Some new forms of Huygens' principle

Several theorems are derived by using the reaction concept. They apply to single frequency sources of finite extent, and to fields which are finite and continuous on a hypothetical closed surface
S
whose inside or outside is source-free. 1) The field on the source-free side of
S
is uniquely determined by the normal components
E_{n}
and
H_{n}
on
S
. 2) For measurements on the source-free side of
S
, the primary source can be replaced by any of the following secondary sources on
S
: (a) Normal electric and magnetic dipoles in free space. (b) Normal electric and magnetic quadrupoles backed by a medium which makes
E_{n} = 0
and
H_{n} = 0
. (c) A certain combination of electric and magnetic normal dipoles and quadrupoles which gives zero field on the source side of
S
. The prescription for (a) requires the solution for the field of the primary source when it is inside a cavity on whose walls
E_{n} = 0
and
H_{n} = 0
. The surface densities of the various components of secondary sources (b) and (c) are given in terms of the free-space primary field. The formulas are comparatively simple when
S
is plane. Many applications are cited including a combination of multipoles, consisting of vertical electric and magnetic dipoles, which is equivalent to a horizontal electric dipole.