Successive iteration of geometrical optics(GO) is suggested to calculate wedge diffraction fields.
For a wedge and given source, the GO field may be obtained when the fields by the half spaces are found and the shadow regions are determined. Futhermore, one may calculate the sources which are equivalent to the discontinuities of the GO field along the shadow boundaries and form a new wedge problem with the equivalent sources instead of the original one.
It is shown that the field generated by the wedge and the equivalent sources equals to the diffraction field which GO requires for the complete solution. Also, it is sown that the field generated by the equivalent sources in the unbounded space, or the incident field in the new wedge problem, equals to the diffraction field approximated by the physical optics.
The new wedge problem is solved here by another application of the GO to approximate the diffraction field and the result is compared with that by the physical optics.
For a validity of the successive iteration of GO, infinte iteration of GO is performed analytically and the convergence is examined for conducting wedges, of which the exact solution is available.
The successive iteration of GO gives an infinite series, which becomes a geometrical series when the terms are evaluated asymptotically far from the edge of the wedge. The ratio of the series is calculated as 3/4 for a wedge angle 90˚ and unit for 0˚, a half plane, without regard to the angle of the observation.
For an arbitrary, but vanishing wedge-angle, the convergence of the successive iteration of GO to the exact solution can be seen from the numerical evaluations of the result up to various oders of iteration.
The suggested method is applied to a dielectric wedge with arbitrary dielectric constant, and the diffration patterns for both polarizations of the incident plane wave are obtained by the first order of iteration of GO.
