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In this paper, a set of new asymptotic approximate expressions for evaluating the electromagnetic (EM) fields generated by a vertical magnetic dipole placed in a dissipative half space is proposed. The lateral wave that guarantees the continuity of the EM fields at the interface is discussed in detail. Using the spectral method, the integral expressions of the field components are obtained. The dominant part is extracted from the lateral wave for large radial distance so that all field components in this situation can be approximately expressed with explicit expressions, which makes the method efficient. Besides, the proposed method has no restriction condition on the parameter choices of different half spaces, so it can be applied in more general situations. Some calculation results and comparisons are given to validate the effectiveness of this extraction method.

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