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

Photonic crystals are materials patterned with a periodicity in dielectric constant, which can create a range of 'forbidden' frequencies called a photonic bandgap. Photons with energies lying in the bandgap cannot propagate through the medium. This provides the opportunity to shape and mould the flow of light for photonic information technology.

Photonic crystals: putting a new twist on light

Modern nanotechnology allows one to scale down various important devices (sensors, chips, fibers, etc.) and thus opens up new horizons for their applications. The efficiency of most of them is based on fundamental physical phenomena, such as transport of wave excitations and resonances. Short propagation distances make phase-coherent processes of waves important. Often the scattering of waves involves propagation along different paths and, as a consequence, results in interference phenomena, where constructive interference corresponds to resonant enhancement and destructive interference to resonant suppression of the transmission. Recently, a variety of experimental and theoretical work has revealed such patterns in different physical settings. The purpose of this review is to relate resonant scattering to Fano resonances, known from atomic physics. One of the main features of the Fano resonance is its asymmetric line profile. The asymmetry originates from a close coexistence of resonant transmission and resonant reflection and can be reduced to the interaction of a discrete (localized) state with a continuum of propagation modes. The basic concepts of Fano resonances are introduced, their geometrical and/or dynamical origin are explained, and theoretical and experimental studies of light propagation in photonic devices, charge transport through quantum dots, plasmon scattering in Josephson-junction networks, and matter-wave scattering in ultracold atom systems, among others are reviewed.

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Fano resonances in nanoscale structures

Achieving control of light-material interactions for photonic device applications at nanoscale dimensions will require structures that guide electromagnetic energy with a lateral mode confinement below the diffraction limit of light. This cannot be achieved by using conventional waveguides or photonic crystals. It has been suggested that electromagnetic energy can be guided below the diffraction limit along chains of closely spaced metal nanoparticles that convert the optical mode into non-radiating surface plasmons. A variety of methods such as electron beam lithography and self-assembly have been used to construct metal nanoparticle plasmon waveguides. However, all investigations of the optical properties of these waveguides have so far been confined to collective excitations and direct experimental evidence for energy transport along plasmon waveguides has proved elusive. Here we present observations of electromagnetic energy transport from a localized subwavelength source to a localized detector over distances of about 0.5 μm in plasmon waveguides consisting of closely spaced silver rods. The waveguides are excited by the tip of a near-field scanning optical microscope, and energy transport is probed by using fluorescent nanospheres.

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Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides.

We propose a new type of optical waveguide that consists of a sequence of coupled high- Q resonators. Unlike other types of optical waveguide, waveguiding in the coupled-resonator optical waveguide (CROW) is achieved through weak coupling between otherwise localized high- Q optical cavities. Employing a formalism similar to the tight-binding method in solid-state physics, we obtain the relations for the dispersion and the group velocity of the photonic band of the CROW's and find that they are solely characterized by coupling factor k 1 . We also demonstrate the possibility of highly efficient nonlinear optical frequency conversion and perfect transmission through bends in CROW's.

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Coupled-resonator optical waveguide:?a proposal and analysis

We demonstrate highly efficient transmission of light around sharp corners in photonic band-gap waveguides. Numerical simulations reveal complete transmission at certain frequencies, and very high transmission $(g95%)$ over wide frequency ranges. High transmission is observed even for 90\ifmmode^\circ\else\textdegree\fi{} bends with zero radius of curvature, with a maximum transmission of 98% as opposed to 30% for analogous conventional dielectric waveguides. We propose a simple one-dimensional scattering theory model with a dynamic frequency-dependent well depth to describe the transmission properties.

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High Transmission through Sharp Bends in Photonic Crystal Waveguides.

Finite difference time domain is a powerful numerical method. We review our modeling and design of optical gratings and 2D photonic crystals, aided by the recently developed quartic perfectly matched layer boundary condition. For optical gratings with a quarter wave phase shift, we show that light can be confined in an air bridge micro-cavity. Such devices exhibit sharp transmission resonances in the stop bands. Photonic crystals also demonstrate strong localization of light so waveguides of air can be formed. In addition, even when the bending radius is zero, the transmission exceeds 0.95 percent.

I. Kurland

Papers

High Transmission through Sharp Bends in Photonic Crystal Waveguides.

Finite differencing of periodic structures