Abstract-This paper presents an eigenfunction expansion of the electric-type dyadic Green's functions for both a unbounded gyroelectric chiral medium and a cylindrically-multilayered gyroelectric chiral medium in terms of the cylindrical vector wave functions. The unbounded and scattering Green dyadics are formulated based on the principle of scattering superposition for the electromagnetic waves, namely, the direct wave and scattered waves. First, the unbounded dyadic Green's functions are correctly derived and some mistakes occurring in the literature are pointed out. Secondly, the scattering dyadic Green's functions are formulated and their coefficients are obtained from the boundary conditions at each interface. These coefficients are expressed in a compact form of recurrence matrices; coupling between TE and TM modes are considered and various wave modes are decomposed one from another. Finally, three cases, where the impressed current source are located in the first, the intermediate, and the last regions respectively, are taken into account in the mathematical manipulation of the coefficient recurrence matrices for the dyadic Green's functions.

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