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Articles you may be interested inPhotonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics Am. J. Phys. 81, 405 (2013); 10.1119/1.4798259Eigenvalue problems of the model from nonlocal continuum mechanics This work of didactic character on geometrical optics consists of two parts, whose main link is the use of methods associated with continuum physics. First, the formalism of continuum physics is applied in order to derive the eikonal equation from the study of propagation of discontinuities in electromagnetic fields in such a way that the eikonal equation is an exact derivation from Maxwell equations. The results obtained are well known from the works of Luneburg ͓Mathematical Theory of Optics ͑California U.P., Berkeley, 1964͔͒, although the method used is new and efficient and provides a good occasion to use the continuum physics beyond its standard applications. Second, from the identity between the differential equation of light rays and the equilibrium equation of a flexible and inextensible string subjected to a conservative force, the analogy between both physical models is inferred. To illustrate this analogy, two applications in the realms of mechanics and optics are shown. The obtained results in statics have been reinterpreted from the dynamical scheme.

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Abstract-The propagation of light in an anisotropic impedancematched metamaterial is studied in the frame of geometrical optics. We prove that directions of fieldsD,B andv (ray velocity) are a triad of conjugate directions with respect to the inverse relative dielectric permittivity tensor and constitutes a local basis, whose reciprocal one is formed by directions ofĒ,H fields and wave-vectork. Consequently, both dual bases are intrinsically related to the physical properties of medium. We have identified these bases with direct and reciprocal bases of a curvilinear coordinates system, showing that physics defines geometry. This identification provides a powerful tool to solve two kinds of problems (direct and inverse ones) that currently arise: In direct problems, medium properties are given and it suffices to know ε =μ tensor at every point, to obtain the wave structure. In inverse problems, medium properties must be found for the rays to propagate along prescribed trajectories. The procedure is applied to an illustrating example.