Transformation optics have developed rapidly in recent years as a novel method to control the propagation of electromagnetic waves or light rays, while conformal mapping is a powerful tool used for decades solving problems in fields. In this paper, following the similarity of both methods on manipulating coordinate meshes, we design transformation optical devices with the help of applications of conformal mapping, e.g., steady state heat transfer and electrostatics. We propose an isotropic optical lens, which transforms a radiating line source into a directional antenna, and both full-wave simulations and geometric interpretations are presented. We also give an alternative derivation of the isotropic waveguide bends, which shows a clear picture from the viewpoint of transformation. All the refractive indices we obtain are larger than one, implying feasibility and broadband property. Using the analog between different physical problems may provide a simple way to design feasible optical devices.
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