  One of the bottlenecks that limit the transition of transformation-optics
devices from concepts to practical use is the non-unit magnetic permeability
generally required from a mathematical transformation. Simple renormalization
of permeability, as used in many previous designs and experiments, introduces
impedance mismatch and thus degrades the functional photonic performance. Here
we propose an area-preserving affine coordinate transformation as a general
method to solve this problem. Ideal transformation-optics functions can be
preserved while nonmagnetism is achieved. As a specific example, we illustrate
how to apply this affine method into the design of a two-dimensional
electromagnetic beam bending adapter. Concerns related to fabrication, such as
anisotropy degree and bending angles, are fully discussed. Our study is a
significant step toward practical use of ideal transformation optics devices
that can be implemented directly with existing dielectric materials.
