## Abstract## Investigating optical vortices created with a single cylinder lensHannarae Annie Nam, Choate Rosemary Hall
This work extends the work of Hamsa Sridhar, a former Simons Fellow, who discovered a way of converting Hermite-Gaussian (HG) laser modes to Laguerre-Gaussian (LG) modes with a single cylinder lens [1]. Her "single lens mode converter" is simpler than the previous design, which used two cylinder lenses, but the generated optical vortex is only approximate. In this work we are investigating several aspects of the optical vortices created by the single lens mode converter, through measurements and simulations. An optical vortex is a phase singularity - a point in a light beam where the phase of the light wave takes on every value and hence is undefined. This ambiguity necessarily results in a point of zero intensity, or dark core. Certain LG modes contain an optical vortex since these specialized laser modes contain azimuthally-varying phases. One possible way of generating such a laser beam is by converting a HG mode into the LG mode by using astigmatic elements (cylinder lenses), which affect the two orthogonal tranverse components (x and y for a beam moving along the z-direction) in different ways. A regular astigmatic mode converter uses the first cylinder lens to introduce astigmatism, and the second cylinder lens to restore the beam to isotropy. However, in the single lens mode converter, the astigmatic beam is not converted back to its isotropic state due to the lack of the second cylinder lens. But the divergence rates of the two beam components are the same, so the beam gradually becomes circular in the far-field where the width difference in the two axes is insignificant. The original concept of this project was to study the quality of the optical vortex mode created by a single lens converter. Prior to any experimentation, we expected that the vortex would pass through a sequence of elliptical shapes when it was focused with a spherical lens, as a result of its residual astigmatism. Very recently, as we tried to observe these shape changes, we discovered that at the midpoint of the focal region where the two beam components share the same width, the vortex disappears and a Hermite-Gaussian mode reappears. We now understand that this happens because the Gouy phase shift gained at the cylindrical lens is totally undone at this midpoint, so the beam is restored to a Hermite Gaussian form there. Future work will seek to model our observations by creating a computer spreadsheet model based on the q-parameter formalism. We would like to thank the Simons Foundation for funding this research, Hamsa Sridhar for helpful discussions, and Prof. Harold Metcalf for establishing and supporting the Laser Teaching Center. Reference
[1] Hamsa Sridhar, Martin G. Cohen and John W. Noe. "Creating optical vortex modes with a single
cylinder lens." Proc. SPIE |