On vanishing and localizing around corners of electromagnetic transmission resonances

Diao, Huaian; Liu, Hongyu; Wang, Xianchao; Yang, Ke

doi:10.1007/s42985-021-00131-6

Cited by 11 publications

(1 citation statement)

References 28 publications

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“…According to the connection mentioned above, the spectral geometric results characterise the patterns of the wave propagation inside a (nearly) invisible/transparent scatterer. It was first discovered in [9] that transmission eigenfunctions are generically vanishing around a corner point and such a local geometric property was further extended to conductive transmission eigenfunctions in [30], elastic transmission eigenfunctions in [6,32] and electromagnetic transmission eigenfunctions in [10,31,33]. Though the two perspectives share some similarities, especially about the vanishing of the wave fields around the geometrically singular places, there are subtle and technical differences.…”

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Local geometric properties of conductive transmission eigenfunctions and applications

Diao¹,

Fei²,

Liu³

2022

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The purpose of the paper is twofold. First, we show that partialdata transmission eigenfunctions associated with a conductive boundary condition vanish locally around a polyhedral or conic corner in R n , n = 2, 3. Second, we apply the spectral property to the geometrical inverse scattering problem of determining the shape as well as its boundary impedance parameter of a conductive scatterer, independent of its medium content, by a single far-field measurement. We establish several new unique recovery results. The results extend the relevant ones in [30] in two directions: first, we consider a more general geometric setup where both polyhedral and conic corners are investigated, whereas in [30] only polyhedral corners are concerned; second, we significantly relax the regularity assumptions in [30] which is particularly useful for the geometrical inverse problem mentioned above. We develop novel technical strategies to achieve these new results.

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