Alternative single integral equation for scattering by a dielectric

The author has developed an approach to the electromagnetic scattering of a plane monochromatic wave by a homogenous dielectric cylinder that leads to a minimum number of integral equations. The fields inside and outside the scatterer are expressed in terms of auxiliary fields that obey a homogeneous Helmholtz equation, have jumps in the field and in the normal derivative on the boundary, and obey the radiation condition at infinity. The author previously defined the auxiliary field U/sub 1/ as equal to the scattered field outside the scatterer, continuous across the boundary, and having a jump in the normal derivative. Here he defines this field so that it has a jump in the function and none in the normal derivative. He does this because the derivative of the tangential field near the edge of a wedge diverges, while the field itself does not.<>