Vol. 173

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues
2022-04-22

Tamm States and Gap Topological Numbers in Photonic Crystals (Invited Paper)

By Junhui Cao, Alexey V. Kavokin, and Anton V. Nalitov
Progress In Electromagnetics Research, Vol. 173, 141-149, 2022
doi:10.2528/PIER22011601

Abstract

We introduce the concept of gap Zak or Chern topological invariants for photonic crystals of various dimensionalities. Specifically, we consider a case where Tamm states are formed at an interface of two semi-infinite Bragg mirrors and derive the formulism for gap Zak phases of two constituent Bragg mirrors. We demonstrate that gap topological numbers are instrumental in studies of interface states both in conventional and photonic crystals.

Citation


Junhui Cao, Alexey V. Kavokin, and Anton V. Nalitov, "Tamm States and Gap Topological Numbers in Photonic Crystals (Invited Paper)," Progress In Electromagnetics Research, Vol. 173, 141-149, 2022.
doi:10.2528/PIER22011601
http://jpier.org/PIER/pier.php?paper=22011601

References


    1. Xiao, D., M.-C. Chang, and Q. Niu, "Berry phase effects on electronic properties," Rev. Mod. Phys., Vol. 82, 1959-Jul. 2007, 2010.
    doi:10.1103/RevModPhys.82.1959

    2. Berry, M. V., "Quantal phase factors accompanying adiabatic changes," Proc. R. Soc. Lond., Vol. 392, No. 1802, 45-57, 1996.

    3. Qiang, W., X. Meng, L. Hui, S. Zhu, and C. T. Chan, "Measurement of the zak phase of photonic bands through the interface states of metasurface/photonic crystal," Physical Review B, Vol. 93, No. 4, 041415.1-041415.5, 2016.

    4. Gao, W. S., M. Xiao, C. T. Chan, and W. Y. Tam, "Determination of zak phase by reflection phase in 1D photonic crystals," Optics Letters, Vol. 40, No. 22, 5259, 2015.
    doi:10.1364/OL.40.005259

    5. Ozawa, T., H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zilberberg, and I. Carusotto, "Topological photonics," Rev. Mod. Phys., Vol. 91, 015006, Mar. 2019.
    doi:10.1103/RevModPhys.91.015006

    6. Wang, F. and Y. Ran, "Nearly flat band with chern number c = 2 on the dice lattice," Phys. Rev. B, Vol. 84, 241103, Dec. 2011.
    doi:10.1103/PhysRevB.84.241103

    7. Hatsugai, Y., T. Fukui, and H. Aoki, "Topological analysis of the quantum hall effect in graphene: Dirac-fermi transition across van hove singularities and edge versus bulk quantum numbers," Phys. Rev. B, Vol. 74, 205414, Nov. 2006.

    8. Kavokin, A., Microcavities. Number No. 16 in Series on Semiconductor Science and Technology, Oxford University Press, Oxford, New York, 2007, OCLC: ocn153553936.

    9. Afinogenov, B. I., V. O. Bessonov, A. A. Nikulin, and A. A. Fedyanin, "Observation of hybrid state of tamm and surface plasmon-polaritons in one-dimensional photonic crystals," Applied Physics Letters, Vol. 103, No. 6, 1800, 2013.
    doi:10.1063/1.4817999

    10. Sasin, M. E., R. P. Seisyan, M. A. Kalitteevski, S. Brand, R. A. Abram, J. M. Chamberlain, A. Y. Egorov, A. P. Vasil'Ev, V. S. Mikhrin, and A. V. Kavokin, "Tamm plasmon polaritons: Slow and spatially compact light," Applied Physics Letters, Vol. 92, No. 25, 824, 2008.
    doi:10.1063/1.2952486

    11. Kavokin, A. V., I. A. Shelykh, and G. Malpuech, "Lossless interface modes at the boundary between two periodic dielectric structures," Physical Review B, Vol. 72, No. 23, 233102, Dec. 2005.
    doi:10.1103/PhysRevB.72.233102

    12. Su, Y., C. Y. Lin, R. C. Hong, W. X. Yang, and R. K. Lee, "Lasing on surface states in vertical-cavity surface-emission lasers," Optics Letters, Vol. 39, No. 19, 2014.
    doi:10.1364/OL.39.005582

    13. Symonds, C., G. Lheureux, J. P. Hugonin, J. J. Greffet, and J. Bellessa, "Confined tamm plasmon lasers," Nano Letters, Vol. 13, No. 7, 3179, 2013.
    doi:10.1021/nl401210b

    14. Symonds, C., A. Lematre, E. Homeyer, J. C. Plenet, and J. Bellessa, "Emission of Tamm plasmon/exciton polaritons," Applied Physics Letters, Vol. 95, No. 15, 151114-151114-3, 2009.
    doi:10.1063/1.3251073

    15. Kavokin, A., I. Shelykh, and G. Malpuech, "Optical Tamm states for the fabrication of polariton lasers," Applied Physics Letters, Vol. 87, No. 26, 193, 2005.
    doi:10.1063/1.2136414

    16. Henriques, J. C. G., T. G. Rappoport, Y. V. Bludov, M. I. Vasilevskiy, and N. M. R. Peres, "Topological photonic Tamm states and the Su-Schrieffer-Heeger model," Phys. Rev. A, Vol. 101, 043811, Apr. 2020.
    doi:10.1103/PhysRevA.101.043811

    17. Xiao, M., Z. Q. Zhang, and C. T. Chan, "Surface impedance and bulk band geometric phases in one-dimensional systems," Phys. Rev. X, Vol. 4, 021017, Apr. 2014.

    18. Zak, J., "Berry's phase for energy bands in solids," Physical Review Letters, Vol. 62, No. 23, 2747-2750, Jun. 1989.
    doi:10.1103/PhysRevLett.62.2747

    19. Ryder, L. H., "The optical berry phase and the gauss-bonnet theorem," European Journal of Physics, Vol. 12, No. 1, 15, 1991.
    doi:10.1088/0143-0807/12/1/003

    20. Holstein, B. R., "The adiabatic theorem and Berry's phase," American Journal of Physics, 57, 1989.

    21. Wang, H.-X., G.-Y. Guo, and J.-H. Jiang, "Band topology in classical waves: Wilsonloop approach to topological numbers and fragile topology," New Journal of Physics, Vol. 21, No. 9, 093029, Sep. 2019.
    doi:10.1088/1367-2630/ab3f71

    22. Gubarev, F. V. and V. I. Zakharov, "The Berry phase and monopoles in non-Abelian gauge theories," International Journal of Modern Physics A, Vol. 17, No. 2, 157-174, 2002.
    doi:10.1142/S0217751X02005840

    23. Kondo, K.-I., "Wilson loop and magnetic monopole through a non-Abelian stokes theorem," Physical Review D, Vol. 77, No. 8, 284-299, 2008.
    doi:10.1103/PhysRevD.77.085029