A fast-Fourier-transform method of topography and interferometry is proposed. By computer processing of a noncontour type of fringe pattern, automatic discrimination is achieved between elevation and depression of the object or wave-front form, which has not been possible by the fringe-contour-generation techniques. The method has advantages over moire topography and conventional fringe-contour interferometry in both accuracy and sensitivity. Unlike fringe-scanning techniques, the method is easy to apply because it uses no moving components.

Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry

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Principles Of Optics Electromagnetic Theory Of Propagation Interference And Diffraction Of Light

The spin Hall effect (SHE) of light, as an analogue of the SHE in electronic systems, is a promising candidate for investigating the SHE in semiconductor spintronics/valleytronics, high-energy physics and condensed matter physics, owing to their similar topological nature in the spin-orbit interaction. The SHE of light exhibits unique potential for exploring the physical properties of nanostructures, such as determining the optical thickness, and the material properties of metallic and magnetic thin films and even atomically thin two-dimensional materials. More importantly, it opens a possible pathway for controlling the spin states of photons and developing next-generation photonic spin Hall devices as a fundamental constituent of the emerging spinoptics. In this review, based on the viewpoint of the geometric phase gradient, we give a detailed presentation of the recent advances in the SHE of light and its applications in precision metrology and future spin-based photonics.

https://iopscience.iop.org/article/10.1088/1361-6633/aa5397/pdf

Recent advances in the spin Hall effect of light

https://science.sciencemag.org/content/sci/152/3724/951.1.full.pdf

Encyclopedia of physics.

Superoscillations are band-limited functions with the counterintuitive property that they can vary arbitrarily faster than their fastest Fourier component, over arbitrarily long intervals. Modern studies originated in quantum theory, but there were anticipations in radar and optics. The mathematical understanding—still being explored—recognises that functions are extremely small where they superoscillate; this has implications for information theory. Applications to optical vortices, sub-wavelength microscopy and related areas of nanoscience are now moving from the theoretical and the demonstrative to the practical. This Roadmap surveys all these areas, providing background, current research, and anticipating future developments.

/pdf/roadmap-on-superoscillations-qjcamt1wa3.pdf

Roadmap on superoscillations

The linear birefringence of uniaxial crystal plates has been known since the 17th century, and it is widely used in numerous optical setups and devices. Here we demonstrate, both theoretically and experimentally, the fine lateral circular birefringence of such crystal plates. We show that this effect is a novel example of the spin-Hall effect of light, i.e., a transverse spin-dependent shift of the paraxial light beam transmitted through the plate. The well-known linear birefringence and the new circular birefringence form an interesting analogy with the Goos–Hanchen and Imbert–Fedorov beam shifts that appear in the light reflection at a dielectric interface. We report experimental observation of the effect in a remarkably simple system of a tilted half-wave plate and polarizers using polarimetric and quantum-weak-measurement techniques for beam-shift measurements. In view of much recent interest in spin–orbit interaction phenomena, our results could find applications in modern polarization optics and nanophotonics.

Spin-Hall effect and circular birefringence of a uniaxial crystal plate

The linear birefringence of uniaxial crystal plates is known since the 17th century, and it is widely used in numerous optical setups and devices. Here we demonstrate, both theoretically and experimentally, a fine lateral circular birefringence of such crystal plates. This effect is a novel example of the spin-Hall effect of light, i.e., a transverse spin-dependent shift of the paraxial light beam transmitted through the plate. The well-known linear birefringence and the new circular birefringence form an interesting analogy with the Goos-Hanchen and Imbert-Fedorov beam shifts that appear in the light reflection at a dielectric interface. We report the experimental observation of the effect in a remarkably simple system of a tilted half-wave plate and polarizers using polarimetric and quantum-weak-measurement techniques for the beam-shift measurements. In view of great recent interest in spin-orbit interaction phenomena, our results could find applications in modern polarization optics and nano-photonics.

Accurate measurement of chirality is essential for the advancement of natural and pharmaceutical sciences. We report here a method to measure chirality using non-separable states of light with geometric phase-gradient in the circular polarization basis, which we refer to as spin-orbit beams. A modified polarization Sagnac interferometer is used to generate spin-orbit beams wherein the spin and orbital angular momentum of the input Gaussian beam are coupled. The out-of-phase interference between counter-propagating Gaussian beams with orthogonal spin states and lateral-shear or/and linear-phase difference between them results in spin-orbit beams with linear and azimuthal phase gradient. The spin-orbit beams interact efficiently with the chiral medium, inducing a measurable change in the center-of-mass of the beam, using the polarization rotation angle and hence the chirality of the medium are accurately calculated. Tunable dynamic range of measurement and flexibility to introduce large values of orbital angular momentum for the spin-orbit beam, to improve the measurement sensitivity, highlight the techniques' versatility.

Spin-orbit beams for optical chirality measurement

The realization of spiral phase optical elements on the cleaved end of an optical fiber by focused ion beam milling is presented. A focused Ga+ ion beam with an acceleration voltage of 30 keV is used to etch continuous spiral phase plates and fork gratings directly on the tip of the fiber. The phase characteristics of the output beam generated by the fabricated structures measured via an interference experiment confirmed the presence of phase singularity in the output beam. The devices are expected to be promising candidates for all-fiber beam shaping and optical trapping applications.

Direct patterning of vortex generators on a fiber tip using a focused ion beam

We describe the spin-Hall effect of light (as well as the angular Goos-Hanchen effect) at a tilted linear-dichroic plate, such as a usual linear polarizer. Although the spin-Hall effect at a tilted polarizer was previously associated with the geometric spin-Hall effect of light (which was contrasted to the regular spin-Hall effect) [Phys. Rev. Lett.112, 113902 (2014) PRLTAO0031-900710.1103/PhysRevLett.112.113902], we show that the effect is actually an example of the regular spin-Hall effect that occurs at tilted anisotropic plates [Optica3, 1039 (2016) OPTIC82334-253610.1364/OPTICA.3.001039]. Moreover, our approach reveals the angular spin-Hall shift, which is absent in the “geometric” approach. We verify our theory experimentally using the method of quantum weak measurements.

C. T. Samlan

Papers

Spin-Hall effect and circular birefringence of a uniaxial crystal plate

Spin-Hall effect and circular birefringence of a uniaxial crystal plate

Spin-orbit beams for optical chirality measurement

Direct patterning of vortex generators on a fiber tip using a focused ion beam

Spin-Hall effect of light at a tilted polarizer.