  Concise and explicit formulas for dyadic Green's functions, representing the
electric and magnetic fields due to a dipole source placed in layered media,
are derived in this paper. First, the electric and magnetic fields in the
spectral domain for the half space are expressed using Fresnel reflection and
transmission coefficients. Each component of electric field in the spectral
domain constitutes the spectral Green's function in layered media. The Green's
function in the spatial domain is then recovered involving Sommerfeld integrals
for each component in the spectral domain. By using Bessel identities, the
number of Sommerfeld integrals are reduced, resulting in much simpler and more
efficient formulas for numerical implementation compared with previous results.
This approach is extended to the three-layer Green's function. In addition, the
singular part of the Green's function is naturally separated out so that
integral equation methods developed for free space Green's functions can be
used with minimal modification. Numerical results are included to show
efficiency and accuracy of the derived formulas.
