We study the Fraunhofer diffraction problem while taking into account the orbital angular momentum of light. In this case, the phase singularity of the light beam is incident on the slit in two different cases: in one, it is incident slightly above the slit, and in the other it is centered on the slit. We observed that the symmetry and the fringe formation in the interference pattern strongly depend on the amount of orbital angular momentum and the slit position in relation to the beam.

Random laser action is obtained in a diffusive weakly scattering regime using an alcohol solution of rhodamine 640 with silica nanoparticles prepared by the Stöber method, with different average diameters of 49, 90, 219, and 490 nm. Particle size and concentration has proven to affect the random laser performance. It is also shown that silica nanoparticles contributes for a much slower photodegradation of the dye molecules than titania nanoparticles that has been used in the majority of the dye random lasers. This fact makes it advantageous to use silica nanoparticles for the fundamental studies of random laser, due to its increase in lifetime under pumping conditions.

We use photon OAM's two-dimensional properties to extend the double-slit to a two-dimensional triple-slit configuration in the shape of an equilateral triangle, obtaining a bidimensional triangular interference pattern at photon level, whose size depends on the OAM amount. We also show that for this pattern, in contrast with the parallel two-and three-slit cases, the azimuthal phase plays a fundamental role, being undistinguishable from the path phase. Our results confirm that only pairs, here associated to path and azimuthal phases, contribute to the two-dimensional photon detection probability, as established by Born's rule.

We analytically and experimentally study the Fraunhofer diffraction of an optical vortex beam possessing noninteger values of the azimuthal index. We show that the Fraunhofer diffraction of this beam presents the birth of a vortex at α=n+ε, where n is an integer number and ε is a small fraction. We discuss this behavior on the basis of the born vortex movement from a position of low intensity to high intensity when α is increased of an integer number in fractional steps of ε.

We study square and triangular optical lattice formation using a diffraction technique with light-possessing orbital angular momentum (OAM). We demonstrate that it is possible to use Fraunhofer diffraction of light by a square aperture to unveil OAM about two times bigger than would be possible with a triangular aperture. We notice that the pattern remains truncated until a topological charge (TC) equal to 20 with good precision. Even though a square pattern cannot be used to determine the TC sign, it is possible to measure high order of the modulus and sign of the TC up to 20, combining patterns of the triangular and square apertures. [4][5][6][7] and diffraction phenomena [8][9][10]. Other applications of light's OAM range from optical manipulation [11] to quantum communication [12,13]. Two recent publications show the importance of this subject applied to optical communications [14] and quantum metrology [15].Particularly interesting is the rich relationship between the phase of light with OAM and diffraction phenomena [9,10,[16][17][18][19][20]. This relationship was well explored by a very simple experiment performed by Hickmann et al.[10]. The basic idea is to observe the Fraunhofer pattern of a diffracted light with OAM by a triangular slit or triangular aperture with the phase singularity aligned on the center of these objects. A truncated triangular optical lattice in the Fraunhofer plane is observed. The size of this optical lattice depends on the amount of OAM, and by counting the number of intensity maxima N of any extern side of the triangular lattice you can obtain the value of TC, m, using a very simple rule, m N − 1. A simple way to understand the formation of this pattern is to observe the diffraction of light with OAM due to each edge of the aperture separately in Fraunhofer plane. Two points must be observed: firstly, the number of fringes due to each edge is proportional to the OAM value, and second, the effect of the azimuthal phase over this diffraction pattern produces a shift proportional to the amount of OAM. By interfering the light diffracted by the three edges, a triangular optical lattice is unveiled. In fact, in [9] the authors showed a detailed study of the diffraction problem of light with OAM by a single slit.They considered two situations where the phase singularity of the light beam strikes on the center of and above a single slit. In the latter case, which is the case for one side of the triangular aperture, the patterns observed are asymmetric and shifted.At this point a very simple question arises: What can we learn about diffracting OAM beam by other polygonal shapes? In [20], results of diffraction of light with OAM by a square aperture were presented. The authors showed numerically and experimentally that a perfect square optical intensity lattice takes place only for even values of the TC.In this Letter, we show a comparative study of the diffraction problem of light with OAM between square and triangular shape. Surprisingly, with a square aperture the value of TC obtai...