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Abstract

For centuries, singularities in wave fields have been a mainstay of interest in multiple areas of physics, ranging from plasma physics, fluid dynamics and atmospheric physics to optics and photonics [1]. In optics, energy and momentum flow around singularities in the interference field can twist to form vortices, which carry angular momentum [2–4]. Singular Optics is the branch of physics that encompasses studies of structured light with localized and extended singularities, such as optical vortices in scalar optical fields and polarization singularities in vector fields [2, 5, 6]. It has been pioneered by the publication of a seminal paper of Nye and Berry 'Dislocations in wave trains' in 1974 [7], and has recently celebrated its 40th anniversary. Optical vortices—just like their analogs in tidal waves, superfluids, and superconductors—are intriguing phenomena with rich physics, which offer fascinating applications in classical and quantum optics. For example, linear and angular momentum of photons in structured optical fields can be utilized to achieve non-contact optical trapping and manipulation of microscopic particles and biological molecules [8, 9]. The inherent orthogonality of optical modes with different orbital angular momentum (OAM) uniquely positions them for applications in polarization and wavelength division multiplexing to increase data capacity of both free-space and fiber-optic communications [10]. Diffraction-free and self-healing propagation of optical vortex fields offers further opportunities in this field [11]. Higher information content of structured light fields along with the possibilities for their quantum entanglement can also play a key role in the development of new protocols for quantum information processing [12–14]. Strong variations of optical fields around singularities makes structured light extremely sensitive to small changes in the medium and illumination conditions, which can be exploited for super-resolution imaging [15, 16], on-chip optical switching [17–19], (bio)chemical sensing [20, 21], spectroscopy [22], solar energy harvesting [23, 24], and astronomical observations [25]. The key property of a vortex is the existence of a topological charge, which, in an optical vortex, takes the form of the winding number of an optical wavefront around the vortex core. Because this topological charge is discrete, or 'quantized', it remains constant under small deformations or defects in the physical system; it can only be altered by a global change, such as mutual annihilation with an anti-vortex, another vortex of the opposite charge. Conservation of topological charges of optical vortices in structured light fields underlies many unusual optical phenomena, including existence of bound optical states in the radiation continuum [26] and topological transformations of optical metamaterials into a hyperbolic regime [27]. In recent years, researchers have found very different and more abstract types of singularities and topological indices, which can appear in optical systems, based on ideas originating in the physics of topological insulators [28–30]. In a periodic optical medium, such as a photonic lattice or crystal, electromagnetic modes form band structures. The energy bands can themselves possess singularities in momentum space, such as Dirac cones in graphene [31] and photonic lattices [32, 33], the latter intimately connected with vortices and angular momentum of light [34, 35]. Within each band, the optical Bloch wavefunctions form a mathematical structure (a 'fiber bundle') defined over the Brillouin zone, which possesses quantized topological charges. Just as a vortex cannot be eliminated by small deformations, a 'topologically non-trivial' band possessing non-zero topological charge cannot be smoothly converted to a 'topologically trivial' band. The field of topological photonics aims to engineer devices to have topologically non-trivial photonic band structures, and to exploit their unusual and striking physical properties. In particular, 2D devices can exhibit topological edge states that circulate in a single direction along their boundaries, and are immune to back-scattering from defects or shape deformations. This was first demonstrated in 2009, using a magnetic photonic crystal operating at microwave frequencies [36]. Thereafter, topological edge states have been observed at the technologically crucial infrared-to-visible frequency range, using helical waveguide lattices and ring resonator lattices [37, 38]. A wide variety of other platforms are now undergoing active investigation, including microwave circuits [39, 40] and polaritonic resonator lattices [41, 42]. This special issue aims to survey the state-of-the-art in singular optics and topological photonics and to chart new research directions. The issue is a contribution to the celebration of the United Nations observance of The International Year of Light and Light-based Technologies, IYL 2015. It is also dedicated to the two remarkable anniversaries celebrated in 2014, the 40th anniversary of the pioneering paper by Nye and Berry [7] and the 85th birthday of Prof Marat Soskin, who has tirelessly spearheaded singular optics as an independent research field for the last 15 years [5]. This special issue contains 31 papers, which highlight the latest developments in this burgeoning research field and bridge fundamental concepts with emerging applications. The issue begins with an article by Barnett and co-authors, in which they lay down a comprehensive overview of the nature of the spin and orbital parts of optical angular momentum [43]. Next, several articles address the issues of non-diffracting beam propagation, effects of turbulence, and beam stabilization. In particular, Garcia-Gracia and Gutiérrez-Vega introduce a family of non-diffracting full Poincaré beams based on a superposition of non-diffracting Mathieu beams [44]. Makris and co-authors theoretically study superoscillatory superpositions of vectorial Bessel beams, which are diffraction-free and can support subwavelength features in their transverse electromagnetic fields, without the presence of evanescent waves [45]. Izdebskaya and colleagues study experimentally and numerically vortex stabilization in non-local media by using co-propagating spatial solitons [46]. Two papers discuss the effects of turbulence in the media on the angular momentum and quantum information content of the light beams. Aksenov et al numerically explore laser beams propagation through turbulent medium and show that the relative fluctuations of the orbital angular momentum decrease with the increase of the initial topological charge of the beam, which offers low-noise method of optical communication based on optical vortices [47]. In turn, Goyal and co-authors experimentally study the secret key rate for quantum key distribution protocols in OAM for free space quantum communication in the presence of turbulence, and find that a quantum key can be securely distributed over distances comparable to those over which the entanglement survives [48]. Morgan et al investigate propagation of modulated multi-petal concentric optical vortex beams through turbid environments to explore the use of beams with OAM in underwater free-space communications links [49]. The next two papers investigate the free-space optical channels multiplexing using twisted light beams. Willner and colleagues discuss design challenges and guidelines in using OAM multiplexing of multiple beams in free-space communications links [50]. Rodenburg et al experimentally demonstrate an interferometric protocol for multiplexing optical states of light, which enables preparation of either coherent superpositions or statistical mixtures of OAM states [51]. Interaction of structured light with matter has been studied by several groups in the context of forming hybrid plasmon-polariton or exciton-polariton vortex states and exciting atoms by twisted photons. Dzedolik and co-authors report on the formation of plasmon polariton vortex lattices on the metal surface formed the interference of the surface plasmon polaritons scattered by curvilinear boundaries [52]. Afanasev and colleagues calculate transition amplitudes and cross sections for excitation of hydrogen-like atoms by twisted photon states, and predict the transition rates into the high-OAM states to be comparable with the rates for electric dipole transitions if the atom is located near the phase singularity [53]. Schultz and colleagues employ a coherent two-photon Raman interaction to interface singular optical beams with a pseudo-spin-1/2 Bose–Einstein condensate, which serves as a q-plate for the atoms enabling conversion between atomic spin and OAM states [54]. Rosanov et al investigate and compare dissipative vortex solitons and their complexes in wide-aperture lasers and in exciton-polariton lasers, and show that while the energy is stored both in the electromagnetic field and in the lasing medium, media with fast response can follow the topology of the field without inertia [55]. In turn, Yaparov and Taranenko report on the theoretical and experimental work on spatial solitons formed in optical bistable oscillators with laser or/and parametric gain, with the focus on the solitons dynamical properties [56]. Tailored light–matter interactions have also been shown to enable shaping, switching and modulation of structured light. Larocque et al demonstrate liquid crystal devices for tailoring the wavefront of optical beams through the Pancharatnam–Berry phase concept and generate an extensive range of shaped optical beams [57]. Silahli and colleagues investigate the differences in the structured light interactions with positive and negative-index materials, and predict azimuthal modulation instability of optical vortices with different topological charges in nonlinear negative-index materials [58]. Laudyn and co-authors study spatial solitons in chiral nemati

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Soskin, M., Boriskina, S. V., Chong, Y., Dennis, M. R., & Desyatnikov, A. (2017, January 1). Singular optics and topological photonics. Journal of Optics (United Kingdom), 19(1). https://doi.org/10.1088/2040-8986/19/1/010401

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