Photonic topological insulator

Photonic topological insulators are artificial electromagnetic materials that support topologically non-trivial, unidirectional states of light.[1] Photonic topological phases are classical electromagnetic wave analogues of electronic topological phases studied in condensed matter physics. Similar to their electronic counterparts, they, can provide robust unidirectional channels for light propagation.[2]

The field that studies these phases of light is referred to as topological photonics, even though the working frequency of these electromagnetic topological insulators may fall in other parts of the electromagnetic spectrum such as the microwave range.[3]

History

Topological order in solid state systems has been studied in condensed matter physics since the discovery of integer quantum Hall effect. 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 insulators) in graphene,[4] and experimental observation of a 2D topological insulator in CdTe/HgTe/CdTe quantum wells in 2007.[5][6]

In 2008, Haldane and Raghu proposed that unidirectional electromagnetic states analogous to (integer) quantum Hall states can be realized in nonreciprocal magnetic photonic crystals.[7] This was followed by the proposals for analogous quantum spin Hall states of electromagnetic waves that are now known as photonic topological insulators.[8][3]

Platforms

Photonic topological insulators are designed using various photonic platforms including coupled ring resonators[9], bi-anisotropic meta-materials, coupled optical fibers, and photonic crystals[10]. More recently, they have been realized in 2D dielectric[11] and plasmonic[12] meta-surfaces.

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[13].

See also

References
  1. Lu, Ling; Joannopoulos, John D.; Soljačić, Marin (November 2014). "Topological photonics". Nature Photonics. 8 (11): 821–829. arXiv:1408.6730. doi:10.1038/nphoton.2014.248. ISSN 1749-4893.
  2. Ozawa, Tomoki; Price, Hannah M.; Amo, Alberto; Goldman, Nathan; Hafezi, Mohammad; Lu, Ling; Rechtsman, Mikael C.; Schuster, David; Simon, Jonathan; Zilberberg, Oded; Carusotto, Iacopo (25 March 2019). "Topological photonics". Reviews of Modern Physics. 91 (1): 015006. arXiv:1802.04173. doi:10.1103/RevModPhys.91.015006.
  3. Khanikaev, Alexander B.; Hossein Mousavi, S.; Tse, Wang-Kong; Kargarian, Mehdi; MacDonald, Allan H.; Shvets, Gennady (March 2013). "Photonic topological insulators". Nature Materials. 12 (3): 233–239. arXiv:1204.5700. doi:10.1038/nmat3520. ISSN 1476-4660.
  4. Kane, C. L.; Mele, E. J. (23 November 2005). "Quantum Spin Hall Effect in Graphene". Physical Review Letters. 95 (22): 226801. arXiv:cond-mat/0411737. doi:10.1103/PhysRevLett.95.226801.
  5. Bernevig, B. Andrei; Hughes, Taylor L.; Zhang, Shou-Cheng (15 December 2006). "Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells". Science. 314 (5806): 1757–1761. arXiv:cond-mat/0611399. doi:10.1126/science.1133734. ISSN 0036-8075.
  6. Hasan, M. Z.; Kane, C. L. (8 November 2010). "Colloquium: Topological insulators". Reviews of Modern Physics. 82 (4): 3045–3067. doi:10.1103/RevModPhys.82.3045.
  7. Haldane, F. D. M.; Raghu, S. (10 January 2008). "Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry". Physical Review Letters. 100 (1): 013904. arXiv:cond-mat/0503588. doi:10.1103/PhysRevLett.100.013904.
  8. Hafezi, Mohammad; Demler, Eugene A.; Lukin, Mikhail D.; Taylor, Jacob M. (November 2011). "Robust optical delay lines with topological protection". Nature Physics. 7 (11): 907–912. arXiv:1102.3256. doi:10.1038/nphys2063. ISSN 1745-2481.
  9. Hafezi, M.; Mittal, S.; Fan, J.; Migdall, A.; Taylor, J. M. (December 2013). "Imaging topological edge states in silicon photonics". Nature Photonics. 7 (12): 1001–1005. arXiv:1302.2153. doi:10.1038/nphoton.2013.274. ISSN 1749-4893.
  10. Wu, Long-Hua; Hu, Xiao (3 June 2015). "Scheme for Achieving a Topological Photonic Crystal by Using Dielectric Material". Physical Review Letters. 114 (22): 223901. arXiv:1503.00416. doi:10.1103/PhysRevLett.114.223901.
  11. Gorlach, Maxim A.; Ni, Xiang; Smirnova, Daria A.; Korobkin, Dmitry; Zhirihin, Dmitry; Slobozhanyuk, Alexey P.; Belov, Pavel A.; Alù, Andrea; Khanikaev, Alexander B. (2 March 2018). "Far-field probing of leaky topological states in all-dielectric metasurfaces". Nature Communications. 9 (1): 1–8. doi:10.1038/s41467-018-03330-9. ISSN 2041-1723.
  12. Honari-Latifpour, Mostafa; Yousefi, Leila (2019). "Topological plasmonic edge states in a planar array of metallic nanoparticles". Nanophotonics. 8 (5): 799–806. doi:10.1515/nanoph-2018-0230. ISSN 2192-8614.
  13. Zhao, Ran; Zhao, Ran; Xie, Guo-Da; Xie, Guo-Da; Chen, Menglin L. N.; Lan, Zhihao; Huang, Zhixiang; Huang, Zhixiang; Sha, Wei E. I. (2020-02-17). "First-principle calculation of Chern number in gyrotropic photonic crystals". Optics Express. 28 (4): 4638–4649. arXiv:2001.08913. doi:10.1364/OE.380077. ISSN 1094-4087.
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