Abstract:
The effect of a pulse produced by an acoustic or electromagnetic
line source oriented parallel to the edge of a perfectly conducting
half plane is considered. The Green's functions for the modified
Helmholtz equation are found by solving for the Green's functions
for a cylinder of sectorial cross-section, then allowing the radius of
the sector to go to infinity to form a wedge, and finally opening the
wedge to form a half plane. The Green's function for the sectorial
domain itself, is determined by first solving the eigenvalue problem
for the sectorial domain. The solution for the half plane is represented
in the form of a Laplace transform integral. Then the solution
for a "Dirac" pulse, which is the inverse Laplace transform of
the Green's function for the modified Helmholtz equation, is directly
available and the result of an arbitrary pulse can be synthesized from
it by integration. The results for several pulses are produced by this
method and explicitly show the "transient" terms.
