Photonic topological insulators are artificial electromagnetic materials that support topologically non-trivial, unidirectional states of light. Photonic topological phases are classical electromagnetic wave analogues of electronic
topological phase
In physics, topological order describes a state or phase of matter that arises system with non-local interactions, such as entanglement in quantum mechanics, and floppy modes in elastic systems. Whereas classical phases of matter such as gases an ...
s studied in
condensed matter physics
Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid State of matter, phases, that arise from electromagnetic forces between atoms and elec ...
. Similar to their electronic counterparts, they, can provide robust unidirectional channels for light propagation. The field that studies these phases of light is referred to as topological photonics.
History
Topological order in solid state systems has been studied in condensed matter physics since the discovery of
integer quantum Hall effect
The quantum Hall effect (or integer quantum Hall effect) is a quantized version of the Hall effect which is observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall resistance exhi ...
. But topological matter attracted considerable interest from the physics community after the proposals for possible observation of symmetry-protected topological phases (or the so-called ''
topological insulator
A topological insulator is a material whose interior behaves as an electrical insulator while its surface behaves as an electrical conductor, meaning that electrons can only move along the surface of the material.
A topological insulator is an ...
s'') in
graphene
Graphene () is a carbon allotrope consisting of a Single-layer materials, single layer of atoms arranged in a hexagonal lattice, honeycomb planar nanostructure. The name "graphene" is derived from "graphite" and the suffix -ene, indicating ...
, and experimental observation of a 2D topological insulator in CdTe/HgTe/CdTe quantum wells in 2007.
In 2008,
Haldane and Raghu proposed that unidirectional electromagnetic states analogous to (integer) quantum Hall states can be realized in nonreciprocal magnetic
photonic crystal
A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of Crystal structure, natural crystals gives rise to X-ray crystallograp ...
s. This prediction was first realized in 2009 in the microwave frequency regime. This was followed by the proposals for analogous
quantum spin Hall states of electromagnetic waves that are now known as photonic topological insulators.
It was later found that topological electromagnetic states can exist in continuous media as well--theoretical and numerical study has confirmed the existence of topological Langmuir-cyclotron waves in continuous magnetized plasmas.
Platforms
Photonic topological insulators are designed using various photonic platforms including optical waveguide arrays, coupled ring resonators, bi-anisotropic
meta-materials, and photonic crystals. More recently, they have been realized in 2D dielectric and plasmonic meta-surfaces. Despite the theoretical prediction,
no experimental demonstration of photonic topological insulator in continuous media has been reported.
Chern number
As an important figure of merit for characterizing the quantized collective behaviors of the wavefunction, Chern number is the topological invariant of quantum Hall insulators. Chern number also identifies the topological properties of the photonic topological insulators (PTIs), thus it is of crucial importance in PTI design. The full-wave finite-difference frequency-domain (FDFD) method based MATLAB program for computing the Chern number has been written. Recently, the finite-difference method has been extended to analyze the topological invariant of non-Hermitian topological dielectric photonic crystals by first-principle Wilson loop calculation. All MATLAB codes can be found at GitHub website.
See also
*
Symmetry-protected topological order
Symmetry-protected topological (SPT) order is a kind of order in absolute zero, zero-temperature quantum-mechanical states of matter that have a symmetry and a finite energy gap.
To derive the results in a most-invariant way, renormalization gro ...
*
Metamaterial
A metamaterial (from the Greek word μετά ''meta'', meaning "beyond" or "after", and the Latin word ''materia'', meaning "matter" or "material") is a type of material engineered to have a property, typically rarely observed in naturally occu ...
References
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Photonics
Electromagnetism