Design of nanophotonic elements with transformation optics

In this contribution we show that the fundamental di?raction limit of optical cavities can be overcome using a transformation-optical approach. Transformation optics has recently provided a new method for the design of devices to control electromagnetic fields, based on the analogy between the macroscopic Maxwell's equations in complex dielectrics and the free-space Maxwell's equations in a curved coordinate system. It offers an elegant approach to exploit the full potential of metamaterials. We show how transformation optics can be used to achieve the opposite effect of an invisibility cloak; instead of prohibiting the electromagnetic waves from entering a predefined region, we encapsulate the light waves within such a finite region. This allows us to design cavities with extraordinary properties. We have been able to demonstrate theoretically the existence of eigenmodes whose wavelength is much larger than the characteristic dimensions of the device. Furthermore, our cavities avoid the bending losses observed in traditional microcavities, so the quality factor is only limited by the intrinsic absorption of the materials. Finally, we also demonstrate how the combination of radial and angular transformations allows
developing cavities without bending losses using right-handed material parameters only.