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

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.

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Integrated Compact Optical Vortex Beam Emitters

Space-variant Pancharatnam-Berry phase optical elements based on computer-generated subwavelength gratings are presented. By continuously controlling the local orientation and period of the grating we can achieve any desired phase element. We present a theoretical analysis and experimentally demonstrate a Pancharatnam-Berry phase-based diffraction grating for laser radiation at a wavelength of 10.6microm.

Space-variant Pancharatnam-Berry phase optical elements with computer-generated subwavelength gratings.

Structured light refers to the generation and application of custom light fields. As the tools and technology to create and detect structured light have evolved, steadily the applications have begun to emerge. This roadmap touches on the key fields within structured light from the perspective of experts in those areas, providing insight into the current state and the challenges their respective fields face. Collectively the roadmap outlines the venerable nature of structured light research and the exciting prospects for the future that are yet to be realized.

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Roadmap on structured light

In this work, we present the realization of a high-phase diffractive axicon. For that purpose, we use a spatial light modulator that exhibits 10π phase modulation. We compare the results with standard diffractive axicons that exhibit 2π phase modulation. We show that high-phase modulation axicons generate Bessel beams with a shorter range and a smaller radius than standard axicons with the same period. We also find that the higher phase modulation regime provides improved diffraction efficiency since fringing effects are reduced. Therefore, dynamic control of Bessel beams is presented, controlled through the phase modulation dynamic range.

Dynamic control of Bessel beams through high-phase diffractive axicons

Generation of Laser Beams by Digital Holograms

Liquid crystal displays allow the easy implementation of diffractive optical elements. However, the shortest focal lengths for lenses are limited by Nyquist conditions. In this work, we show that focal lengths much lower than this Nyquist limit can be encoded onto devices having a large phase-dynamic range. Experimental results are included with a display showing 10π phase modulation reducing the Nyquist limit by a factor of about 1/10.

Encoding lenses with focal lengths lower than the Nyquist limit using high phase-modulation displays.

We present the use of a q -plate device operating at the 1550 nm telecommunications wavelength. A prototype liquid-crystal device from Citizen Holdings Co. is demonstrated to be useful for the generation of vector beams and orbital angular momentum transfer at this important wavelength.

Generation of vector beams at 1550 nm telecommunications wavelength using a segmented q-plate

In this paper we will revise the application of twisted nematic liquid crystal displays (TN-LCD) as spatial light modulators (SLM) for image processing and diffractive optics. In general two kind of responses are desired for the mentioned applications: amplitude­-only and phase-only modulation. In general the users of commercially available LCDs do not know the optical properties of the used material. Thus, a reverse-engineering approach is needed to optimize the LCD response. First, we show a simplified model, that we recently proposed, for the orientation of the LC molecules. The model allows the determination of the physical parameters of the LCD by means of simple intensity measurements. Second, we demonstrate the capability of the model to provide very accurate predictions of the optical transmission. Therefore, we can perform computer searches for the optimum orientation of the added polarizing elements to obtain the required optical transmission. We demonstrate the need to insert wave plates in front and behind the LCD to obtain either amplitude-only or phase-only regimes with the LCD. Finally, we show the application of the optimized LCD to display images and filters in optical image processing, as well as we show the design of diffractive optical elements and apodizers.

Ignacio Moreno

Papers

Dynamic control of Bessel beams through high-phase diffractive axicons

Generation of Laser Beams by Digital Holograms

Encoding lenses with focal lengths lower than the Nyquist limit using high phase-modulation displays.

Generation of vector beams at 1550 nm telecommunications wavelength using a segmented q-plate

Optimization of liquid crystal displays behavior in optical image processing and in diffractive optics