A Simplified Method for Measuring Wavefront Tilt in an Optical Vortex

Daniel Minkin, Portledge School, Locust Valley, NY; John Noe, Harold Metcalf and Anand Sivaramakrishnan, Laser Teaching Center and Department of Physics and Astronomy, Stony Brook University


Optical vortices are a topic of considerable recent interest. The unusual phase distribution of an optical vortex makes its wavefront helical, like a spiral staircase. The Poynting vector P(x,y) = ExB of a beam of light is normal to the wavefront. In a uniform beam of light, called a plane wave, P is always parallel to the z axis, the direction of propagation. In an optical vortex beam P makes a small angle (the skew angle) with respect to the z-axis, and this angle varies with the azimuthal angle phi and the radius r. Thus the Poynting vector describes a spiral around the z-axis, as shown in the Figure below [1].

The skew angle distribution of an optical vortex beam has recently been directly measured for the first time by Leach et al. [2]. They used a Shack-Hartmann wavefront sensor, an expensive commercial device with many applications in optical testing, medical optics, and astronomy. The wavefront sensor consists of an array of very small, closely spaced, lenses that form a pattern of spots on a CCD camera element. When a plane-wavefront beam is incident on the lens array the resulting spots are precisely uniformly spaced, but with a helical wavefront beam they are very slightly shifted, by just a few microns, in a specific pattern that resembles a vortex. Software in the device calculates each centroid shift; the skew angle is this shift divided by the focal length of the lenslets.

We propose to make a simplified Shack-Hartmann device which will consist of just one ordinary lens (focal length ~100 mm) preceded by a 500 micron diameter pinhole. The lens and pinhole will be rigidly attached to an existing Electrim 1000N CCD camera, and this whole assembly will be mounted on an 2-D translation stage. The stage will be tested to assure that it itself will not tilt the apparatus, causing a false effect. A number of images will be recorded as the pinhole is set to different points on the optical vortex. We hope that analysis of these images with the free NIH-image software will produce a skew angle map similar to that of Leach et al. [2].


[1] From the cover of Optical Angular Momentum, edited by Allen, Barnett and Padgett (IOP Publishing, Philadelphia, 2003).

[2] J. Leach et al., "Direct measurement of the skew angle of the Poynting vector in a helically phased beam," Optics Express 14, 11919 (2006).

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