Unique determination of periodic polyhedral structures by scattered electromagnetic fields
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- by Gang Bao, Hai Zhang and Jun Zou PDF
- Trans. Amer. Math. Soc. 363 (2011), 4527-4551 Request permission
Abstract:
This work is concerned with the unique determination of a periodic diffraction grating profile in three dimensions by some scattered electromagnetic fields measured above the grating. In general, it is well known that global uniqueness may not be true when the measurement is only taken for one incident field. Our goal is to completely characterize the global uniqueness properties when the periodic structure is of polyhedral type. Corresponding to each incident plane wave, we are able to classify all unidentifiable structures into three classes and show that any periodic polyhedral structure can be uniquely determined by one incident field if and only if it belongs to none of the three classes. Consequently, the minimum number of incident waves required for the unique determination of a periodic polyhedral structure can be easily read.References
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Additional Information
- Gang Bao
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
- Email: bao@math.msu.edu
- Hai Zhang
- Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
- MR Author ID: 890053
- Email: zhangh20@msu.edu
- Jun Zou
- Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, People’s Republic of China
- ORCID: 0000-0002-4809-7724
- Email: zou@math.cuhk.edu.hk
- Received by editor(s): April 30, 2009
- Published electronically: April 19, 2011
- Additional Notes: The first author was supported in part by the NSF grants DMS-0604790, DMS-0908325, CCF-0830161, EAR-0724527, and DMS-0968360, and by the ONR grant N00014-02-1-0365.
The third author was substantially supported by Hong Kong RGC grants (Projects 404606 and 404407) and partially supported by the Cheung Kong Scholars Programme through Wuhan University. - © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 363 (2011), 4527-4551
- MSC (2010): Primary 35R30, 35Q61, 78A45
- DOI: https://doi.org/10.1090/S0002-9947-2011-05334-1
- MathSciNet review: 2806682