  Transformation optics (TO) has been used to propose various novel optical
devices. With the help of metamaterials, several intriguing designs, such as
invisibility cloaks, have been implemented. However, as the basic units should
be much smaller than the working wavelengths to achieve the effective material
parameters, and the sizes of devices should be much larger than the wavelengths
of illumination to work within the light-ray approximation, it is a big
challenge to implement an experimental system that works simultaneously for
both geometric optics and wave optics. In this letter, by using a
gradient-index micro-structured optical waveguide, we realize a device of
conformal transformation optics (CTO) and demonstrate its self-focusing
property for geometry optics and Talbot effect for wave optics. In addition,
the Talbot effect in such a system has a potential application to transfer
digital information without diffraction. Our findings demonstrate the photon
controlling ability of CTO in a feasible experiment system.
