The refraction and reflection are basic phenomena in the propagation of all kinds of waves, such as light waves, electromagnetic waves and acoustic waves, when they encounter the interface among different kinds of materials. Because of the rigorous limitation of classical laws, traditional optical components such as spherical lenses and parabolic mirrors must be designed with various non-planar geometric shapes to control the flow of light, which makes these devices bulky and heavy. During the last several hundred years, many efforts have been devoted to make optical components thin and lightweight. One particular example is the diffractive gratings and lenses, where the wavefront can be constructed by locally tuning the transmittance in a two-dimensional space. However, the diffractive devices are suffering from the low diffraction efficiency and large chromatic dispersion, making them difficult to be used in practical optical systems.