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

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

Smart materials offering great freedom in manipulating electromagnetic radiation have been developed. This exciting new concept was realized by Tie Jun Cui and co-workers at the Southeast University, China, who developed digital metamaterials consisting of two kinds of unit cells whose different phase responses allow them to act as ‘0’ and ‘1’ bits. These cells can be judiciously arranged in sequences to enable controlled manipulation of electromagnetic waves. This is one-bit coding; higher-bit coding is possible by employing more kinds of unit cells. The researchers developed a metamaterial cell whose binary response can be controlled by a biased diode. By using a field-programmable gate array, they demonstrated that this digital metamaterial can be programmed. Such metamaterials are attractive for controlling radiation beams in antennas and for realizing other ‘smart’ metamaterials.

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Coding metamaterials, digital metamaterials and programmable metamaterials

Photonic bandgap crystals can reflect light for any direction of propagation in specific wavelength ranges1,2,3. This property, which can be used to confine, manipulate and guide photons, should allow the creation of all-optical integrated circuits. To achieve this goal, conventional semiconductor nanofabrication techniques have been adapted to make photonic crystals4,5,6,7,8,9. A potentially simpler and cheaper approach for creating three-dimensional periodic structures is the natural assembly of colloidal microspheres10,11,12,13,14,15. However, this approach yields irregular, polycrystalline photonic crystals that are difficult to incorporate into a device. More importantly, it leads to many structural defects that can destroy the photonic bandgap16,17. Here we show that by assembling a thin layer of colloidal spheres on a silicon substrate, we can obtain planar, single-crystalline silicon photonic crystals that have defect densities sufficiently low that the bandgap survives. As expected from theory, we observe unity reflectance in two crystalline directions of our photonic crystals around a wavelength of 1.3 micrometres. We also show that additional fabrication steps, intentional doping and patterning, can be performed, so demonstrating the potential for specific device applications.

On-chip natural assembly of silicon photonic bandgap crystals

The ideal material for nanophotonic applications will have a large refractive index at optical frequencies, respond to both the electric and magnetic fields of light, support large optical chirality and anisotropy, confine and guide light at the nanoscale, and be able to modify the phase and amplitude of incoming radiation in a fraction of a wavelength. Artificial electromagnetic media, or metamaterials, based on metallic or polar dielectric nanostructures can provide many of these properties by coupling light to free electrons (plasmons) or phonons (phonon polaritons), respectively, but at the inevitable cost of significant energy dissipation and reduced device efficiency. Recently, however, there has been a shift in the approach to nanophotonics. Low-loss electromagnetic responses covering all four quadrants of possible permittivities and permeabilities have been achieved using completely transparent and high-refractive-index dielectric building blocks. Moreover, an emerging class of all-dielectric metamaterials consisting of anisotropic crystals has been shown to support large refractive index contrast between orthogonal polarizations of light. These advances have revived the exciting prospect of integrating exotic electromagnetic effects in practical photonic devices, to achieve, for example, ultrathin and efficient optical elements, and realize the long-standing goal of subdiffraction confinement and guiding of light without metals. In this Review, we present a broad outline of the whole range of electromagnetic effects observed using all-dielectric metamaterials: high-refractive-index nanoresonators, metasurfaces, zero-index metamaterials and anisotropic metamaterials. Finally, we discuss current challenges and future goals for the field at the intersection with quantum, thermal and silicon photonics, as well as biomimetic metasurfaces.

All-dielectric metamaterials

We propose to use transformation optics to generate a general illusion such that an arbitrary object appears to be like some other object of our choice. This is achieved by using a remote device that can transform the scattered light outside a virtual boundary into that of the object chosen for the illusion, irrespective of the profile and direction of the incident light. This type of illusion device also enables people to see through walls. Our work extends the concept of cloaking as a special form of illusion to the wider realm of illusion optics.

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Illusion optics: the optical transformation of an object into another object.

Based on the concept of complementary media, we propose an invisibility cloak operating at a finite frequency that can cloak an object with a prespecified shape and size within a certain distance outside the shell. The cloak is comprised of a dielectric core and an "antiobject" embedded inside a negative index shell. The cloaked object is not blinded by the cloaking shell since it lies outside the cloak. Full-wave simulations in two dimensions have been performed to verify the cloaking effect.

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Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell.

The behaviour of sound waves in phononic crystals—metamaterials with spatially varying acoustic characteristics—is similar to that of electrons in solids. Now, phononic band inversion and Zak phases have been measured for a 1D phononic system.

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Geometric phase and band inversion in periodic acoustic systems

The ability to withstand shear is one of the properties that distinguishes a solid from a liquid. The proposal of an elastic metamaterial that in one direction only supports compressional waves, and therefore is fluid-like, and in the other supports compressional as well as shear waves represents a hybrid between fluids and solids that may lead to new applications.

Hybrid elastic solids

Surface impedance is an important concept in classical wave systems such as photonic crystals (PCs). For example, the condition of an interface state formation in the interfacial region of two different one-dimensional PCs is simply Z_SL +Z_SR=0, where Z_SL (Z_SR)is the surface impedance of the semi-infinite PC on the left- (right-) hand side of the interface. Here, we also show a rigorous relation between the surface impedance of a one-dimensional PC and its bulk properties through the geometrical (Zak) phases of the bulk bands, which can be used to determine the existence or non-existence of interface states at the interface of the two PCs in a particular band gap. Our results hold for any PCs with inversion symmetry, independent of the frequency of the gap and the symmetry point where the gap lies in the Brillouin Zone. Our results provide new insights on the relationship between surface scattering properties, the bulk band properties and the formation of interface states, which in turn can enable the design of systems with interface states in a rational manner.

Zhao-Qing Zhang

Papers

Illusion optics: the optical transformation of an object into another object.

Complementary media invisibility cloak that cloaks objects at a distance outside the cloaking shell.

Geometric phase and band inversion in periodic acoustic systems

Hybrid elastic solids

Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems