Low-loss directional cloaks without superluminal velocity or magnetic response

The possibility of making an optically large (many wavelengths in diameter) object appear invisible has been a subject of many recent studies. Exact invisibility scenarios for large (relative to the wavelength) objects involve (meta)materials with superluminal phase velocity (refractive index less than unity) and/or magnetic response. We introduce a new approximation applicable to certain device geometries in the eikonal limit: piecewise-uniform scaling of the refractive index. This transformation preserves the ray trajectories, but leads to a uniform phase delay. We show how to take advantage of phase delays to achieve a limited (directional and wavelength-dependent) form of invisibility that does not require loss-ridden (meta)materials with superluminal phase velocities.