Riemannian Geometrical Optics: Surface Waves in Diffractive Scattering

Riemannian Geometrical Optics: Surface Waves in Diffractive Scattering

The geometrical diffraction theory, in the sense of Keller, is here reconsidered as an obstacle problem in the Riemannian geometry. The first result is the proof of the existence and the analysis of the main properties of the diffracted rays, which follow from the non-uniqueness of the Cauchy problem for geodesics in a Riemannian manifold with boundary. Then, the axial caustic is here regarded ...

Controlled Scattering of Light Waves: Optimal Design of Diffractive Optics

Multilevel silicon diffractive optics for terahertz waves

A multilevel microfabrication process has been developed to produce silicon Fresnel lenses for terahertz waves. A repeated binary fabrication process was used to create lenses with up to eight levels in complexity and these lenses have been compared to both less complex structures and refractive optic lenses. The microfabrication required deep reactive ion etching and multilevel resist processi...

Scattering of Surface Waves

In this chapter the theory of scattering of elastic surface waves is described. Since surface waves are guided along the surface of materials, the scattering properties of surface waves are useful for probing the heterogeneity of the material near the surface as well as perturbations of the free surface. This has applications in the detection of surface defects (Steg and Klemens, 1974) and in s...

A Fast Method for Linear Waves Based on Geometrical Optics

We develop a fast method for solving the one-dimensional wave equation based on geometrical optics. From geometrical optics (e.g., Fourier integral operator theory or WKB approximation) it is known that high-frequency waves split into forward and backward propagating parts, each propagating with the wave speed, with amplitude that is slowly changing depending on the medium coefficients, under t...