We present a method for the creation of optical vortices by using a deformable mirror. Optical vortices of integer and fractional charge were successfully generated at a wavelength of 633 nm and observed in the far field (2000 mm). The obtained intensity patterns proved to be in agreement with the theoretical predictions on integer and fractional charge optical vortices. Interference patterns between the created optical vortex carrying beams and a reference plane wave were also produced to verify and confirm the existence of the phase singularities.
We present a mode purity comparison between optical vortices (OVs) generated by a static multilevel phase plate with 16 or 32 phase steps and a vortex generated with a segmented deformable mirror with 37 actuators. Computer simulations show the intensity and phase of the vortices generated with the two methods. The deformable mirror, by being reconfigurable, shows better mode purity for high charge OVs, while the static phase plate mode efficiency declines due to the fixed number phase quantization.
In the sport of American football, the quarterback (QB) is the player almost always responsible for throwing the ball downfield to an open receiver. That important throw requires him to make a split second decision to launch the ball at the correct speed and angle to guarantee it lands directly into the hands of the receiver. In this paper we model the decision for two cases. The authors first consider the case of a receiver running at constant acceleration and find that, for a successful throw, the ball's launch angle depends only on the receiver's constant acceleration while the ball's initial speed is not a factor. Secondly, the article discusses the more realistic case of a receiver running at a variable acceleration showing that the QB can perform a successful throw for various angle/ball's initial speed combinations in which the angle and speed are approximately linearly related.
The propagation of vortex beams as an information carrier for free-space laser communications has been proposed as a method for propagating through weak and strong atmospheric turbulence. This paper shows simulations of vortex charge conservation through turbulence and an analysis of the results. We also show an experimental demonstration of the generation of optical vortices with both integral and fractional charge using a segmented deformable mirror. OPTICAL VORTICESAn optical vortex (also known as a screw dislocation or phase singularity) is a zero of an optical field, a point of zero intensity [1], with a helical phase structure, hence the name optical vortex. The generalized functional form for a field hosting an optical vortex is, in a plane transverse to propagation direction, locally given bywhere ( ) A r can be any square integrable, continuous and smooth complex amplitude wave function in cylindrical polar coordinates. The phase argument θ represents the distinctive, transverse vortex phase profile, impressing a linear phase increase in the azimuthal direction to the field. The charge of a vortex can be an integer or fraction, and also positive or negative, depending on the handedness of the twist. Figure 1 shows a map of the phase profile of a vortex beam. The phase jumps by a value 2 t π at the discontinuity. Vortex beams have been successfully employed in optical tweezers applications [2], because they offer the advantage of trapping and spinning low index (with respect to the hosting medium) dielectric particles in their zero intensity region. Vortex carrying beams also have interesting potential for use in free-space optical communications [3]. Of particular interest is the ability of vortex beams to conserve their charge through atmospheric turbulence and fog [4,5]. It can be shown ([6], Chapter 5) that the phase along a path enclosing any optical vortex must change by an integer multiple of 2π. This integer multiple is known as the topological charge t and may be defined mathematically by the following path integral:where C represents the contour of integration and dl represents an infinitesimal vector path element. It is to be noted that this integral returns the net topological charge contained within the contour. *mscipion@uncc.edu; phone 704-607-7053
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