FIG. 2.6 The geometry of diffraction, showing the reflection of x-rays at a given angle θ by parallel lattice planes with Miller indices, hkl. Relative to the upper black x-ray photon, the red x-ray photon has to travel an extra distance ABC to give the constructive interference required for diffraction. More about this image found in The geometry of diffraction, showing the reflection of x-rays at a given an...

FIG. 8.4 The left and right panels display, severally, the intensity distribution in the experimentally created OS- and IS-centered vortex solitons, with winding number S = 1, in the PhR medium, supported by the square-shaped virtual photonic lattice ( Fleischer et al., 2004) . More about this image found in The left and right panels display, severally, the intensity distribution in...

FIG. 8.1 The left panel shows the scheme of the creation of the effective square-shaped lattice as the interference pattern formed by counterpropagating pairs of ordinary-polarization beams (designated by black arrows). They illuminate the PhR medium in two directions transverse to the direction of the propagation of the soliton-building extraordinary-polarization beams (the red arrow). The right panel: the experimentally observed distribution of the local optical density in the interference pattern, which plays the role of the photonic lattice acting upon the soliton-building beam ( Fleischer et al., 2005) . More about this image found in The left panel shows the scheme of the creation of the effective square-sha...

FIG. 8.11 The intensity and phase distribution (left and right panels, respectively) of the stable ring-shaped chain of alternating vortex and antivortex solitons, produced by the numerical solution of the model of the PhR medium with the self-attractive saturable nonlinearity and embedded hexagonal photonic lattice. This prediction is similar to the experimentally observed state displayed in Fig. 8.10 ( Terhalle et al., 2008) . More about this image found in The intensity and phase distribution (left and right panels, respectively) ...

FIG. 8.3 The left panel: the intensity distribution in the experimentally created IS-centered vortex soliton, with winding number S = 1, in the PhR medium, supported by the square-shaped virtual photonic lattice. The middle and right panels: the intensity and phase structure of the same vortex soliton, as predicted by the numerical solution of the respective model. In the right panel, white circles denote the location of the intensity peaks from the middle panel ( Neshev et al., 2004 ). More about this image found in The left panel: the intensity distribution in the experimentally created IS...

FIG. 8.10 The left and right panels show, severally, the experimentally observed intensity distribution and interferogram of the phase pattern in the stable ring-shaped chain of alternating vortices and antivortices with winding numbers S = +1 and −1. The central position is occupied by a zero-vorticity intensity peak. Red and blue circles designate the location of individual vortices and antivortices in the phase interferogram. The experiment was run in the PhR medium with the embedded hexagonal photonic lattice ( Terhalle et al., 2008) . More about this image found in The left and right panels show, severally, the experimentally observed inte...