Holger Then

Utilization of Photon Orbital Angular Momentum in the Low-Frequency Radio Domain

We show numerically that vector antenna arrays can generate radio beams that exhibit spin and orbital angular momentum characteristics similar to those of helical Laguerre-Gauss laser beams in paraxial optics. For low frequencies (< or = 1 GHz), digital techniques can be used to coherently measure the instantaneous, local field vectors and to manipulate them in software. This enables new types of experiments that go beyond what is possible in optics. It allows information-rich radio astronomy and paves the way for novel wireless communication concepts.

Stimulated Raman and Brillouin Backscattering of Collimated Beams Carrying Orbital Angular Momentum

We study theoretically the exchange of angular momentum between electromagnetic and electrostatic waves in a plasma, due to the stimulated Raman and Brillouin backscattering processes. Angular momentum states for plasmon and phonon fields are introduced for the first time. We demonstrate that these states can be excited by nonlinear wave mixing, associated with the scattering processes. This could be relevant for plasma diagnostics, both in laboratory and in space. Nonlinearly coupled paraxial equations and instability growth rates are derived.

Hyperbolic universes with a horned topology and the cosmic microwave background anisotropy

We analyse the anisotropy of the cosmic microwave background (CMB) in hyperbolic universes possessing a non-trivial topology with a fundamental cell having an infinitely long horn. The aim of this paper is twofold. On the one hand, we show that the horned topology does not lead to a flat spot in the CMB sky maps in the direction of the horn as stated in the literature. On the other, we demonstrate that a horned topology having a finite volume could explain the suppression of the lower multipoles in the CMB anisotropy as observed by COBE and WMAP.

Maaß cusp forms for large eigenvalues

We investigate the numerical computation of Maa2ss cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed r = 40000. These eigenvalues are the largest that have so far been found in the case of the modular group. They are larger than the 130millionth eigenvalue.

Cosmic microwave background alignment in multi-connected universes

The low multipoles of the cosmic microwave background (CMB) anisotropy possess some strange properties like the alignment of the quadrupole and the octopole, and the extreme planarity or the extreme sphericity of some multipoles, respectively. In this paper the CMB anisotropy of several multi-connected space forms is investigated with respect to the maximal angular momentum dispersion and the Maxwellian multipole vectors in order to settle the question whether such spaces can explain the low multipole anomalies in the CMB. PACS numbers: 98.80.-k, 98.70.Vc, 98.80.EsThe low multipoles of the cosmic microwave background (CMB) anisotropy possess some strange properties such as the alignment of the quadrupole and the octopole, and the extreme planarity or the extreme sphericity of some multipoles. In this paper, the CMB anisotropy of several multi-connected space forms is investigated with respect to the maximal angular momentum dispersion and the Maxwellian multipole vectors in order to settle the question of whether such spaces can explain the low multipole anomalies in the CMB. The following spaces are considered: the Picard topology in hyperbolic space, three spherical spaces (Poincare dodecahedron, binary tetrahedron and binary octahedron) and a hypertorus in flat space. Although these spaces are able to produce the large-scale suppression of the CMB anisotropy, they do not describe the CMB alignment. From the models considered, the Picard universe shows the strongest alignment properties.

Bounds and algorithms for the K-Bessel function of imaginary order

Using the paths of steepest descent, we prove precise bounds with numerical implied constants for the modified Bessel function

Hyperbolic Geometry and Applications in Quantum Chaos and Cosmology: Numerical Computation of Maass Waveforms and an Application to Cosmology

{K}_{ir} (x)

Kronecker’s Limit Formula, Holomorphic Modular Functions, and q-Expansions on Certain Arithmetic Groups

of imaginary order and its first two derivatives with respect to the order. We also prove precise asymptotic bounds on more general (mixed) derivatives without working out numerical implied constants. Moreover, we present an absolutely and rapidly convergent series for the computation of

Angular Momentum Radio

{K}_{ir} (x)

Certain aspects of holomorphic function theory on some genus zero arithmetic groups

and its derivatives, as well as a formula based on Fourier interpolation for computing with many values of