UNIQUENESS FOR PHASELESS INVERSE ELASTIC SCATTERING PROBLEM FOR PERIODIC STRUCTURES IN 2D AND 3D

. This paper establishes uniqueness results of inverse elastic scattering problem with phaseless near-field data in periodic structures in R2 and periodic/biperiodic structures in R3. We use a superposition of two point sources in each periodic unit with different positions as the incident field, and measure the phaseless near-field data on a line parallel to x1-axis in 2D, or on a plane parallel to (x1, x2)-plane in 3D. We first calculate the explicit formula of quasi-periodic/quasi-biperiodic Green's functions of Lame system in R3. Then, to establish the uniqueness results, the reciprocity relations for point sources, scattered fields, and total fields are derived. Finally, with the help of Rayleigh's expansion, the uniqueness results are proved. The quasiperiodic/quasi-biperiodic Green's functions of Lame system in R3, the reciprocity relations, and Rayleigh's expansion in R3 are novel results as important by-products in the proof process.