Lateral electromagnetic pulses generated by a vertical dipole on the boundary between two dielectrics

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Abstract
An exact solution in terms of elementary functions is obtained in the time domain for the vertical electric field Ez(ρ,t) and the transverse magnetic field Bφ(ρ,t) of a dipole located on the plane boundary z=0 between air (region 2, z0) when the dipole is excited by a single delta-function current pulse. The vertical electric field on the boundary consists of a delta-function pulse that travels in the air with the velocity c, an oppositely directed delta-function pulse that travels in the dielectric with the smaller velocity c/ε1/2, an amplitude structure that varies in time between the two pulses, and a final static electric field due to the charges left on the dipole. The horizontal magnetic field is similar. For comparison, the vertical electric field in the equatorial plane of the same dipole in a homogeneous dielectric is also derived. The comparison indicates that the field along the boundary is a surface-wave or lateral pulse.