Geodesic
The reciprocity gap functional method for an impedance inverse scattering problem in chiral media
Athanasiadou, E. S. 1
1 Department of Mathematics , National and Kapodistrian University of Athens, Panepistimiopolis GR-15784, Athens, Greece
Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 2, p. 79-89.

Voir la notice de l'article provenant de la source International Scientific Research Publications

A time-harmonic electromagnetic wave is scattered by a buried object. We assume that the scattering object has an impedance boundary surface and it is embedded in a piecewise homogeneous isotropic background chiral medium. Using a chiral reciprocity gap operator and appropriate density properties of chiral Herglotz wave functions we solve an inverse scattering problem for reconstruction of the shape of the scatterer from the knowledge of the tangential components of electric and magnetic fields, without requiring any a priori information of the physical properties. Furthermore, a characterization of the surface impedance of the scattering object is proved.
DOI : 10.22436/jnsa.016.02.01
Classification : 35Q60, 35R30, 78A46, 35P25
Keywords: Inverse scattering, reciprocity gap functional, chiral media, impedance boundary condition

Athanasiadou, E. S.  1

1 Department of Mathematics , National and Kapodistrian University of Athens, Panepistimiopolis GR-15784, Athens, Greece 
@article{JNSA_2023_16_2_a0,
     author = {Athanasiadou, E. S. },
     title = {The reciprocity gap functional method for an impedance inverse scattering problem in chiral media},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {79-89},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2023},
     doi = {10.22436/jnsa.016.02.01},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.02.01/}
}
TY  - JOUR
AU  - Athanasiadou, E. S. 
TI  - The reciprocity gap functional method for an impedance inverse scattering problem in chiral media
JO  - Journal of nonlinear sciences and its applications
PY  - 2023
SP  - 79
EP  - 89
VL  - 16
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.02.01/
DO  - 10.22436/jnsa.016.02.01
LA  - en
ID  - JNSA_2023_16_2_a0
ER  - 
%0 Journal Article
%A Athanasiadou, E. S. 
%T The reciprocity gap functional method for an impedance inverse scattering problem in chiral media
%J Journal of nonlinear sciences and its applications
%D 2023
%P 79-89
%V 16
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.02.01/
%R 10.22436/jnsa.016.02.01
%G en
%F JNSA_2023_16_2_a0
Athanasiadou, E. S. . The reciprocity gap functional method for an impedance inverse scattering problem in chiral media. Journal of nonlinear sciences and its applications, Tome 16 (2023) no. 2, p. 79-89. doi : 10.22436/jnsa.016.02.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.016.02.01/

[1] Ammari, H.; N´ed´elec, J. C. Time-harmonic electromagnetic fields in thin chiral surved layeres, SIAM J. Math. Anal., Volume 29 (1998), pp. 395-423 | DOI

[2] Arens, T.; Hagemann, F.; Hettlich, F.; Kirsch, A. The definition and measurement of electromagnetic chirality, Math. Meth. Appl. Sci., Volume 41 (2018), pp. 559-572 | DOI | Zbl

[3] Athanasiadis, C. E.; Athanasiadou, E. S.; Kikeri, E. The reciprocity gap operator for electromagnetic scattering in chiral media, Appl. Anal., Volume 14 (2022), pp. 5006-5016 | Zbl | DOI

[4] Athanasiadis, C.; Kardasi, E. Beltrami Herglotz functions for electromagnetic scattering theory in chiral media, Appl. Anal., Volume 84 (2005), pp. 145-163 | Zbl | DOI

[5] Athanasiadis, C. E.; Natroshvili, D.; Sevroglou, V.; Stratis, I. G. An application of the reciprocity gap functional to inverse mixed impedance problems in elasticity, Inverse Probl., Volume 26 (2010), pp. 1-19 | Zbl | DOI

[6] Athanasiadis, C. E.; Sevroglou, V. I.; Skourogiannis, K. I. The direct electromagnetic scattering problem by a mixed impedance screen in chiral media, Appl. Anal., Volume 91 (2012), pp. 2083-2093 | DOI | Zbl

[7] Athanasiadis, C. E.; Sevroglou, V.; Skourogiannis, K. I. The inverse electromagnetic scattering problem by a mixed impedance screen in chiral media, Inverse Probl. Imaging, Volume 9 (2015), pp. 951-970 | Zbl | DOI

[8] Cakoni, F.; Colton, D. Qualitative Methods in Inverse Elctromagnetic Scattering Theory, Springer-Verlag, Berlin, 2006 | DOI

[9] Cakoni, F.; Colton, D. Target identification of buried coated objects, Comput. Appl. Math., Volume 25 (2006), pp. 269-288 | DOI | Zbl

[10] Cakoni, F.; Colton, D.; Monk, P. The electromagnetic inverse scattering problem for partially coated Lipschitz domains, Proc. R. Soc. Edinb. A: Math., Volume 134 (2004), pp. 661-682 | DOI

[11] Cakoni, F.; Colton, D.; Monk, P. The Linear sampling method in inverse electromagnetic scattering, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2011 | DOI | Zbl

[12] Cakoni, F.; Fares, M.; Haddar, H. Analysis of two linear sampling methods applied to electromagnetic imaging of buried objects, Inverse Probl., Volume 22 (2006), pp. 845-867 | DOI | Zbl

[13] Cakoni, F.; Haddar, H. Identification of partially coated anisotropic buried objects using electromagnetic Cauchy data, J. Integral Equ. Appl., Volume 19 (2007), pp. 359-389 | Zbl | DOI

[14] Charnley, M.; Wood, A. Object identification in Radar imaging via the reciprocity gap method, Radio Sci., Volume 55 (2020), pp. 1-10 | DOI

[15] Colton, D.; Haddar, H. An application of the reciprocity gap functional to inverse scattering theory, Inverse Probl., Volume 21 (2005), pp. 383-398 | Zbl | DOI

[16] Lakhtakia, A. Beltrami Fields in Chiral Media, World Scientific, Singapore, 1994

[17] Lakhtakia, A.; Varadan, V. K.; Varadan, V. V. Time-harmonic electromagnetic fields in chiral media, Springer-Verlag, Berlin, 1989 | DOI

[18] Lindell, I.; Sihvola, A.; Tretyakov, S.; Viitanen, A. J. Electromagnetic waves in chiral and bi-isotropic media, Artech House, , 1994

[19] Monk, F. Finite Element Methods for Maxwell’s Equations, Oxford University Press, New York, 2003 | DOI

[20] Sun, Y.; Guo, Y.; Ma, F. The reciprocity gap functional method for the inverse scattering problem for cavities, Appl. Anal., Volume 95 (2016), pp. 1327-1346 | Zbl | DOI

[21] Wang, Z.; Cheng, F.; Winsor, T.; Liu, Y. Optical Chiral Metamaterials: a Review of the Fundamentals, Fabrication Methods and Applications, Nanotechnology, Volume 27 (2016), pp. 1-20

[22] Zeng, F.; Liu, X.; Sun, J.; Xu, L. Reciprocity gap method for an interior inverse scattering problem, J. Inverse Ill-Posed Probl., Volume 25 (2017), pp. 57-68 | Zbl | DOI

Cité par Sources :