Approaches to achieve broadband optical transformation devices with transmuted singularity

Many optical instruments with dielectric singularities cannot be manufactured directly. Their singularities can be transmuted through optical transformation, and equivalent physical media can be built to perform the same optical behaviors. The transformed physical media are usually anisotropic and inhomogeneous and, therefore, difficult to fabricate. In this work, several mathematical approaches are proposed to produce a transformed lens with all the elements of the material tensors to be no less than unity. This increases the ease of implementation, as natural materials may be used, which substantially widens the bandwidth of the transformed devices. Although we focus on an omnidirectional retroreflection lens as an example, the approaches developed here are universal and applicable to a wide class of devices with dielectric singularities.