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

In this chapter, we will restrict our attention to the ferrites and a few other closely related materials. The great interest in ferrites stems from their unique combination of a spontaneous magnetization and a high electrical resistivity. The observed magnetization results from the difference in the magnetizations of two non-equivalent sub-lattices of the magnetic ions in the crystal structure. Materials of this type should strictly be designated as “ferrimagnetic” and in some respects are more closely related to anti-ferromagnetic substances than they are to ferromagnetics in which the magnetization results from the parallel alignment of all the magnetic moments present. We shall not adhere to this special nomenclature except to emphasize effects, which are due to the existence of the sub-lattices.

Ferromagnetic materials

Transformation optics describes the capability to design the path of light waves almost at will through the use of metamaterials that control effective materials properties on a subwavelength scale. In this review, the physics and applications of transformation optics are discussed.

Transformation optics and metamaterials

We present an experimental demonstration of self-guiding electromagnetic edge states existing along the zigzag edge of a honeycomb magnetic photonic crystal. These edge states are shown to possess unidirectional propagation characteristics that are robust against various types of defects and obstacles. In particular, they allow for the unidirectional transport of electromagnetic energy without requiring an ancillary cladding layer.

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Experimental realization of self-guiding unidirectional electromagnetic edge states.

We demonstrate a sharply asymmetric reflection in a geometrically symmetric magnetic metamaterial (MM) system, which originates from the coupling of electromagnetic (EM) wave to magnetic surface plasmon resonance states and the broken time reversal symmetry in MM. Based on this effect, we have designed unidirectional EM waveguide, wave bender, and beam splitter. Our simulations indicate that the designs possess the merits of robustness against strong defect and disorder, controllability with an external magnetic field, in addition to the finite working bandwidth and the high transmission efficiency.

Magnetically controllable unidirectional electromagnetic waveguiding devices designed with metamaterials

We demonstrate a dramatically molded reflection of an electromagnetic (EM) wave from the magnetic metamaterial (MM) surface occurring near the magnetic surface plasmon (MSP) resonance. It is found that on one side of the source the reflected field nearly cancels the incoming field, giving rise to a shadowy region near the MM surface, while on the other side the reflected field considerably enhances the incoming field, resulting in a brightened region. Our analysis indicates that this effect arises from the coupling of the EM wave to the MSP band states which exhibit giant circulations going only in one direction due to the broken time reversal symmetry in MMs. Possible applications based on this effect are manifested in designing a robust one-way EM waveguide (OEMW), a ${90}^{\ifmmode^\circ\else\textdegree\fi{}}$ beam bender, and a beam splitter, which are shown to work even in deep subwavelength lateral scale ($~\ensuremath{\lambda}/10$), with $\ensuremath{\lambda}$ the wavelength of the propagating EM wave. Furthermore, the dependence of the OEMW on the channel width, the robustness of the OEMW against the defect and disorder, and the tunability of the working frequency by an external magnetic field are also studied.

Molding reflection from metamaterials based on magnetic surface plasmons

We conduct a rigorous study on the properties of an artificial electromagnetic black hole for transverse magnetic modes. A multilayered structure of such a black hole is then proposed as a reduced variety for easy experimental implementations. An actual design of composite materials based on the effective medium theory is given with only five kinds of real isotropic materials. The finite element method confirms the functionality of such a simple design.

A simple design of an artificial electromagnetic black hole

By employing the angular spectrum representation, we successfully derive the partial-wave expansion coefficients of the circular Airy beams (CABs) with different polarizations, based on which the scattering of a spherical particle in the CABs is solved exactly. Special attention is focused on exploring the potential applications of the CABs in the abruptly autofocusing (AAF) property and optical manipulation of microparticle by optical force. It is found that both the linear and circular polarizations are the best candidates to implement the AAF property robustly against strong disturbance by a large-sized particle. In addition, although the CABs can be intensively focused to a small region, resulting in an abrupt increase of light intensity by two orders of magnitude at the focal point and enabling three-dimensional stable trapping of a Rayleigh particle near the focal point, the usual CABs fail to generate an optical force outweighing the Brownian force to achieve a stable transverse trapping in the region before the focal point. On the other hand, a Mie particle can be confined transversely in the primary ring and accelerated along the curved trajectory of CABs to the focal point, then pushed further all the way through the focal point rather than being trapped therein, and eventually accelerated further along a straight trajectory in the direction of light propagation over 100 wavelengths, due to the weak diffraction characteristic of a morphed Bessel-like beam of CABs. The exotic curved-straight trajectory transport of particles by the CABs may find applications in the case where the transport path is partly blocked.

Abruptly autofocusing property and optical manipulation of circular Airy beams

Based on the Mie scattering theory and Maxwell stress tensor method, we investigate the transverse optical force (TOF) acting on chiral particles illuminated by a zero-order Bessel beam. It is demonstrated that the particle chirality can induce an azimuthal optical force (AOF), resulting in orbital motion of particles around the optical beam axis. The AOF depends strongly on particle loss as well as the handedness of chirality, with its amplitude capable of changing by over an order of magnitude by particle's chiral loss. The other component of TOF, the radial optical force (ROF), is much less sensitive to the magnitude and handedness of the particle chirality as well as the loss when the chirality is small. Analytical result based on dipole approximation reveals that the AOF arises from the direct coupling of particle chirality to both the spin angular momentum (SAM) and optical vorticity (curl of Poynting vector), exhibiting a conversion of optical SAM of an incident beam to mechanical orbital angular momentum of an illuminated particle. Differently, the ROF originates from the transverse gradient force. In addition, particle chirality yields a negative contribution to the gradient force; thus the ROF can be attenuated and even reversed in direction when particle chirality is sufficiently large. These characteristics of TOF might find applications in chirality detection as well as sorting chiral particles of different handedness and separating them from conventional ones.

Wanli Lu

Papers

Magnetically controllable unidirectional electromagnetic waveguiding devices designed with metamaterials

Molding reflection from metamaterials based on magnetic surface plasmons

A simple design of an artificial electromagnetic black hole

Abruptly autofocusing property and optical manipulation of circular Airy beams

Tailoring azimuthal optical force on lossy chiral particles in Bessel beams