Harmon ; Markus Wohlgennant; Michael E. The physical processes are largely understood when exciton formation and recombination lead to the magnetic field effects.
November 4, The application of topology, the mathematics studying conserved properties through continuous deformations, is creating new opportunities within photonics, bringing with it theoretical discoveries and a wealth of potential applications.
This field was inspired by the discovery of topological insulators, in which interfacial electrons transport without dissipation even in the presence of impurities. Similarly, the use of carefully-designed wave-vector space topologies allows the creation of interfaces that support new states of light with useful and interesting properties.
In particular, it suggests the realization of unidirectional waveguides that allow light to flow around large imperfections without back-reflection.
The present review explains the underlying principles and highlights how topological effects can be realized in photonic crystals, coupled resonators, metamaterials and quasicrystals. Frequency, wavevector, polarization and phase are degrees of freedom that are often used to describe a photonic system.
In the last few years, topology —a property of a photonic material that characterizes the quantized global behavior of the wavefunctions on its entire dispersion band— has been emerging as another indispensable ingredient, opening a path Wang-kong tse thesis to the discovery of fundamentally new states of light and possibly revolutionary applications.
Possible practical applications of topological photonics include photonic circuitry less dependent on isolators and slow light insensitive to disorder.
Topological ideas in photonics branch from exciting developments in solid-state materials, along with the discovery of new phases of matter called topological insulators [1, 2]. Topological insulators, being insulating in their bulk, conduct electricity on their surfaces without dissipation or backscattering, even in the presence of large impurities.
The first example was the integer quantum Hall effect, discovered in In quantum Hall states, two-dimensional 2D electrons in a uniform magnetic field form quantized cyclotron orbits of discrete eigenvalues called Landau levels.
When the electron energy sits within the energy gap between the Landau levels, the measured edge conductance remains constant within the accuracy of about one part in a billion, regardless of sample details like size, composition and impurity levels.
InHaldane proposed a theoretical model to achieve the same phenomenon but in a periodic system without Landau levels , the so-called quantum anomalous Hall effect. Posted on arXiv inHaldane and Raghu transcribed the key feature of this electronic model into photonics [4, 5].
They theoretically proposed the photonic analogue of the quantum anomalous Hall effect in photonic crystals , the periodic variation of optical materials, molding photons the same way as solids modulating electrons.
Three years later, the idea was confirmed by Wang et al. Those studies spurred numerous subsequent theoretical [9—13] and experimental investigations [14—16]. The works cited above demonstrated unidirectional edge waveguides transmit electromagnetic waves without back-reflection even in the presence of arbitrarily large disorder: Topological photonics promises to offer unique, robust designs and new device functionalities to photonic systems by providing immunity to performance degradation induced by fabrication imperfections or environmental changes.
In this review, we present the key concepts, experiments, and proposals in the field of topological photonics. Starting with an introduction to the relevant topological concepts, we introduce the 2D quantum Hall phase through the stability of Dirac cones [4, 5], followed by its realizations in gyromagnetic photonic crystals [7, 8, 13], in coupled resonators [9, 10, 16] and waveguides , in bianisotropic metamaterials  and in quasicrystals .
We then extend our discussions to three dimensions, wherein we describe the stability of line nodes and Weyl points and their associated surface states . We conclude by considering the outlook for further theoretical and technological advances.
For example, the six objects in Fig. The yellow sphere can be continuously deformed into the white spoon, so they are topologically equivalent. The torus and coffee cup are also topologically equivalent, and so too are the double torus and tea pot. Different topologies can be mathematically characterized by integers called topological invariants, quantities that remain the same under arbitrary continuous deformations of the system.
For the above closed surfaces, the topological invariant is the genus, and it corresponds to the number of holes within a closed surface. Objects having the same topological invariant are topologically equivalent: Only when a hole is created or removed in the object does the topological invariant change.
This process is a topological phase transition. Material-systems in photonics have topologies, defined on 2 Ordinary waveguide b Topologically-protected waveguide y air, metal, Trivial Bragg mirror reflectors Each pair has the same topological invariant called genus.
A topological phase transition takes place on the right, but not on the left. The topological invariant of a 2D dispersion band is the Chern number C in Box 1a quantity that characterizes the quantized collective behavior of the wavefunctions on the band.
Once a physical observable can be written as a topological invariant, it only changes discretely; thus, it will not respond to continuous small perturbations.
These perturbations can be arbitrary continuous changes in the material parameters. Optical mirrors reflect light of a given frequency range: Mirrors, that is, have frequency gaps in analogy to the energy gaps of insulators. The sum of the Chern numbers of the dispersion bands below the frequency gap labels the topology of a mirror.Nonlinear and anisotropic polarization rotation in two dimensional Dirac materials Ashutosh Singh,1 Saikat Ghosh,1 and Amit Agarwal1, 1Department of Physics, Indian Institute of Technology Kanpur, Kanpur - , India (Dated: February 2, ) We predict nonlinear optical polarization rotation in two dimensional massless Dirac systems in-.
Apr 09, · We have observed the well-kown quantum Hall effect (QHE) in epitaxial graphene grown on silicon carbide (SiC) by using, This thesis describes a semianalytic self-similar model of the collapse of rotating isothermal molecular cloud cores with both Hall and ambipolar diffusion, Tse, Wang-Kong; Das Sarma, S.
The International Significance of Comrade Mao-Tse Tung’s Theory of People’s War. It was on the basis of the lessons derived from the people’s wars in China that Comrade Mao Tse-tung, using the simplest and the most vivid language, advanced the famous thesis that “political power grows out of .
Tilahun, John Tolsma, Maxim Trushin, James Wang-Kong Tse, Fengcheng Wu, Ming Xie, and Fan Zhang. Thanks to Becky Drake, Annie Harding, and Michele Land eld, for their assistance and support. Special thanks to Karin Everschor-Sitte and Matthias Sitte for proofreading parts of this thesis, and to Inti Sodemann, for many stimulating conversations.
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