The spontaneous emergence of vector vortex beams with nonuniform polarization distribution is reported in a vertical-cavity surface-emitting laser (VCSEL) with frequency-selective feedback. Antivortices with a hyperbolic polarization structure and radially polarized vortices are demonstrated. They exist close to and partially coexist with vortices with uniform and nonuniform polarization distributions characterized by four domains of pairwise orthogonal polarization. The spontaneous formation of these nontrivial structures in a simple, nearly isotropic VCSEL system is remarkable and the vector vortices are argued to have solitonlike properties.

A tomographic system which includes a spatial filter suitable to detect phase projections is described. This system is expecting to render 2-D images of slices of transparent object distributions employing well-known tomographic reconstruction techniques for parallel projections. Real and complex spatial filters are considered, including very classical Schlieren filtering techniques, as dark field, Foucault knife-edge, phase-knife edge, phase contrast and others.More recent methods, as fractional methods (fractional derivatives and fractional Hilbert) are also considered.Experimental results using real filters and glass samples are also included.

In this work, fractional-derivative filtering is proposed to be incorporated in the system which detects projections emerging from an object as wave front phase variations only. Because it is well known that the square of the derivative of fractional order q=Y2 S linearly proportional to the first order derivative, a real spatial filter with amplitude transmittance proportional to the square root of the frequency has been proposed in order to obtain irradiance variations linearly related with the derivative of phase for phase object detection [1]. Corresponding analysis is shown, where parallel phase projections are filtered with such a spatial filter prior to backprojection for reconstruction. Instead of performing integration of projections, description of the tomographic imaging process of the resulting space filtered backprojections is carried out and the twodimensional equivalence of the filter is discussed. Numerical examples are provided.