Transformation-optical design of sharp waveguide bends and corners

Transformation optics is a recently appreciated approach for designing complex electromagnetic media. Here, we describe the extension of transformation optical techniques to include waveguide boundary conditions. We illustrate the use of finite embedded coordinate transformations to design a medium that can be incorporated into a waveguide bend or corner, rendering the structure reflectionless. The expected behavior of the waveguide bends is confirmed with numerical simulations.