The most widespread approach to anisotropic media is dyadic analysis. However, to get a geometrical picture of a dielectric tensor, one has to resort to a coordinate system for a matrix form in order to obtain, for example, the index-ellipsoid, thereby obnubilating the deeper coordinate-free meaning of anisotropy itself. To overcome these shortcomings we present a novel approach to anisotropy: ...

In this work we consider stability of recovery of the conductivity and attenuation coefficients of the stationary Maxwell and Schrödinger equations from a complete set of (Cauchy) boundary data. By using complex geometrical optics solutions we derive some bounds which can be viewed as an evidence of increasing stability in these inverse problems when frequency is growing.

Dark-field X-ray microscopy, DFXM, is a new full-field imaging technique that non-destructively maps the structure and local strain inside deeply embedded crystalline elements in three dimensions. In DFXM an objective lens placed along diffracted beam to generate magnified projection image of volume. this work, general formalism based on geometrical optics provided for diffraction imaging, vali...

Particles or structures of size comparable to the incident wavelength and located on flat substrates may hold much smaller defects, whose detection and characterization is numerically analyzed. For metallic scattering systems, calculations based on the Extinction Theorem of the physical optics show that geometrical information about the defect can be obtained by partially integrating the backsc...

We review the geometrical-optics evolution of an electromagnetic wave propagating along a curved ray trajectory in a gradient-index dielectric medium. A Coriolis-type term appears in Maxwell equations under transition to the rotating coordinate system accompanying the ray. This term describes the spin-orbit coupling of light which consists of (i) the Berry phase responsible for a trajectory-dep...

Geometrical optics is extended so as to provide a model for spinning light rays via the coadjoint orbits of the Euclidean group characterized by color and spin. This leads to a theory of “geometrical spinoptics” in refractive media. Symplectic scattering yields generalized Snell-Descartes laws that include the recently discovered optical Hall effect. MSC : 78A05; 37J15; 70H40 Preprint : CPT-200...