Global uniqueness for determining an inverse electromagnetic scattering medium and its physical coefficients

Abstract Consider an inverse scattering of electromagnetic plane waves by an inhomogeneous penetrable conductive medium containing some unknown impenetrable obstacles. We establish the global uniqueness results for our inverse problem in determining the conductive medium D , the electric permittivity ɛ , the conductivity σ , the surface conductivity η , the internal embedded objects D 0 and its physical properties from the wave-field measurements corresponding to the incident electromagnetic plane waves. The global uniqueness proof is based on a new version on the a prior estimates for the magnetic wave-fields, the constructions of well-posed conductive transmission systems related to Maxwell equations in a suitable domain and various auxiliary Dirichlet boundary value problems in related annular domains. It is worthily mentioned that the simultaneous identification of ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>,</mml:mo> <mml:mi>σ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>η</mml:mi> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>D</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mrow> <mml:mi mathvariant="script">B</mml:mi> </mml:mrow> </mml:mrow> </mml:math> ) for our inverse problem can be shown without knowing the a prior physical properties for the conductive medium D and its embedded objects D 0 .