It is well known that “vector” diffraction theory needs to be invoked to describe the propagation of light through apertures having dimensions on the order of the wavelength of light. For regions close to the aperture, use of Kirchhoff boundary conditions in the aperture plane is invalid. The Hertz vector formalism provides a way to describe the diffraction of light beams through apertures havi...

An analysis is presented to estimate the perturbation of morphology-dependent optical resonances (MDRs) of spherical dielectric cavities due to acceleration. In the model, the optical cavity is attached to a rigid base that is accelerating. Hertz contact theory is used to describe the contact surface between the base and the sphere, and the Navier equation is solved to obtain an expression for ...

We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We fin...

Raymond Alphonsus Heising (Fig. 1), born in 1888, contributed to the development of radio by demonstrating (in 1923, at the age of 35) the first transatlantic radio communication using single-sideband modulation. Heising’s contribution built on the work of a small number of prominent pioneers in the development of radio communication [1]. The German physicist Heinrich Hertz, in a series of spec...

Principal eigenvectors of the data covariance matrix or the subspace spanned by them, called PCA subspace, provide optimal solutions to several information representation tasks. Recently, many neural approaches have been proposed for learning them (see, e.g., Hertz r t a/. 1991; Oja 1992). A well-known algorithm for learning the PCA subspace of the input vectors is so-called Op’s subspace rule ...

A comprehensive investigation of the frequency-noise spectral density of a free-running midinfrared quantum-cascade laser is presented for the first time. It provides direct evidence of the leveling of this noise down to a white-noise plateau, corresponding to an intrinsic linewidth of a few hundred hertz. The experiment is in agreement with the most recent theory on the fundamental mechanism o...

Hertz vector diffraction theory is applied to a focused TEM00 Gaussian light field passing through a circular aperture. The resulting theoretical vector field model reproduces plane-wave diffractive behavior for severely clipped beams, expected Gaussian beam behavior for unperturbed focused Gaussian beams as well as unique diffracted-Gaussian behavior between the two regimes. The maximum intens...

The energy of a d-dimensional Fermi system typically varies only along d(c)=1 ("radial") dimensions. We consider d(c)=1+epsilon and study a transition to superconductivity in an epsilon expansion. The nontrivial fixed point describes a scale invariant theory with an effective space-time dimension D=d(c)+1. Remarkably, the results can be reproduced by the Hertz-Millis action for the superconduct...

Using nonparaxial vector diffraction theory derived using the Hertz vector formalism, integral expressions for the electric and magnetic field components of light within and beyond an apertured plane are obtained for an incident plane wave. For linearly polarized light incident on a circular aperture, the integrals for the field components and for the Poynting vector are numerically evaluated. ...

A classification of partially hyperbolic diffeomorphisms on 3-dimensional manifolds with (virtually) solvable fundamental group is obtained. If such a diffeomorphism does not admit a periodic attracting or repelling two-dimensional torus, it is dynamically coherent and leaf conjugate to a known algebraic example. This classification includes manifolds which support Anosov flows, and it confirms...