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

The resonant modes of plasmonic nanoparticle structures made of gold or silver endow them with an ability to manipulate light at the nanoscale. However, owing to the high light losses caused by metals at optical wavelengths, only a small fraction of plasmonics applications have been realized. Kuznetsov et al. review how high-index dielectric nanoparticles can offer a substitute for these metals, providing a highly flexible and low-loss route to the manipulation of light at the nanoscale.

Science , this issue p. [10.1126/science.aag2472][1]

 [1]: /lookup/doi/10.1126/science.aag2472

http://science.sciencemag.org/content/sci/354/6314/aag2472.full.pdf

Optically resonant dielectric nanostructures

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new andpromising methods for the numerical solution of nonlinear partial differential equations. The bookprovides an introduction for graduate students and researchers. Working knowledge of calculus isrequired and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellularautomata are outlined in Chapter 2. The properties of various LGCA and special coding techniquesare discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessarytheoretical background for LGCA and LBM. The properties of lattice Boltzmann models and amethod for their construction are presented in Chapter 5.

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Lattice-Gas Cellular Automata and Lattice Boltzmann Models

Theoretical analysis suggests that there exists an optical attractive force capable of “pulling” microparticles towards a light source. This backwards force is generated by using interference to optimize the scattering of light in the forwards direction.

Optical pulling force

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 propose a theory to explain optical trapping by optical vortices (OVs), which are emerging as important tools to trap mesoscopic particles. The common perception is that the trapping is solely due to the gradient force and that it may be characterized by three real force constants. However, we show that the OV trap can exhibit complex force constants, implying that the trapping must be stabilized by ambient damping. At different damping levels, particles exhibit remarkably different dynamics, such as stable trapping and periodic and aperiodic orbital motions.

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Theory of optical trapping by an optical vortex beam.

We study the edge states in two-dimensional photonic crystals arising from a singular point in $k$ space at which two dispersion surfaces intersect. The zigzag edge states in a honeycomb lattice for TM polarization are analogous to the electronic ones in graphene nanoribbons. Electromagnetic modes at the zigzag edges of such photonic crystals consisting of ferrite rods are allowed to propagate only along one direction. The one-way propagation is insensitive to imperfections on the zigzag edge.

/pdf/one-way-edge-mode-in-a-magneto-optical-honeycomb-photonic-220an42wku.pdf

One-way edge mode in a magneto-optical honeycomb photonic crystal

A lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels is presented by introducing a boundary condition for elastic and moving boundaries. The mass conservation for the boundary condition is tested in detail. The viscous flow in elastic vessels is simulated with a pressure-radius relationship similar to that of the Pulmonary blood vessels. The numerical results for steady flow agree with the analytical prediction to very high accuracy, and the simulation results for pulsatile flow are comparable with those of the aortic flows observed experimentally. The model is expected to find many applications for studying blood flows in large distensible arteries, especially in those suffering from atherosclerosis. stenosis. aneurysm, etc.

Zhifang Lin

Papers

Optical pulling force

Experimental realization of self-guiding unidirectional electromagnetic edge states.

Theory of optical trapping by an optical vortex beam.

One-way edge mode in a magneto-optical honeycomb photonic crystal

Lattice Boltzmann method for simulating the viscous flow in large distensible blood vessels.