Application of inverse, strict conformal transformation to design waveguide devices

Integration of transformation optics with development of metamaterials offers great opportunities to create exotic material with electromagnetic functionality absent from nature. It has already led to several significant advancements in physical conceptions and technological applications such as invisible cloaking. Unfortunately practical application is often restricted by the complex requirements on material properties imposed by the general optical transformation theory. It is therefore necessary to relax the stringent requirements of materials properties in order to practicably use the power of transformation optics to design exotic optical devices. Development of new coordinate transformation mathematics to compromise between the stringent materials properties and the ultimate performance required by a useful novel device is required. In this work the authors employed strict conformal transformation to design physical materials that could guide light in a predetermined way. A simple and efficient numerical approach based on unusual inverse transformation is proposed here to quickly solve partial differential equations and construct the mapping relationship. The results showed that a transformed optical device could be made by purely using isotropic dielectric materials. Two application examples were numerically proposed to verify the versatility of conformal transformation and the robustness of the inverse approach. One was a 90 degrees waveguide beam bend, and the other was a waveguide-type beam splitter or coupler.