since only a finite numbers of modes can propagate without attenuation inside the core, the problem is similar to the one-dimensional inverse medium problem. In particular, the inverse problem suffers from a lack of uniqueness and is known to be severely ill-posed. To overcome these difficulties, we consider multi-frequency scattering data. The uniqueness of solution to the inverse problem is established from the far field scattering information over an interval of low frequencies.
