The near-field and far-field properties of the cylindrical modal expansions with application in the image theorem

Theoretically, we have derived the closed form expressions for modal expansion coefficients of cylindrical harmonies (TE/TM) on arbitrary surfaces with two equivalent methods: the near-field Green's function method and the Near-Field Far-Field (NF-FF) transform method. For narrow-band fields, expressions of TE/TM modal expansion coefficients can be separated into the back-scattered wave and the forward-propagating wave in the context of the image theorem approximation. Also, we give a theoretical criterion for the validity of the image theorem. Numerical confirmations are shown. The theory has many applications including mirror and launcher designs for high-power gyrotrons.