A convergent spherical electromagnetic wave in an inhomogeneous multi-connected waveguide in the form of a hiconical horn is investigated. The analysis is Performed for the microwave frequency range and actual properties of a metal forming the walls of the biconical horn. It is shown that attenuation in a biconical horn made of a well-conducting metal is small up to the dimensions of an order of 1 nm. The properties of the metal biconical horn at optical frequencies are estimated.
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