In a similar fashion to diffusers or other highly scattering media, multimode fibres deliver coherent light signals in the form of apparently random speckled patterns. In contrast to other optically random environments, multimode fibres feature remarkably faithful cylindrical symmetry. Our experimental studies challenge the commonly held notion that classifies multimode fibres as unpredictable optical systems. Instead, we demonstrate that commercially available multimode fibres are capable of performing as extremely precise optical components. We show that, with a sufficiently accurate theoretical model, light propagation within straight or even significantly deformed segments of multimode fibres may be predicted up to distances in excess of hundreds of millimetres. Harnessing this newly discovered predictability in imaging, we demonstrate the unparalleled power of multimode fibre-based endoscopes, which offer exceptional performance both in terms of resolution and instrument footprint. These results thus pave the way for numerous exciting applications, including high-quality imaging deep inside motile organisms.T he theoretical description of light transport processes within ideal multimode fibres (MMFs) has been developed for over half a century 1-4 . This elaborate theoretical model is, however, frequently considered inadequate to describe real-life MMFs, which are manufactured by drawing melted silica preforms. Such fibres are commonly seen as unreliable, and the inherent randomization of light propagating through them is typically attributed to undetectable deviations from the ideal fibre structure. It is a commonly held belief that this additional chaos is unpredictable and that its influence grows with the length of the fibre. Despite this, light transport through MMFs remains deterministic.The prospect of deterministic light propagation within MMFs has only recently been used through methods of digital holography and by adopting the concept of empirical measurement of the transformation matrix (TM) 5-11 . This technique, developed in studies of light propagation through highly turbid media 12-17 , has opened a new window of opportunity for MMFs to become extremely narrow and minimally invasive endoscopes, allowing sub-micrometre resolution imaging in deep regions of sensitive tissues 9,18 .However attractive, this technology suffers from several major limitations, the most critical being the lack of flexible operation. Any bending or looping of the fibre results in changes to its TM, rendering the imaging heavily impaired. All current methods exploiting MMFs for imaging require open optical access to the distal end of the fibre during the time-consuming measurement of the TM. Furthermore, this characterization must be repeated upfront for every intended configuration (deformation) and any axial distance of the focal plane behind the fibre before the system can be used for imaging 7,19 . The necessity to determine the TM empirically is therefore a major bottleneck of the technology, and it would be immense...

The author proposes the methodology of transformation optics in orthogonal coordinates to obtain the material parameters of the transformation media from the mapping in orthogonal coordinates. Several examples are given to show the applications of such a methodology by using the full-wave simulations. PACS number(s): 41.20.Jb, 42.25.Fx

Transformation optics is a concept used in some metamaterials to guide light on a predetermined path. In this approach, the materials implement coordinate transformations on electromagnetic waves to create the illusion that the waves are propagating through a virtual space. Transforming space by appropriately designed materials makes devices possible that have been deemed impossible. In particular, transformation optics has led to the demonstration of invisibility cloaking for microwaves, surface plasmons and infrared light. Here, on the basis of transformation optics, we implement a microwave device that would normally require a dielectric singularity, an infinity in the refractive index. To fabricate such a device, we transmute a dielectric singularity in virtual space into a mere topological defect in a real metamaterial. In particular, we demonstrate an omnidirectional retroreflector, a device for faithfully reflecting images and for creating high visibility from all directions. Our method is robust, potentially broadband and could also be applied to visible light using similar techniques.