Current methods for generating Bessel beams are limited to fixed beam sizes or, in the case of conventional adaptive optics, relatively long switching times between beam shapes. We analyze the multiscale Bessel beams created using an alternative rapidly switchable device: a tunable acoustic gradient index (TAG) lens. The shape of the beams and their nondiffracting, self-healing characteristics ...

X-ray mirrors with high focusing performances are commonly used in different sectors of science, such as X-ray astronomy, medical imaging and synchrotron/free-electron laser beamlines. While deformations of the mirror profile may cause degradation of the focus sharpness, a deliberate deformation of the mirror can be made to endow the focus with a desired size and distribution, via piezo actuato...

Improving the performance of photovoltaics is important for increased deployment in a broad range of applications. In this article, it is shown that combining detailed models for full-wave optics with one or more other physics models represents an emerging field of research. In particular, connections are made with geometric optics, electronic transport, and thermal transport. First, structures...

Transformation optics is an emergent field of engineering with a great impact on recent developments in advanced optical devices. With the help of differential geometry, transformation optics allows us to fully control electromagnetic fields in an unprecedented manner. On the other hand, variational principles mathematically describe in a concise and elegant way a great variety of natural pheno...

The continuous spectrum, near its innmum, of the Lapla-cian for certain classes of`doubly-warped' complete Riemannian met-rics on the interiors of compact manifolds with boundary is examined using geometric optics. General conditions on the geometry of an algebra of vector elds leading to a calculus of pseudodiierential operators are described and, once veriied in this particular case, the asso...

Recent work by Jaffe and Scardicchio has expressed the optical approximation to the Casimir effect as a sum over geometric quantities. The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in R to describe reflection of rays off a surface. This allows the quantities in the optical approximation to the Casimir effect to be calculat...

The aim of this paper is to study oscillatory solutions of nonlinear hyperbolic systems in the framework developed during the last decade by J.-L. Joly, G. Métivier, and J. Rauch. Here we focus mainly on rectification effects, that is, the interaction of oscillations with a mean field created by the nonlinearity. A real interaction can occur only under some geometric conditions described in [JM...

We study the interaction of (slowly modulated) high frequency waves for multi-dimensional nonlinear Schrödinger equations with gauge invariant power-law nonlinearities and non-local perturbations. The model includes the Davey–Stewartson system in its elliptic-elliptic and hyperbolic-elliptic variant. Our analysis reveals a new localization phenomenon for non-local perturbations in the high freq...

We provide a justification with rigorous error estimates showing that the leading term in weakly nonlinear geometric optics expansions of highly oscillatory reflecting pulses is close to the uniquely determined exact solution for small wavelengths ε. Pulses reflecting off fixed noncharacteristic boundaries are considered under the assumption that the underlying boundary problem is uniformly spe...