Image Ellipticity from Atmospheric Aberrations

We investigate the ellipticity of the point-spread function (PSF) produced by imaging an unresolved source with a telescope, subject to the effects of atmospheric turbulence. It is important to quantify these effects in order to understand the errors in shape measurements of astronomical objects, such as those used to study weak gravitational lensing of field galaxies. The PSF modeling involves either a Fourier transform of the phase information in the pupil plane or a ray-tracing approach, which has the advantage of requiring fewer computations than the Fourier transform. Using a standard method, involving the Gaussian weighted second moments of intensity, we then calculate the ellipticity of the PSF patterns. We find significant ellipticity for the instantaneous patterns (up to more than 10%). Longer exposures, which we approximate by combining multiple (N) images from uncorrelated atmospheric realizations, yield progressively lower ellipticity (as 1 / sqrt(N)). We also verify that the measured ellipticity does not depend on the sampling interval in the pupil plane using the Fourier method. However, we find that the results using the ray-tracing technique do depend on the pupil sampling interval, representing a gradual breakdown of the geometric approximation at high spatial frequencies. Therefore, ray tracing is generally not an accurate method of modeling PSF ellipticity induced by atmospheric turbulence unless some additional procedure is implemented to correctly account for the effects of high spatial frequency aberrations. The Fourier method, however, can be used directly to accurately model PSF ellipticity, which can give insights into errors in the statistics of field galaxy shapes used in studies of weak gravitational lensing.Comment: 9 pages, 5 color figures (some reduced in size). Accepted for publication in the Astrophysical Journa

Hamiltonian and Phase-Space Representation of Spatial Solitons

We use Hamiltonian ray tracing and phase-space representation to describe the propagation of a single spatial soliton and soliton collisions in a Kerr nonlinear medium. Hamiltonian ray tracing is applied using the iterative nonlinear beam propagation method, which allows taking both wave effects and Kerr nonlinearity into consideration. Energy evolution within a single spatial soliton and the exchange of energy when two solitons collide are interpreted intuitively by ray trajectories and geometrical shearing of the Wigner distribution functions.Comment: 12 pages, 5 figure

Spin-to-Orbital Angular Momentum Conversion and Spin-Polarization Filtering in Electron Beams

We propose the design of a space-variant Wien filter for electron beams that induces a spin half-turn and converts the corresponding spin angular momentum variation into orbital angular momentum of the beam itself by exploiting a geometrical phase arising in the spin manipulation. When applied to a spatially coherent input spin-polarized electron beam, such a device can generate an electron vortex beam, carrying orbital angular momentum. When applied to an unpolarized input beam, the proposed device, in combination with a suitable diffraction element, can act as a very effective spin-polarization filter. The same approach can also be applied to neutron or atom beams.Comment: 9 pages, 5 figure