Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues.

Quantum Cryptography

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

We describe a method to estimate the capacity limit of fiber-optic communication systems (or ?fiber channels?) based on information theory. This paper is divided into two parts. Part 1 reviews fundamental concepts of digital communications and information theory. We treat digitization and modulation followed by information theory for channels both without and with memory. We provide explicit relationships between the commonly used signal-to-noise ratio and the optical signal-to-noise ratio. We further evaluate the performance of modulation constellations such as quadrature-amplitude modulation, combinations of amplitude-shift keying and phase-shift keying, exotic constellations, and concentric rings for an additive white Gaussian noise channel using coherent detection. Part 2 is devoted specifically to the "fiber channel.'' We review the physical phenomena present in transmission over optical fiber networks, including sources of noise, the need for optical filtering in optically-routed networks, and, most critically, the presence of fiber Kerr nonlinearity. We describe various transmission scenarios and impairment mitigation techniques, and define a fiber channel deemed to be the most relevant for communication over optically-routed networks. We proceed to evaluate a capacity limit estimate for this fiber channel using ring constellations. Several scenarios are considered, including uniform and optimized ring constellations, different fiber dispersion maps, and varying transmission distances. We further present evidences that point to the physical origin of the fiber capacity limitations and provide a comparison of recent record experiments with our capacity limit estimation.

Capacity Limits of Optical Fiber Networks

This Review article provides an overview of the fundamental origins and important applications of the main spin–orbit interaction phenomena in modern optics that play a crucial role at subwavelength scales. Light carries both spin and orbital angular momentum. These dynamical properties are determined by the polarization and spatial degrees of freedom of light. Nano-optics, photonics and plasmonics tend to explore subwavelength scales and additional degrees of freedom of structured — that is, spatially inhomogeneous — optical fields. In such fields, spin and orbital properties become strongly coupled with each other. In this Review we cover the fundamental origins and important applications of the main spin–orbit interaction phenomena in optics. These include: spin-Hall effects in inhomogeneous media and at optical interfaces, spin-dependent effects in nonparaxial (focused or scattered) fields, spin-controlled shaping of light using anisotropic structured interfaces (metasurfaces) and robust spin-directional coupling via evanescent near fields. We show that spin–orbit interactions are inherent in all basic optical processes, and that they play a crucial role in modern optics.

Spin-orbit interactions of light

We have detected a spin-dependent displacement perpendicular to the refractive index gradient for photons passing through an air-glass interface. The effect is the photonic version of the spin Hall effect in electronic systems, indicating the universality of the effect for particles of different nature. Treating the effect as a weak measurement of the spin projection of the photons, we used a preselection and postselection technique on the spin state to enhance the original displacement by nearly four orders of magnitude, attaining sensitivity to displacements of ∼1 angstrom. The spin Hall effect can be used for manipulating photonic angular momentum states, and the measurement technique holds promise for precision metrology.

http://science.sciencemag.org/content/sci/319/5864/787.full.pdf

Observation of the Spin Hall Effect of Light via Weak Measurements

We report the first experimental verification of Berry's topological phase. The key element in the experiment was a single-mode, helically wound optical fiber, inside which a photon of a given helicity could be adiabatically transported around a closed path in momentum space. The experiment confirmed at the classical level that the angle of rotation of linearly polarized light in this fiber gives a direct measure of Berry's phase. The topological nature of this effect was also verified, i.e., the rotation was found to be independent of deformations of fiber path if the solid angle of the path in momentum space stayed constant.

Observation of Berry's topological phase by use of an optical fiber.

By using cw laser diodes operating at 1.26 and 1.34 μm, the cross talk caused by stimulated Raman scattering in a 21-km single-mode fiber was measured to be −25.2 dB at a pump-power level of 1.0 mW. The Raman-gain coefficient was calculated to be 0.57 × 10−11 cm/W, which is in good agreement with previously reported values measured with high-power pulsed lasers.

Cross talk caused by stimulated Raman scattering in single-mode wavelength-division multiplexed systems

Radiation loss characteristics are calculated for the first two LP modes of a double-clad lightguide structure in which the inner cladding forms a low refractive-index well between the core and the outer cladding. The higher-order mode is defined to be effectively cut off at wavelengths where the LP(11) mode power is sufficiently attenuated to ensure negligible modal noise due to interference between LP(01) and LP(11) modes. Calculations apply for various deposited cladding thicknesses and findings can be easily extrapolated if specifications are changed for system requirements on the minimum unspliced fiber length or the extinction ratio between P(11) and P(01) mode powers, Re = 10 log P(11)/P(01). The latter is specified at points such as splice joints where modal noise is generated. Theoretical results are correlated with measurements in order to determine the effective cutoff wavelength for fibers in which leaky-mode loss mechanisms dominate. The procedure should be extremely useful for determining the shortest usable wavelength for single-mode lightwave systems.

Leaky-mode loss of the second propagating mode in single-mode fibers with index well profiles.

A gap between the fiber endfaces constitutes one of the extrinsic loss mechanisms in optical fiber connectors. Fur­ thermore, the optical loss in a connector with a gap is affected by environmental conditions such as temperature, pressure, and mechanical vibrations.' To improve the design of low-loss connectors and to investigate the environmental ef­ fects on the connectors, it is necessary to measure in situ the fiber endface separation in assembled connectors. A me­ chanical approach in which one of the fiber ends is replaced by a transducer has been pursued. However, the preparation of the modified sample connector is tedious, and the mea­ surement results obtained may not be representative for de­ ployed connectors. Optical approaches are preferable to mechanical ones, since they can be simple and nondestructive and are readily applicable to deployed connectors. Interference phenomena in fiber connectors were most re­ cently discussed by Wagner and Sandahl who showed that a change in the fiber endface separation could be measured by counting interference fringes. This Letter describes a measurement of the absolute separation between two fiber endfaces using a white light interference technique. Consider two single-mode fiber ends which are separated by a distance d, and suppose a plane wave of light with wavelength X is propagating through the gap (Fig. 1). Since the reflectivity of the fiber ends is low {R ;$ 0.04), one can neglect multiple reflections to simplify the analysis. One can show, however, that an analysis which includes multiple re­ flections gives exactly the same result as far as the endface separation measurement is concerned. Fig. 1. Schematic diagram of the gap between two optical fiber ends.

Akira Tomita

Papers

Observation of Berry's topological phase by use of an optical fiber.

Cross talk caused by stimulated Raman scattering in single-mode wavelength-division multiplexed systems

Leaky-mode loss of the second propagating mode in single-mode fibers with index well profiles.

Interferometric technique for measuring small gaps in single- and multimode fiber connectors

Erratum: Observation of Berry's topological phase by use of an optical fiber [Phys. Rev. Lett. 57, 937 (1986)]