Pupil inversion Mach-Zehnder interferometry for diffraction-limited optical astronomical imaging.

We present theoretical and laboratory experimental results on a robust interferometric device based on pupil inversion, or 180° rotational shearing interferometry. The image of an astronomical object degraded by the atmosphere turbulence can be restored (ideally up to the diffraction limit) by a numerical post-processing of the interferogram. Unlike previous Michelson configurations that return half of the light to the sky, the Mach-Zehnder interferometer has no fundamental losses when both outputs are used. The interferogram is formed by two overlapped images of the telescope pupil, but one of them is spatially inverted, and out of phase by π/2 only in its half. This optical operation is achieved in a robust way by inserting a refractive optical image inverter and a binary phase plate in one of the arms of the interferometer. In this way, the system has no polarization dependence or moving parts since the plate allows the object to be retrieved numerically from just one interferogram (single exposition) or a few independent interferograms. For that, several algorithms are proposed. Likewise, we include a laboratory proof-of-concept in which a diffraction-limited image is obtained in spite of presence of aberrations and photon noise.

Graded-index profiles produced by ion exchange in an interacting system.

We numerically solve a diffusion-type equation for the accumulated interdiffusion coefficient in an interacting system (nonideal ion-exchange reaction) by using a modified Crank-Nicolson algorithm. We obtain exact and approximate index profiles in such a way that bump effects found in experimental ionic concentrations in glass are explained as a result of cation-cation interactions.

Beam modes in graded-index media and topological phases.

The change in the polarization plane of light vector beams retaining their shape (beam modes) under propagation through gradient-index media is evaluated as a topological phase acquired by cyclic and noncyclic evolutions of these beams on their projective Hilbert space (momentum sphere). The polarization changes are evaluated by means of the characteristic parameters of the light beam selected.