Structuring Light for Investigating Optical Vortices

Vortices are well known in our world: tornadoes, hurricanes, and quickly stirred iced tea all demonstrate the vortex phenomenon. In addition to these classical fluids, vortices exist in laser light. While classical fluid vortex dynamics is one of the oldest studied physics problems, the study of optical vortices is only a few decades old. Paralleling the community’s curiosity of quantized vortices in quantum fluids, such as super fluid helium and Bose-Einstein condensate, there is immense interest in the study of optical vortices. In this article, we cover the basic theory of structuring light to generate optical vortices and then discuss experiments performed to study their characteristics and dynamics

Quantized Optical Vortex-array Eigenstates in a Rotating Frame

Linear combinations of Bessel beams can be used to effectively trap light within cylindrical domains. Such hard traps can be used to produce states that exhibit stationary arrays of optical vortices from the perspective of a steadily rotating frame. These patterned singularities can be engineered to have singularities of the same or mixed charges and the requisite rotation rates are quantized even though the setting is purely linear. A hydrodynamic interpretation is that the vortices are at rest within a compressible, two-dimensional fluid of light

The Anatomy of Geometric Phase for an Optical Vortex Transiting a Lens

We present an analytical means of quantifying the fractional accumulation of geometric phase for an optical vortex transiting a cylindrical lens. The standard fiber bundle of a Sphere of Modes is endowed with a Supplementary Product Space at each point so that the beam waists and their positions can be explicitly tracked as functions of lens transit fraction. The method is applied to quantify the accumulation of geometric phase across a single lens as a function of initial state and lens position within the beam. It can be readily applied to a series of lenses as well.Comment: 10 pages, 13 figure

Pump-tailored Alternative Bell State Generation in the First-Order Hermite-Gaussian basis

We demonstrate entangled-state swapping, within the Hermite-Gaussian basis of first-order modes, directly from the process of spontaneous parametric down-conversion within a nonlinear crystal. The method works by explicitly tailoring the spatial structure of the pump photon such that it resembles the product of the desired entangled spatial modes exiting the crystal. Importantly, the result is an entangled state of balanced HG modes, which may be beneficial in applications that depend on symmetric accumulations of geometric phase through optics or in applications of quantum sensing and imaging with azimuthal sensitivity. Furthermore, the methods are readily adaptable to other spatial mode bases

Initial Optical Vortex Amplitude Structure Determines Pair Annihilation

We show that annihilation dynamics between oppositely charged optical vortex pairs can be manipulated by modifying only the initial size of the vortex cores. When sufficiently close together, vortices with strongly overlapped cores annihilate more quickly than vortices with smaller cores that must wait for diffraction to cause meaningful core overlap. We present numerical simulations and experimental measurements for vortices with hyperbolic tangent cores of various initial sizes. We also show that decreasing the core size of an annihilating pair can prevent the annihilation event

Experimental measurement of the geometric phase of non-geodesic circles

We present and implement a method for the experimental measurement of geometric phase of non-geodesic (small) circles on any SU(2) parameter space. This phase is measured by subtracting the dynamic phase contribution from the total phase accumulated. Our design does not require theoretical anticipation of this dynamic phase value and the methods are generally applicable to any system accessible to interferometric and projection measurements. Experimental implementations are presented for two settings: (1) the sphere of modes of orbital angular momentum, and (2) the Poincar\'e sphere of polarizations of Gaussian beams

Characterizing Vortex Beams from a Spatial Light Modulator with Collinear Phase-shifting Holography

We demonstrate collinear phase-shifting holography for measuring complex optical modes of twisted light beams with orbital angular momentum (OAM) generated by passing a laser through a spatial light modulator (SLM). This technique measures the mode along the direction of propagation from the SLM and requires no additional optics, so it can be used to aid alignment of the SLM, to efficiently check for the effects of beam wander, and to fully characterize generated beams before use in other experiments. Optimized error analysis and careful SLM alignment allow us to generate and measure OAM with purity as high as 99.9%