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

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

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.

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

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are reviewed. In particular, how the paramount and genuinely NH concept of exceptional degeneracies, at which both eigenvalues and eigenvectors coalesce, leads to phenomena drastically distinct from the familiar Hermitian realm is discussed. An immediate consequence is the ubiquitous occurrence of nodal NH topological phases with concomitant open Fermi-Seifert surfaces, where conventional band-touching points are replaced by the aforementioned exceptional degeneracies. Furthermore, new notions of gapped phases including topological phases in single-band systems are detailed, and the manner in which a given physical context may affect the symmetry-based topological classification is clarified. A unique property of NH systems with relevance beyond the field of topological phases consists of the anomalous relation between bulk and boundary physics, stemming from the striking sensitivity of NH matrices to boundary conditions. Unifying several complementary insights recently reported in this context, a picture of intriguing phenomena such as the NH bulk-boundary correspondence and the NH skin effect is put together. Finally, applications of NH topology in both classical systems including optical setups with gain and loss, electric circuits, and mechanical systems and genuine quantum systems such as electronic transport settings at material junctions and dissipative cold-atom setups are reviewed.

Exceptional topology of non-Hermitian systems

Visible, circularly polarised light can be transformed into light-carrying orbital angular momentum by a plasmonic metasurface. That is the finding of Ebrahim Karimi and co-workers at the University of Ottawa in Canada and the University of Rochester in the United States. Light with orbital angular momentum (owing to a twisted phase front) is traditionally generated using specially designed optical elements such as spatial light modulator, cylindrical lens mode converters and q-plate. The researchers have now shown that a plasmonic metasurface comprising an array of nano-antennas can couple spin-to-orbital angular momentum at thickness much smaller than the wavelength of the light with an efficiency of around 3%. The conversion takes place due to the birefringence present in the nanostructure array. This approach could yield ultrathin generators of visible light with orbital angular momentum, for potential applications in spectroscopy, imaging, sensing and quantum information.

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Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface

We describe the polarization topology of the vector beams emerging from a patterned birefringent liquid crystal plate with a topological charge q at its center (q-plate). The polarization topological structures for different q-plates and different input polarization states have been studied experimentally by measuring the Stokes parameters point-by-point in the beam transverse plane. Furthermore, we used a tuned q=1/2-plate to generate cylindrical vector beams with radial or azimuthal polarizations, with the possibility of switching dynamically between these two cases by simply changing the linear polarization of the input beam.

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Polarization pattern of vector vortex beams generated by q-plates with different topological charges

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system Finally, we prove the robustness of the measure by introducing dynamical disorder in the system This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems The detection of topological invariants in the bulk remains challenging even in state-of-the-art experiments Here, Cardanoet al propose a method to read-out the Zak phases and topological invariants in one-dimensional chiral systems and detect those in a photonic quantum walk of twisted photons

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Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

Spin–orbit optical phenomena involve the interaction of the photon spin with the light wave propagation and spatial distribution, mediated by suitable optical media. Here we present a short overview of the emerging photonic applications that rely on such effects.

Spin–orbit photonics

We present a convenient method to generate vector beams of light having polarization singularities on their axis, via partial spin-to-orbital angular momentum conversion in a suitably patterned liquid crystal cell. The resulting polarization patterns exhibit a C-point on the beam axis and an L-line loop around it, and may have different geometrical structures such as "lemon", "star", and "spiral". Our generation method allows us to control the radius of L-line loop around the central C-point. Moreover, we investigate the free-air propagation of these fields across a Rayleigh range.

Generation and dynamics of optical beams with polarization singularities

The “quantum walk” has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space. We report the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons. In contrast to previous implementations, the whole process develops in a single light beam, with no need of interferometers; it requires optical resources scaling linearly with the number of steps; and it allows flexible control of input and output superposition states. Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets. Our demonstration introduces a novel versatile photonic platform for quantum simulations.

https://advances.sciencemag.org/content/advances/1/2/e1500087.full.pdf

Filippo Cardano

Papers

Polarization pattern of vector vortex beams generated by q-plates with different topological charges

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons

Spin–orbit photonics

Generation and dynamics of optical beams with polarization singularities

Quantum walks and wavepacket dynamics on a lattice with twisted photons