Generalized transformation design: metrics, speeds, and diffusion - Kinsler,P; McCall,MW (Wave Motion, 2017)
We show that a unified and maximally generalized approach to spatialtransformation design is possible, one that encompasses all second order waves,rays, and diffusion processes in anisotropic media. Until the final step, it isunnecessary to specify the physical process for which a specific transformationdesign is to be implemented. The principal approximation is the neglect of waveimpedance, an attribute that plays no role in ray propagation, and is thereforeirrelevant for pure ray devices; another constraint is that for waves thespatial variation in material parameters needs to be sufficiently smallcompared with the wavelength. The key link between our general formulation anda specific implementation is how the spatial metric relates to the speed ofdisturbance in a given medium, whether it is electromagnetic, acoustic, ordiffusive. Notably, we show that our generalised ray theory, in allowing foranisotropic indexes (speeds), generates the same predictions as does a wavetheory, and the results are closely related to those for diffusion processes.