Generation of an optical vortex with a segmented deformable mirror Robert K. Tyson, Marco Scipioni,* and Jaime Viegas Department of Physics and Optical Science, University of North Carolina at Charlotte, 9201 University City Boulevard, Charlotte, North Carolina 28223, USA *Corresponding author: mscipion@uncc.edu Received 3 March 2008; revised 5 May 2008; accepted 28 October 2008; posted 29 October 2008 (Doc. ID 93346); published 20 November 2008 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. © 2008 Optical Society of America OCIS codes: 050.4865, 260.0260, 030.7060, 070.7345, 350.4600. 1. Optical vortices An optical vortex (also known as a screw dislocation or phase singularity) is a zero of an optical field, a point of zero intensity [1]. Light is twisted like a cork- screw around its axis of propagation [2,3]. Because of the twisting, the light waves at the axis itself cancel each other out. An optical vortex looks like a ring of light with a dark hole in the center. The vortex is gi- ven a number, called the topological charge ℓ, related to the orbital angular momentum of the field. The wavefront of an optical vortex is a continuous surface consisting of ℓ embedded helicoids, each with ℓλ pitch, spaced from each other at one wavelength λ. As an example, Fig. 1 represents the wavefront of a charge ℓ ¼ 3 vortex propagating along the z axis, illustrating the three intertwined helicoids. The generalized functional form for a field hosting an optical vortex is, in a plane transverse to propa- gation direction, locally given by f ðr; θÞ¼ Aðr; θÞe iℓθ ; ð1Þ where Aðr; θÞ 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 in- crease in the azimuthal direction to the field. The charge of a vortex can be an integer or fraction, and also be positive or negative, depending on the handedness of the twist. Figure 2 shows a map of the phase profile of a vortex beam. The phase jumps by a value ℓ2π at the discontinuity. Vortex beams have been successfully employed in optical tweezers applications [4–7] 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 communica- tions [8–11]. Of particular interest is the ability of vortex beams to conserve their charge through atmo- spheric turbulence [12]. Also, vortex beams “self- heal” around obstacles [13] and experiments have shown that vortices are conserved through fog [14]. These properties make it an ideal extension to con- ventional coding schemes, such as on–off keying or coherent modulation techniques. 0003-6935/08/336300-07$15.00/0 © 2008 Optical Society of America 6300 APPLIED OPTICS / Vol. 47, No. 33 / 20 November 2008