Wigner function for highly convergent three-dimensional wave fields

Wigner function for nonparaxial wave fields.

The generalized optical transfer function and the spectral correlation function are investigated for nonparaxial two-dimensional wave fields. The angle-impact marginal of the four-dimensional Wigner function is derived directly. For focused wave fields of semiangle greater than 90 degrees, the spectral correlation function exhibits overlapping and interference. For focused wave fields for which...

Simulated holographic three-dimensional intensity shaping of evanescent-wave fields

Three-dimensional Wave Polynomials

We demonstrate a specific power series expansion technique to solve the three-dimensional homogeneous and inhomogeneous wave equations. As solving functions, so-called wave polynomials are used. The presented method is useful for a finite body of certain shape. Recurrent formulas to improve efficiency are obtained for the wave polynomials and their derivatives in a Cartesian, spherical, and cyl...

The Wigner distribution function for the one-dimensional parabose oscillator

In the beginning of the 1950’s, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum mechanics the socalled Wigner distribution is considered to be the closest quantum analogue of the classical probability distribution over the phase space. ...

A convergent boundary integral method for three-dimensional water waves

We design a boundary integral method for time-dependent, threedimensional, doubly periodic water waves and prove that it converges with O(h3) accuracy, without restriction on amplitude. The moving surface is represented by grid points which are transported according to a computed velocity. An integral equation arising from potential theory is solved for the normal velocity. A new method is deve...