ABSTRACT
Coordinate transformations have been widely used in the past, in various domains of physics, to resolve boundary-value problems. Conformal mappings are particularly well suited to analyze problems of electrostatic or fluid mechanics, which satisfy the same Laplace equation. Their application to the Helmholtz equation seems to be more recent to our best knowledge. They were used at the end of the sixties to study waveguide problems and were applied to diffraction problems at the beginning of the seventies. This chapter presents applications of the two kinds of transformations. First, the conformal mapping technique, initially developed to study perfectly conducting gratings, before being extended to finite conductivity gratings second, a nonconformal coordinate transformation, which is able to tackle both kinds of gratings. The electric permittivity and magnetic permittivity are second-order tensors. In a specific coordinate transformation they are subjected to the laws of transformation of tensors.
