actual equation) consisting of the Bessel function. Photons in a hypergeometric-Gaussian beam have an orbital angular momentum of mħ. The integer m also gives the strength of the vortex at the beam's centre. Spin angular momentum of circularly polarized light can be converted into orbital angular momentum. Creation Several methods exist to create hypergeometric-Gaussian modes, including with a spiral phase plate, computer-generated holograms, mode conversion, a q-plate, or a spatial light modulator. Static spiral phase plate(s) or mirror(s) are spiral-shaped pieces of crystal or plastic that are engineered specifically to the desired topological charge and incident wavelength. They are efficient, yet expensive. Adjustable spiral phase plates can be made by moving a wedge between two sides of a cracked piece of plastic. Off-axis spiral phase mirrors can be used to mode convert high-power and ultra-short lasers. Computer-generated holograms (CGHs) are the calculated interferogram between a plane wave and a Laguerre-Gaussian beam which is transferred to film. The CGH resembles a common Ronchi linear diffraction grating, save a "fork" dislocation. An incident laser beam creates a diffraction pattern with vortices whose topological charge increases with diffraction order. The zero order is Gaussian, and the vortices have opposite helicity on either side of this undiffracted beam. The number of prongs in the CGH fork is directly related to the topological charge of the first diffraction order vortex. The CGH can be blazed to direct more intensity into the first order. Bleaching transforms it from an intensity grating to a phase grating, which increases efficiency. Mode conversion requires Hermite-Gaussian (HG) modes, which can easily be made inside the laser cavity or externally by less accurate means. A pair of astigmatic lenses introduces a Gouy phase shift which creates an LG beam with azimuthal and radial indices dependent upon the input HG. A spatial light modulator is a computer-controlled electronic liquid-crystal device which can create dynamic vortices, arrays of vortices, and other types of beams by creating a hologram of varying refractive indices. This hologram may be a fork pattern, a spiral phase plate, or some similar pattern with non-zero topological charge. Deformable mirror made of segments can be used to dynamically (with a rate of up to a few kHz) create vortices, even if illuminated by high power lasers. A q-plate is a birefringent liquid crystal plate with an azimuthal distribution of the local optical axis, which has a topological charge q at