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IEEE Transactions on Antennas and Propagation
Volume 46 Number 11, November 1998

Decomposition of Electromagnetic Boundary Conditions at Planar Interfaces with Applications to TE and TM Field Solutions

Page 1687.

Abstract:

Electromagnetic fields in homogeneous source-free regions can be decomposed into fields that are TE and TM with respect to a particular reference direction (e.g., the z direction). If transverse sources exist, both TE and TM fields may be excited simultaneously. This paper considers the case of two infinite regions having a common planar interface and prescribed sources (surface currents) on the interface. The source currents are decomposed in a manner consistent with the decomposition of the fields. Accordingly, a procedure is established for describing the boundary conditions at the interface in terms of the longitudinal field components E_z, H_z, and the surface currents \bar{J}_s. The development is unique in that the continuity of the transverse field components at the boundary are not explicitly considered but interpreted in terms of z-directed fields. This boundary condition approach is shown to give results consistent with those obtained by matching the tangential fields at the interface using vector transforms. A simple example illustrating the procedure using a ring of current in free-space is presented.

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