Electromagnetic scattering by a triaxial homogeneous penetrable ellipsoid: Low‐frequency derivation and testing of the localized nonlinear approximation

The field resulting from the illumination by a localized time‐harmonic low‐frequency source (typically a magnetic dipole) of a voluminous lossy dielectric body placed in a lossy dielectric embedding is determined within the framework of the localized nonlinear approximation by means of a low‐frequency Rayleigh analysis. It is sketched (1) how one derives a low‐frequency series expansion in positive integral powers of ( jk ), where k is the embedding complex wavenumber, of the depolarization dyad that relates the background electric field to the total electric field inside the body; (2) how this expansion is used to determine the magnetic field resulting outside the body and how the corresponding series expansion of this field, up to the power 5 in ( jk ), follows once the series expansion of the incident electric field in the body volume is known up to the same power; and (3) how the needed nonzero coefficients of the depolarization dyad (up to the power 3 in ( jk )) are obtained, for a general triaxial ellipsoid and after careful reduction for the geometrically degenerate geometries, with the help of the elliptical harmonic theory. Numerical results obtained by this hybrid low‐frequency approach illustrate its capability to provide accurate magnetic fields at low computational cost, in particular, in comparison with a general purpose method‐of‐moments code.