TY - JOUR
T1 - Efficient Calculation of the Electromagnetic Dyadic Green's Function in Spherical Layered Media
AU - Okhmatovski, Vladimir I.
AU - Cangellaris, Andreas C.
N1 - Funding Information:
Manuscript received January 4, 2002; revised December 12, 2002. This work was supported in part by an Army Research Office – Multidisciplinary University Research Initiative (MURI), under the Spatial and Quasi-Optical Power Combining Grant DAAG-55-97-0132.
PY - 2003/12
Y1 - 2003/12
N2 - A numerical methodology is proposed for the evaluation of the electromagnetic fields of an electric or magnetic dipole of arbitrary orientation in spherical stratified media. The proposed methodology is based on the numerical solution of the differential equation in the radial coordinate that is satisfied by each coefficient in the spherical harmonics expansion of the governing Helmholtz equation. More specifically, the finite-difference solution of this equation may be cast in a pole-residue form that allows the analytic evaluation of the spherical harmonics series by means of the Watson transformation. Thus, a closed-form expression is obtained for the electromagnetic fields in terms of a short series of associated Legendre functions Pνm(cos(θ)) of integer order m and complex degree ν. The number of terms in the series is strongly dependent on the angle θ, and decreases very fast when the point of observation moves away from the source. The method allows for arbitrary variation in the permittivity and permeability profiles in the radial directions.
AB - A numerical methodology is proposed for the evaluation of the electromagnetic fields of an electric or magnetic dipole of arbitrary orientation in spherical stratified media. The proposed methodology is based on the numerical solution of the differential equation in the radial coordinate that is satisfied by each coefficient in the spherical harmonics expansion of the governing Helmholtz equation. More specifically, the finite-difference solution of this equation may be cast in a pole-residue form that allows the analytic evaluation of the spherical harmonics series by means of the Watson transformation. Thus, a closed-form expression is obtained for the electromagnetic fields in terms of a short series of associated Legendre functions Pνm(cos(θ)) of integer order m and complex degree ν. The number of terms in the series is strongly dependent on the angle θ, and decreases very fast when the point of observation moves away from the source. The method allows for arbitrary variation in the permittivity and permeability profiles in the radial directions.
KW - Green's function
KW - Layered media
KW - Wave propagation over curved surfaces
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U2 - 10.1109/TAP.2003.820952
DO - 10.1109/TAP.2003.820952
M3 - Article
AN - SCOPUS:1142301895
SN - 0018-926X
VL - 51
SP - 3209
EP - 3220
JO - IEEE Transactions on Antennas and Propagation
JF - IEEE Transactions on Antennas and Propagation
IS - 12
ER -