Departmental Papers (ESE)


In our earlier work, we introduced a definition for the electric charge "fractional-order" multipoles using the concept of fractional derivatives and integrals [l]. Here, we utilize that definition to introduce a detailed image theory for the two-dimensional (2-D) electrostatic potential distributions in front of a perfectly conducting wedge with arbitrary wedge angles, and for the three-dimensional potential in front of a perfectly conducting cone with arbitrary cone angles. We show that the potentials in the presence of these structures can be described equivalently as the electrostatic potentials of sets of equivalent "image" charge distributions that effectively behave as "fractional-order" multipoles; hence, the name "fractional" image methods. The fractional orders of these so-called fractional images depend on the wedge angle (for the wedge problem) and on the cone angle (for the cone problem). Special cases where these fractional images behave like the discrete images are discussed, and physical justification and insights into these results are given.

Document Type

Journal Article

Date of this Version

December 1996


Copyright 1996 IEEE. Reprinted from IEEE Transactions on Antennas and Propagation, Volume 44, Issue 12, December 1996, pages 1565-1574.

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Date Posted: 26 June 2007

This document has been peer reviewed.