Related papers: Line geometry and electromagnetism II: wave motion
Geometrical optics describes, with good accuracy, the propagation of high-frequency plane waves through an electromagnetic medium. Under such approximation, the behaviour of the electromagnetic fields is characterised by just three…
Beginning with addition and multiplication which are intrinsic to a Koch-type curve, I formulate and solve a wave equation that describes wave propagation along a fractal coastline. As opposed to the examples known from the literature I do…
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function \sigma =d^{2}/2. One suggests a new general method of the…
The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is…
The magnetic focusing of electrons has proven its utility in fundamental studies of electron transport. Here we report the direct imaging of magnetic focusing of electron waves, specifically in a two-dimensional electron gas (2DEG). We see…
Transformation equations for physical quantities that characterize plane electromagnetic wave propagation in transparent optical media are presented. The Doppler effect, and measurements performed by an observer moving with the wave are…
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function $ d$, or by the world function $\sigma =d^{2}/2$. One suggests a new general method of the…
We show that in order to guide waves, it is sufficient to periodically truncate their edges. The modes supported by this type of wave guide propagate freely between the slits, and the propagation pattern repeats itself. We experimentally…
A brief overview of the current state of the problem of electromagnetic field singularities arising from the refraction and scattering of light by material objects is given. The discussion begins with caustics arising from ray tracing in…
Gravitational waves propagate at the speed of light in general relativity, because of its special relativistic basis. However, light propagation is linked to the electromagnetic phenomena, with the permittivity and permeability constants as…
Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics…
The general method to obtain solutions of the Maxwellian equations from scalar representatives is developed and applied to the diffraction of electromagnetic waves. Kirchhoff's integral is modified to provide explicit expressions for these…
Soft interfaces can mediate interactions between particles bound to them. The force transmitted through the surface geometry on a particle may be expressed as a closed line integral of the surface stress tensor around that particle. This…
Small amplitude inhomogeneous plane waves are studied as they propagate on the free surface of a predeformed semi-infinite body made of Bell constrained material. The predeformation corresponds to a finite static pure homogeneous strain.…
Recently, a lot of effort has been dedicated to developing next-generation optoelectronic devices based on two-dimensional materials, thanks to their unique optical properties that are significantly different from those of their bulk…
Two basic classes of electromagnetic media, recently defined and labeled as those of P media and Q media, are generalized to define the class of PQ media. Plane wave propagation in the general PQ medium is studied and the quartic dispersion…
Choosing the appropriate geometry in which to express the equations of fundamental physics can have a determinant effect on the simplicity of those equations and on the way they are perceived. The point of departure in this paper is the…
Conformal isometry algebras of plane wave geometry are studied. Then, based on the requirement of conformal invariance, a definition of masslessness is introduced and gauge invariant equations of motion, subsidiary conditions, and…
The geometry of a light wavefront, evolving from a initial flat wavefront in the 3-space associated with a post-Newtonian relativistic spacetime, is studied numerically by means of the ray tracing method. For a discretization of the…
In this paper we study the influence of an electric field on a two dimen-sional waveguide. We show that bound states that occur under a geometrical deformation of the guide turn into resonances when we apply an electric field of small…