We observe that optical activity in light scattering can be probed using types of illuminating light other than single plane (or quasi plane) waves and that this introduces new possibilities for the study of molecules and atoms. We demonstrate this explicitly for natural Rayleigh optical activity which, we suggest, could be exploited as a new form of spectroscopy for chiral molecules through th...

When a circularly polarized plane wave is normally incident on a slab of a structurally chiral material with local 4̄2m point group symmetry and a central twist defect, the slab can function as either a narrowband reflection hole filter for co–handed plane waves or an ultranarrowband transmission hole filter for cross–handed plane waves, depending on its thickness and the magnitude of the applie...

This paper presents the complete algorithm of site response analysis of nonhomogeneous topographic structures using transient two-dimensional boundary element method (BEM). Seismic behaviour of various topographic features including canyon, half plane, sedimentary filled valley and ridge sections, subjected to incident SV and P waves are analysed. The analysis shows the efficiency of the propos...

Plane waves and modal waves of the Timoshenko beam model are characterized in closed form by introducing robust matrix basis that behave according to the nature of frequency and wave or modal numbers. These new characterizations are given in terms of a finite number of coupling matrices and closed form generating scalar functions. Through Liouville's technique, these latter are well behaved at ...

In this paper, we are interested with the spectral study of an operator given by an elastic topographical waveguide, a deformed half-space, of which the cross-section is a local perturbation of a homogeneous half-plane. We look for guided waves propagating more rapidly than Rayleigh waves (which mathematically would correspond to embedded eigenvalues) and prove that there are no guided waves pr...

Refractive gravitational waves are a generalisation of impulsive waves on a null hypersurface in which the metric is discontinuous but a weaker continuity condition for areas holds. A simple example of a plane wave is examined in detail and two arguments are given that this should be considered a solution of Einstein’s vacuum field equations. The study of these waves is motivated by quantum gra...

The paper discuses the effect of initial stresses on the reflection coefficients of plane waves in a dissipative medium. Basic governing equations are formulated in context of Biot's incremental deformation theory. These governing equations are solved analytically to obtain the dimensional phase velocities of plane waves propagating in plane of symmetry. Closed-form expressions for the reflecti...

We consider the Dirac equation with two different four-potentials of the plane electromagnetic waves. We derive the partial differential equation for the wave function, which is generalized form of the Volkov equation. We find the solutions of the Dirac equation for two orthogonal plane waves. We determine the modified Compton formula for the scattering of two photons on an electron.

This paper describes an L1 regularized variational framework for developing a spatially localized basis, compressed plane waves, that spans the eigenspace of a differential operator, for instance, the Laplace operator. Our approach generalizes the concept of plane waves to an orthogonal real-space basis with multiresolution capabilities.

The numerical dispersion relation governing the propagation of homogeneous plane waves in a finite-difference time-domain (FDTD) grid is well known. However, homogeneous plane waves, by themselves, do not form a complete basis set capable of representing all valid field distributions. A complete basis set is obtained by including inhomogeneous waves where, in the physical world, constant phase ...