There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Wave propagation and group velocity

Thirty years ago, Coullet et al. proposed that a special optical field exists in laser cavities bearing some analogy with the superfluid vortex. Since then, optical vortices have been widely studied, inspired by the hydrodynamics sharing similar mathematics. Akin to a fluid vortex with a central flow singularity, an optical vortex beam has a phase singularity with a certain topological charge, giving rise to a hollow intensity distribution. Such a beam with helical phase fronts and orbital angular momentum reveals a subtle connection between macroscopic physical optics and microscopic quantum optics. These amazing properties provide a new understanding of a wide range of optical and physical phenomena, including twisting photons, spin-orbital interactions, Bose-Einstein condensates, etc., while the associated technologies for manipulating optical vortices have become increasingly tunable and flexible. Hitherto, owing to these salient properties and optical manipulation technologies, tunable vortex beams have engendered tremendous advanced applications such as optical tweezers, high-order quantum entanglement, and nonlinear optics. This article reviews the recent progress in tunable vortex technologies along with their advanced applications.

/pdf/optical-vortices-30-years-on-oam-manipulation-from-2yknluuuga.pdf

Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities

Emerging applications based on optical beams carrying orbital angular momentum (OAM) will probably require photonic integrated devices and circuits for miniaturization, improved performance, and enhanced functionality. We demonstrate silicon-integrated optical vortex emitters, using angular gratings to extract light confined in whispering gallery modes with high OAM into free-space beams with well-controlled amounts of OAM. The smallest device has a radius of 3.9 micrometers. Experimental characterization confirms the theoretical prediction that the emitted beams carry exactly defined and adjustable OAM. Fabrication of integrated arrays and demonstration of simultaneous emission of multiple identical optical vortices provide the potential for large-scale integration of optical vortex emitters on complementary metal-oxide–semiconductor compatible silicon chips for wide-ranging applications.

/pdf/integrated-compact-optical-vortex-beam-emitters-1443e933nn.pdf

Integrated Compact Optical Vortex Beam Emitters

Near‐field optical‐scanning (NFOS) microscopy or ‘‘optical stethoscopy’’ provides images with resolution in the 20‐nm range, i.e., a very small fraction of an optical wavelength. Scan images of metal films with fine structures presented in this paper convincingly demonstrate this resolution capability. Design of an NFOS microscope with tunnel distance regulation, its theoretical background, application potential, and limitations are discussed.

Near‐field optical‐scanning microscopy

We report a new, to our knowledge, technique for encoding amplitude information onto a phase-only filter with a single liquid-crystal spatial light modulator. In our approach we spatially modulate the phase that is encoded onto the filter and, consequently, spatially modify the diffraction efficiency of the filter. Light that is not diffracted into the first order is sent into the zero order, effectively allowing for amplitude modulation of either the first-order or the zero-order diffracted light. This technique has several applications in both optical pattern recognition and image processing, including amplitude modulation and inverse filters. Experimental results are included for the new technique.

Encoding amplitude information onto phase-only filters

The Hilbert transform is useful for image processing because it can select which edges of an input image are enhanced and to what degree the edge enhancement occurs. However, the transform operation is one dimensional and is not applicable for arbitrarily shaped two-dimensional objects. We introduce a radially symmetric Hilbert transform that permits two-dimensional edge enhancement. We implement one-dimensional, two-dimensional, and radial Hilbert transforms with a programmable phase-only liquid-crystal spatial light modulator. Experimental results are presented.

Image processing with the radial Hilbert transform: theory and experiments

We show how to two dimensionally encode the polarization state of an incident light beam using a parallel-aligned liquid-crystal spatial light modulator (LCSLM). Each pixel of the LCSLM acts as a voltage-controlled wave plate and can be programmed over a 2pi phase range at a wavelength of 514.5 nm. Techniques are reviewed for either rotating the major axis of elliptically polarized light or for converting an input linearly polarized beam into an arbitrary elliptically polarized beam. Experimental results are demonstrated in which we generate various two-dimensional spatial patterns of polarized light. Several potential applications are suggested. We also report an unexpected edge-enhancement effect that might be useful in image processing applications.

Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator

The potential of the extremely inexpensive Radio Shack liquid-crystal television (LCTV) as a two-dimensional spatial light modulator has been investigated. The LCTV modulates the transmission of coherent or incoherent light and can either be electronically addressed through a microcomputer or optically addressed with a TV camera. We have measured the transmission characteristics of the device, examined its diffraction pattern, and tested its use as an input device for an optical correlator. We have discovered that, with proper modifications, it has potential for optical-data-processing applications.

Optical-data-processing properties of a liquid-crystal television spatial light modulator.

We present a method to generate complete arbitrary spatially variant polarization modulation of a light beam by means of a parallel aligned nematic liquid crystal spatial light modulator (SLM). We first analyze the polarization modulation properties in a transmission mode. We encode diffraction gratings onto the SLM and show how to achieve partial polarization control of the zero order transmitted light. We then extend the technique to a double modulation scheme, which is implemented using a single SLM divided in two areas in a reflective configuration. The polarization states of the transmitted beam from the first pass through the first area are rotated using two passes through a quarter wave plate. The beam then passes through the second area of the SLM where additional polarization information can be encoded. By combining previously reported techniques, we can achieve complete amplitude, phase and polarization control for the diffracted light that allows the creation of arbitrary diffractive optical elements including polarization control. Theoretical analysis based on the Jones matrix formalism, as well as excellent experimental results are presented.

http://tecnopto.edu.umh.es/wp-content/uploads/sites/605/2014/05/Opt.Exp_.2012-Complete-polarization-control-of-light-from-a-liquid-crystal-spatial-light-modulator.pdf

Jeffrey A. Davis

Papers

Encoding amplitude information onto phase-only filters

Image processing with the radial Hilbert transform: theory and experiments

Two-dimensional polarization encoding with a phase-only liquid-crystal spatial light modulator

Optical-data-processing properties of a liquid-crystal television spatial light modulator.

Complete polarization control of light from a liquid crystal spatial light modulator