N. Engheta, ELECTROSTATIC FRACTIONAL IMAGE METHODS FOR PERFECTLY CONDUCTING WEDGES AND CONES, IEEE transactions on antennas and propagation, 44(12), 1996, pp. 1565-1574
In our earlier work, we introduced a definition for the electric charg
e ''fractional-order'' multipoles using the concept of fractional deri
vatives and integrals [1], Here, we utilize that definition to introdu
ce 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 fr
ont of a perfectly conducting cane with arbitrary cone angles, We show
that the potentials in the presence of these structures can be descri
bed equivalently as the electrostatic potentials of sets of equivalent
''image'' charge distributions that effectively behave as ''fractiona
l-order'' multipoles; hence, the name ''fractional'' image methods, Th
e fractional orders of these so-called fractional images depend on the
wedge angle (for the wedge problem) and on the cone angle (for the co
ne problem), Special cases where these fractional images behave like t
he discrete images are discussed, and physical justification and insig
hts into these results are given.